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Education Research:
Selected Research on Standards, Achievement, Learning, Assessment, and Technology Integration

Standards, Raising Achievement, Assessment, How People Learn

 

American Educational Research Association. (2000, July). Position statement concerning high-stakes testing in preK-12 education.

The American Educational Research Association (AERA) is the nation's largest professional organization devoted to the scientific study of education.  AERA's position statement on high-stakes testing is based on the 1999 Standards for Educational and Psychological Testing. The Standards represent a professional consensus concerning sound and appropriate test use in education and psychology. The statement includes that high-stakes testing should meet all of the following criteria:

• Protection against high-stakes decisions based on a single test; availability of alternative assessments where appropriate
• Availability to adequate resources and opportunity to learn prior to stakeholders being held accountable for failure to meet standards
• Validation for each separate intended use
• Full disclosure of likely negative consequences of high-stakes testing programs
• Alignment between the test and the curriculum; high stakes tests should not be limited to testing curriculum that is easiest to measure
• Validity of passing scores and achievement levels
• Opportunities for meaningful remediation for examinees who fail high-stakes tests
• Appropriate attention to language differences among examinees
• Appropriate attention to students with disabilities
• Careful adherence to explicit rules for determining which students are to be tested
• Sufficient reliability for each intended use
• Ongoing evaluation of intended and unintended effects of high-stakes testing

American Federation of Teachers. (2001). Making standards matter. https://www.aft.org/periodical/american-educator/winter-2001/making-standards-matter-2001

This report in four sections examined state efforts at setting standards, curriculum development, assessment, incentives, and intervention for students at risk of not meeting standards.  It does not address professional development.  The AFT made several recommendations.  For example, states should (p. 7):

• Provide examples of standards and student work at various grades and performance levels so that teachers, students, parents, and the public have a shared understanding of what is expected.
• Specify the learning continuum in the core subjects to show the progression and development of critical knowledge and skills from grade to grade.
• Identify instructional resources--reading materials, textbooks, software, and so forth--that are aligned to the standards.
• Provide performance indicators to clarify the quality of student work required for mastery of the content standards
• Develop lesson plan data banks that include exemplary lessons and student work related to instruction in the standards.

American Psychological Association, Coalition for Psychology in Schools and Education. (2015). Top 20 principles from psychology for preK–12 teaching and learning. https://www.apa.org/ed/schools/teaching-learning/top-twenty-principles.pdf

The American Psychological Association, Coalition for Psychology in Schools and Education (2015) conducted research to identify the top 20 principles from psychology "that would be of greatest use in the context of preK–12 classroom teaching and learning, as well as the implications of each as applied to classroom practice. Each principle is named and described, relevant supporting literature is provided, and its relevance for the classroom is discussed" (p. 3).  The principles are grouped into the following categories:

• How do students think and learn? (8 principles)
• What motivates students? (4 principles)
• Why are social context, interpersonal relationships, and emotional well-being important to student learning? (3 principles)
• How can the classroom best be managed? (2 principles)
• How to assess student progress? (3 principles)

Australian Council for Educational Research posted a number of relevant publications on brain-based research and learning: https://www.acer.org/au

Banilower, E. R., Smith, P. S., Weiss, I. R., Malzahn, K. A., Campbell, K. M., & Weis, A. M. (2013). Report of the 2012 National Survey of Science and Mathematics Education. Chapel Hill, NC: Horizon Research, Inc.  https://eric.ed.gov/?id=ED541798

The Report of the 2012 National Survey of Science and Mathematics Education "details the results of a survey of 7,752 science and mathematics teachers in schools across the United States. Areas addressed include: teacher backgrounds and beliefs, teachers as professionals, science and mathematics courses, instructional objectives and activities, instructional resources, and factors affecting instruction."  The entire report or selected chapters can be downloaded.  The following are among the multiple conclusions:

• "[S]cience and mathematics teachers, especially in the elementary and middle grades, do not have strong content preparation in their respective subjects ... A large majority of teachers in all subject/grade-range categories believe that it is better to cover fewer topics in depth.  However, many believe that students should be given definitions for new vocabulary at the beginning of instruction, that teachers should explain an idea to students before having them consider evidence for it" (pp. 31-32), and that "hands-on activities should be used primarily to reinforce ideas students have already learned, despite recommendations that these be used to help students develop their initial understanding of key concepts" (p. 22).

• "Workshops are the most prevalent form of professional development, and participation in teacher study groups is also quite common. ... The emphasis of these professional development opportunities ... has largely been on planning instruction to enable students at different levels of achievement to enhance their understanding, monitoring student understanding during instruction, and assessing student understanding at the end of instruction on a topic. Learning how to use hands-on/manipulatives has also been focused on heavily in mathematics professional development, especially at the elementary level" (pp. 50-51).

• "In mathematics, although most middle schools offer Algebra 1, relatively few students complete it prior to 9th grade" (pp. 66-67).

• "Explanation of ideas and whole group discussion are also very prominent in mathematics instruction, as is the use of textbook/worksheet problems. Having students engage in practices consistent with the Common Core State Standards for Mathematics, such as explaining and justifying methods for solving a problem and comparing/contrasting different solution methods, is also a common weekly occurrence across grade ranges, although the frequency of use decreases as grade range increases. For example, 78 percent of elementary classes have students consider multiple representations in solving a problem at least once per week, compared to only 65 percent of high school classes. Similar to science, the use of technology in mathematics instruction is fairly low across grade levels" (p. 89).

• "Across both science and mathematics, the same three publishers dominate [Houghton Mifflin Harcourt, McGraw-Hill, and Pearson], accounting for at least 75 percent of the market at each level. ... more than 70 percent of teachers in both subjects rate their textbooks as good or better. ... Textbooks appear to exert substantial influence on instruction, from the amount of class time spent using the textbook (especially in mathematics) to the ways teachers use them to plan for and organize instruction. At the same time, it is clear that teachers deviate from their published materials substantially, both skipping parts of the text (most often because teachers know of something better) and supplementing with other materials (most often to provide additional practice or to differentiate instruction)" (p. 107).

• "In mathematics, only two factors are seen as a serious problem in a substantial proportion of schools: low student interest in the subject and low student reading abilities. Lack of student interest is more likely to be seen as a serious problem in middle and high schools than in elementary schools" (p. 116).

• "[T]he use of special instructional arrangements—e.g., subject matter specialists or pull-out instruction for enrichment and/or remediation—is much more prevalent in mathematics than in science, perhaps because of accountability pressures associated with mathematics. The availability of federal funds for mathematics instruction probably also plays a role. ... [P]rograms to encourage student interest in mathematics are strikingly uncommon. For example, less than one-third of schools offer mathematics clubs. ... In mathematics, the substantial influence of state standards is evident in multiple ways, among them school-wide efforts to discuss and align instruction with standards" (p. 125).

Barley, Z., Lauer, P. A., Arens, S. A., Apthorp, H. S., Englert, K. S., Snow, D., & Akiba, M. (2002). Helping at-risk students meet standards: A synthesis of evidence-based classroom practices. Aurora, CO: Mid-continent Research for Education and Learning. https://eric.ed.gov/?id=ED475904

This research synthesis provides evidence of five strategies to help low-achieving students meet standards:

• cognitively oriented instruction
• heterogeneous grouping structures
• tutoring
• peer tutoring
• computer-assisted instruction.

Booth, J. L., McGinn, K. M., Barbieri, C., Begolli, K. N., Chang, B., Miller-Cotto, D., Young, L. K., & Davenport, J. L. (2017). Evidence of cognitive science principles that impact learning in mathematics. https://eric.ed.gov/?id=ED586306

Booth and her colleagues (2017) reviewed the evidence on several principles that show especial promise for improving mathematics instruction.  Those include scaffolding, distributed practice, and feedback for improving memory and focus; worked examples, interleaved practice,and abstract and concrete representations to promote induction and refinement; and error reflection and analogical comparison geared toward improving sense making and understanding.  They also include evidence on how to use these principles to improve instruction.  For a brief summary of those principles, see Table 13.1, p. 299, in this chapter 13, published in the book: Acquisition of Complex Arithmetic Skills and Higher-Order Mathematics Concepts.

Brodersen, R. M., & Melluso, D. (2017). Summary of research on online and blended learning programs that offer differentiated learning options (REL 2017–228). Washington, DC: U.S. Department of Education, Institute of Education Sciences, National Center for Education Evaluation and Regional Assistance, Regional Educational Laboratory Central. https://ies.ed.gov/ncee/rel/Products/Publication/3832

Brodersen and Melluso (2017) summarized "the methodology, measures, and findings of research on the influence on student achievement outcomes of K–12 online and blended face-to-face and online learning programs that offer differentiated learning options. The report also describes the characteristics of the learning programs."  Their findings revealed "In some of the most rigorous studies, statistically significant positive effects were found for four blended learning programs: Cognitive Tutor Algebra I, LeapTrack, READ 180, and Time To Know" (p. 1).  "Studies were included only if the programs they examined directly involved a teacher in the delivery and monitoring of instruction and the study report clearly stated that the online or blended learning program being examined was used to support differentiated instruction. Online programs that were completely software-driven and that did not have a teacher facilitator were excluded" (pp. 2-3).  Although 162 studies were reviewed, only 17 met eligibility criteria for inclusion.  The excluded studies "did not focus on K–12 programs, assessed standalone online programs, or did not clearly offer differentiated learning options" (p. 9).  Within the included studies, 15 used a randomized controlled trial or quasi-experimental design; and the other two were correlational studies.  "The 17 studies examined 14 different online or blended learning programs" (p. 3).  The report includes a list with 37 names of online and blended learning programs, most of which focus on math and/or reading (English language arts).

Deans for Impact. (2015). The Science of Learning. Austin, TX: Deans for Impact.  http://deansforimpact.org/resources/the-science-of-learning/

In the Science of Learning, the Deans for Impact (2015) provide a valuable summary of cognitive science research on how learning takes place.  In just 10 pages, you'll find concise cognitive principles and practical implications for the classroom related to six key questions on how students understand new ideas, learn and retain new information, and solve problems; how learning transfers to new situations; what motivates students to learn; and common misconceptions about how students think and learn.

Dunlosky, J., Rawson, K., Marsh, E., Nathan, M., & Willingham, D. (2013). Improving students' learning with effective learning techniques: Promising  directions from cognitive and educational psychology. Psychological Science in the Public Interest, 14(1), 4-58. https://pcl.sitehost.iu.edu/rgoldsto/courses/dunloskyimprovinglearning.pdf

Dunlosky, Rawson, Marsh, Nathan, and Willingham (2013) elaborate on "10 learning techniques in detail and offer recommendations about their relative utility. ... The techniques include elaborative interrogation, self-explanation, summarization, highlighting (or underlining), the keyword mnemonic, imagery use for text learning, rereading, practice testing, distributed practice, and interleaved practice" (p. 4).  Details of each technique are provided separately and include its description and why it works, the general effects of the technique, effects of the technique in representative educational contexts, issues in implementation, and an overall assessment.

Per Dunlosky and colleagues, "the techniques vary widely with respect to their generalizability and promise for improving student learning. Practice testing and distributed practice received high utility assessments because they benefit learners of different ages and abilities and have been shown to boost students’ performance across many criterion tasks and even in educational contexts. Elaborative interrogation, self-explanation, and interleaved practice received moderate utility assessments. The benefits of these techniques do generalize across some variables, yet despite their promise, they fell short of a high utility assessment because the evidence for their efficacy is limited" (p. 5).

Further, the remaining five techniques of summarization, highlighting, the keyword mnemonic, imagery use for text learning, and rereading received a low utility assessment.  "These techniques were rated as low utility for numerous reasons. Summarization and imagery use for text learning have been shown to help some students on some criterion tasks, yet the conditions under which these techniques produce benefits are limited, and much research is still needed to fully explore their overall effectiveness. The keyword mnemonic is difficult to implement in some contexts, and it appears to benefit students for a limited number of materials and for short retention intervals. Most students report rereading and highlighting, yet these techniques do not consistently boost students’ performance, so other techniques should be used in their place (e.g., practice testing instead of rereading)" (p. 5).

Fuchs, L.S., Newman-Gonchar, R., Schumacher, R., Dougherty, B., Bucka, N., Karp, K.S., Woodward, J., Clarke, B., Jordan, N. C., Gersten, R., Jayanthi, M., Keating, B., & Morgan, S. (2021). Assisting Students Struggling with Mathematics: Intervention in the Elementary Grades (WWC 2021006). Washington, DC: National Center for Education Evaluation and Regional Assistance (NCEE), Institute of Education Sciences, U.S. Department of Education. https://ies.ed.gov/ncee/wwc/PracticeGuide/26

In this practice guide, Fuchs and colleagues elaborated on six recommendations with tier 1 strong evidence for implementation:

1. Systematic Instruction: Provide systematic instruction during intervention to develop student understanding of mathematical ideas.
2. Mathematical Language: Teach clear and concise mathematical language and support students’ use of the language to help students effectively communicate their understanding of mathematical concepts.
3. Representations: Use a well-chosen set of concrete and semi-concrete representations to support students’ learning of mathematical concepts and procedures.
4. Number Lines: Use the number line to facilitate the learning of mathematical concepts and procedures, build understanding of grade-level material, and prepare students for advanced mathematics.
5. Word Problems: Provide deliberate instruction on word problems to deepen students’ mathematical understanding and support their capacity to apply mathematical ideas.
6. Timed Activities: Regularly include timed activities as one way to build fluency in mathematics.  (p. 3, Table 1)

Gandal, M. (2001, September). Standards: Here today, here tomorrow. Educational Leadership, 59(1) 6-13.  https://www.ascd.org/el/articles/standards-here-today-here-tomorrow

Standards must be teachable to have an impact on what goes on in the classroom.  Teachable standards contain clarity and specificity.  In other words, they contain enough detail and precision so that teachers, students, and parents know what is to be learned.  Making decisions as to what all students should learn is difficult.  Including everything that a student could learn helps no one.  This "laundry list" tends to undermine the power of standards as common expectations.  Teachers feel overwhelmed by the enormity of what needs to be taught, and hence, in-depth coverage of concepts suffers.

According to Gandal, those who design tests that measure state standards might consider three key principles:

• If it's not in the standards, it shouldn't be on the test.
• When the standards are rich and rigorous, the tests must be as well.
• Tests should become more challenging in each succeeding grade.

Professional development linked to standards is key, but lacking for the majority of teachers in the United States. Noting results of Education Week's Quality Counts 2001: A Better Balance survey, Gandal stated "fewer than half of teachers in the United States say that they have plenty of access to curriculum guides, textbooks, or other teaching materials or to specific training connected to state standards" (p. 9).

If standards truly define essential skills and knowledge that students should acquire, then students must be given a fighting chance to reach them, be it more time or extra targeted help on weaknesses through intervention and support programs.  Schools require a focused curriculum aligned to standards. Students should have adequate preparation time for tests and multiple opportunities to retake tests, if they do not succeed on a first try.

Gayler, K., Chudowsky, N., Kober, N., Hamilton, M., & Yeager, M. (2004, August). State high school exit exams 2004 annual report: A maturing reform. Washington, D.C.: Center on Education Policy. https://web.archive.org/web/20170508182020/https://www.cep-dc.org/displayDocument.cfm?DocumentID=252

Gayler, Chudowsky, Kober, Hamilton, and Yeager presented findings and recommendations about exit exams in 2004, which is the third annual report on this topic.  In six chapters, the authors addressed how exit exams are affecting curriculum, instruction, and students; the characteristics of exit exams and how well they align with state standards; the kinds of exit exam supports and options that states are providing for students; the kinds of changes that states are making in exit exam systems; and how well exit exams are connected to other education policies such as No Child Left Behind.  State profiles are included.

Gayler, K., Chudowsky, N., Kober, N., & Hamilton, M. (2003, August). State high school exit exams 2003 annual report: Put to the test. Washington, D.C.: Center on Education Policy. http://web.archive.org/web/20170508175256/https://www.cep-dc.org/displayDocument.cfm?DocumentID=251

Gayler, Chudowsky, Kober, and Hamilton presented findings and recommendations about exit exams based on a survey study of 24 states with current or planned exit exams.  This five chapter report, which is supported by review of literature on relevant studies of the prior year, addresses how exit exams are affecting curriculum, instruction, and students; the main features of state exit exams as they existed in 2003; the cost of implementing state exit exams; and the challenges that states face as they implement exit exams.  This report also includes state high school exit exam profiles (data and descriptions) for all 24 states that have or plan to have mandatory exit exams by 2008. Test types administered are either standards-based, minimum competency, or end-of-course.

Among findings:

• NCLB legislation is starting to impact the performance goals, content, and timetables of state exit exam systems.
• Exit exams appear to encourage school districts to cover more of the content in state standards, better align curriculum with state standards, and add remedial and special courses to address needs of students at risk of failing.
• Costs of implementing such systems are substantial, with many states expecting school districts to foot most of the bill.  Hidden costs include that for professional development of teachers and prevention services for students at risk of failing.  Such services include, for example, revamping instruction to align it with state standards, instituting early reading and math programs to prevent failure, and implementing special instructional programs to help English language learners and students with disabilities to learn the knowledge and skills being tested.

Gersten, R., Beckmann, S., Clarke, B., Foegen, A., Marsh, L., Star, J. R., & Witzel, B. (2009, April). Assisting students struggling with mathematics: Response to Intervention (RtI) for elementary and middle schools (NCEE 2009-4060). Washington, DC: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education. https://ies.ed.gov/ncee/wwc/PracticeGuide/2

The authors' "goal in this practice guide is to provide suggestions for assessing students’ mathematics abilities and implementing mathematics interventions within an RtI framework, in a way that reflects the best evidence on effective practices in mathematics interventions" (p. 4).  Eight recommendations are included, along with a list of 12 examples of math problems to illustrate concepts.

Hodgen, J., Foster, C., Marks, R., & Brown, M. (2018). Evidence for review of mathematics teaching: Improving mathematics in key stages two and three: Evidence review. London: Education Endowment Foundation. https://eric.ed.gov/?id=ED612295

This review was commissioned by the Education Endowment Foundation in the UK.  Hodgen, Foster, Marks, and Brown synthesized the best available international research on teaching math to children aged 9-14 in a quest to answer a broad question: What is the evidence regarding the effectiveness of different strategies for teaching mathematics?  Additional questions were included on "related to aspects of pupil learning, pedagogy, the use of resources, the teaching of specific mathematical content [e.g., algebra, number and calculation, geometry, statistics and probability], and pupil attitudes and motivation" (p. 4).  To capture results of a broad spectrum of original studies, they focused on using "existing meta-analyses and systematic reviews."  In this 200 page review, Hodgen and colleagues also presented an overview of developing mathematics competency.

The following are selected highlights among findings where the strength of evidence was HIGH:

• Feedback and formative assessment: "Feedback should be used sparingly and predominantly reserved for more complex tasks, where it may support learners’ perseverance. The well-established literature on misconceptions and learners’ understandings in mathematics provides a fruitful framework to guide assessment and feedback in mathematics." (p. 7)
• Collaborative learning (CL): CL "has a positive effect on attainment and attitude for all students, although the effects are larger at secondary. ... The evidence suggests that students need to be taught how to collaborate, and that this may take time and involve changes to the classroom culture." (p. 7)
• Calculators: "Calculator use does not in general hinder students’ skills in arithmetic. When calculators are used as an integral part of testing and teaching, their use appears to have a positive effect on students’ calculation skills. Calculator use has a small positive impact on problem solving. The evidence suggests that primary students should not use calculators every day, but secondary students should have more frequent unrestricted access to calculators. As with any strategy, it matters how teachers and students use calculators. When integrated into the teaching of mental and other calculation approaches, calculators can be very effective for developing non-calculator computation skills; students become better at arithmetic in general and are likely to self-regulate their use of calculators, consequently making less (but better) use of them." (p. 10)
• Concrete manipulatives: "Concrete manipulatives can be a powerful way of enabling learners to engage with mathematical ideas, provided that teachers ensure that learners understand the links between the manipulatives and the mathematical ideas they represent. Whilst learners need extended periods of time to develop their understanding by using manipulatives, using manipulatives for too long can hinder learners’ mathematical development." (p. 11)
• Textbooks: "The organisation of the mathematics classroom and how textbooks can enable teachers to develop students’ understanding of, engagement in and motivation for mathematics is of greater significance than the choice of one particular textbook rather than another" (p. 12).

The review of other pedagogies included discussion, explicit teaching and direct instruction, mastery learning, problem solving, peer and cross-age tutoring, misconceptions; and thinking skills, metacognition, self-regulation.  The review of other resources and tools also included technological tools and computer-assisted instruction, other representations beyond using concrete manipulatives, and the use of tasks.

Ito, M., Horst, H. A., Bittanti, M.,  Boyd, D., Herr-Stephenson, B., Lange, P. G., Pascoe, C. J., & Robinson, L. (2008, November).  Living and learning with new media: Summary of findings from the digital youth project. The John D. and Catherine T. MacArthur Foundation Reports on Digital Media and Learning. https://files.eric.ed.gov/fulltext/ED536072.pdf

Ito and colleagues presented findings from an ethnographic study, called "the most extensive U.S. study of youth media use" to date.  It was conducted over three years (2005-2008). More than 800 youth and their parents were interviewed by a team of 28 researchers and collaborators at the University of Southern California and the University of California, Berkeley.  The team spent more than 5000 hours observing teens involved with social networking sites, and examined diaries of youth who documented their everyday use of digital media. Results contribute to an understanding of how young people learn and develop social skills online and have implications for educators.

Major findings included:

• Youth use online media to extend friendships and interests.
• Youth engage in peer-based, self-directed learning online.

Implications included:

• Adults should facilitate young people's engagement with digital media. Contrary to adult perceptions, while hanging out online, youth are picking up basic social and technical skills they need to fully participate in contemporary society. Erecting barriers to participation deprives teens of access to these forms of learning.
• Given the diversity of digital media, it is problematic to develop a standardized set of benchmarks against which to measure young people’s technical and new media literacy.
• Youth using new media often learn from their peers, not teachers or adults. Yet, in interest-driven participation, adults have an important role to play (e.g. in setting learning goals).
• To stay relevant in the 21st century, education institutions need to keep pace with the rapid changes introduced by digital media.

Jenifer, J. B., Rosek, C. S., Levine, S. C., & Beilock, S. L. (2022, March 14). Effort(less) exam preparation: Math anxiety predicts the avoidance of effortful study strategies. Journal of Experimental Psychology: General. https://psycnet.apa.org/doiLanding?doi=10.1037%2Fxge0001202 Also see: https://www.researchgate.net/publication/359224127_
Effortless_exam_preparation_Math_anxiety_predicts_
the_avoidance_of_effortful_study_strategies

In their study of math exam preparation and math anxiety, Jenifer, Rosek, Levine, and Beilock (2022) included the following test prep strategies: "reading textbook section(s) for the first time, rereading textbook section(s), reviewing homework solutions, solving practice problems, reading examples of solved problems, and reviewing notes" (p. 3).  They found that problem-solving was the most effortful study strategy and that "math anxiety was associated with less planned engagement with effortful problem-solving during studying. Moreover, the avoidance of effortful problem-solving engagement partially mediated the association between math anxiety and exam performance, marking it as a potential target for intervention" (p. 1).

Jenifer, Rosek, Levine, and Beilock (2022) found that "math-anxious students avoid engaging with effortful study strategies, specifically solving practice problems, when preparing for a math exam" (p. 4).  When solving problems, "math-anxious students were less likely to prioritize harder practice problems compared to their less anxious peers" (p. 4).  Further, "math anxiety was related to how effortful students perceived particular study strategies to be, with greater anxiety being associated with ranking solving practice problems as more effortful and with ranking rereading the textbook as less effortful. These findings seem to suggest that math-anxious students’ avoidance of effortful study strategies may be caused by biased perceptions of the amount of effort required for certain study behaviors" (p. 6).

The study involved a survey of 260 students enrolled in AP Calculus in a public school.

Kauffman, D., Johnson, S. M., Kardos, S. M., Liu, E., & Peske, H. G. (2002, March). Lost at sea: New teachers' experiences with curriculum and assessment. Teachers College, Columbia University: Teachers College Record, 104(2), 273-300. https://www.academia.edu/9191102/Lost_at_Sea_New_Teachers_Experiences_with_Curriculum_and_Assessment

Research that included semi-structured interviews and brief surveys was conducted in 1999-2000 with a diverse group of 50 first and second year Massachusetts teachers working in a wide range of  public schools to uncover their experiences with curriculum and assessment.  Kauffman and colleagues indicated the results of the study might not be generalizeable to the nation as a whole, but do have an implication for practice.

In terms of the interaction of state standards and curricula, research revealed:

• New teachers were often expected to use the state curriculum framework as the actual curriculum.
• If curricula and teaching guides were at the school, they often did not fully align with the curriculum framework.
• The state frameworks covered too much content.
• Teachers experienced anxiety with too much content to cover and insufficient guidance on what topics to cover in depth and what topics to just introduce.  Without support, teachers tended to focus on content addressed on the standardized test by "piecing together test-related materials and by using specific MCAS questions as the basis for instruction" (p. 290).

The authors recommended actions in three arenas: state policy, curriculum research and development, and collaboration around curriculum at the school site. Beyond developing standards and assessments, states must support their implementation.  Research is necessary to evaluate the effectiveness of existing materials, the conditions under which those materials will be effective, and to develop additional materials for use in various academic subjects.  School-based collaboration around curriculum development would go a long way towards orienting new teachers to the curriculum and helping them learn what to teach and how to teach it.

Kraft, M., & Falken, G. (2021, January-December). A blueprint for scaling tutoring and mentoring across public schools. AERA Open, 7(1), 1-21. https://journals.sagepub.com/doi/pdf/10.1177/23328584211042858

Mathew Kraft and Grace Falken (2021) explored "how to make access to individualized instruction and academic mentoring more equitable by taking tutoring to scale as a permanent feature of the U.S. public education system."  They began with a review of literature on tutoring and mentoring and the nature of existing tutoring programs. They outlined "a blueprint for integrating federally funded and locally delivered tutoring into the school day. High school students would serve as tutors/mentors in elementary schools via an elective class, college students in middle schools via federal work-study, and 2- and 4-year college graduates in high schools via AmeriCorps.  [They] envision[ed] an incremental, demand-driven expansion process with priority given to high-needs schools. [Their] blueprint highlights a range of design tradeoffs, implementation challenges, and program costs." (Abstract section).

They expanded on the following design principles:

• Tutoring Is a School-Wide Program.
• Tutoring Is With the Same Tutors/Mentors.
• Tutoring Is a Part of the School Day.
• Tutoring Is Individualized.
• Tutoring Is a High-Dosage Intervention.
• Tutors/Mentors Receive Intensive, Ongoing Training.
• Tutors/Mentors Provide Instruction Based on HighQuality Instructional Materials. (pp. 7-8)

Kraft and Falken proposed "integrating 30 minutes of tutoring into the school day across K-12 public schools."  District adoption should be voluntary and districts should be able to shape their own program implementation.  "District Experiences Should Inform Ongoing Revisions to the Blueprint" (p. 8).

This article is detailed, well researched, and worth investigating.  The publisher's online version is at https://journals.sagepub.com/doi/full/10.1177/23328584211042858 with supplemental material.

Marzano, R. (2003). What works in schools: Translating research into action. Alexandria, VA: ASCD. Available: https://amzn.to/423pMqz

Robert Marzano (2003, p. 27) found that the 241 benchmark statements in the 2000 NCTM K-12 standards document (Principles and Standards for School Mathematics, pp. 392-402) actually contain 741 instructional concepts. Therefore, a sequence and organization of standards into essential content is necessary to ensure that students have adequate time to learn it, which is key to achievement. 

Marzano synthesized 35 years of research on effective schooling and identified 11 school, teacher, and student level factors that have the greatest affect on student achievement:

School Level

• Guaranteed and viable curriculum
• Challenging goals and effective feedback
• Parent and community involvement
• Safe and orderly environment
• Collegiality and professionalism

Teacher Level

• Instructional strategies
• Classroom management
• Classroom curriculum design

Student Level

• Home environment
• Learned intelligence and background knowledge
• Motivation

McIntosh, S. (2012, September). State high school exit exams: A policy in transition. Washington, D.C.: Center on Education Policy. https://files.eric.ed.gov/fulltext/ED535957.pdf

This 11th annual report on the state of high school exit exams is based on data collected from personnel in 45 state education departments.  Shelby McIntosh from the CEP reported three broad conclusions:

1. High School exit exams remain a substantial force in education policy with 25 states administering such exams in 2011-2012.  Exit exams current affect nearly 7 of 10 students across the nation.
2. Exit exams are becoming assessments of college and career readiness. Many states plan to use the Common Core State Standards, and often the common assessments, as a vehicle for this transition.
3. Although the success of exit exam policies remains questionable, much can be learned from past implementations of new policies.  Namely, successful implementation of a new exit exam policy often depends on states' willingness to maintain the support of key state leaders and the public, implement the new policies over several years rather than all at once, and make a full financial commitment.  There are many challenges to a new policy implementation, such as "opposition from key education stakeholders, political disagreements or changes in state leadership, legal battles, low student passing rates, and high costs" (p. 1). "States have often responded to these challenges by offering alternate routes to graduation or alternate diplomas for some or all students and/or by funding remediation programs for students who struggle to pass exit exams" (p. 1).

McNeil, N. M., Grandau, L., Knuth, E. J., Alibali, M. W., Stephens, A. C., Hattikudur, S., & Krill, D. E. (2006). Middle-school students' understanding of the equal sign: The books they read can't help. Cognition and Instruction, 24(3), 367–385. https://labweb.education.wisc.edu/knuth/taar/papers_rep_pub/CI_galley.pdf

"This study examined how 4 middle school textbook series (2 skills-based, 2 standards-based) present equal signs. Equal signs were often presented in standard operations-equals-answer contexts (e.g., 3 + 4 = 7) and were rarely presented in nonstandard operations on both sides contexts (e.g., 3 + 4 = 5 + 2). They were, however, presented in other nonstandard contexts (e.g., 7 = 7). Two follow-up experiments showed that students’ interpretations of the equal sign depend on the context. The other nonstandard contexts were better than the operations-equals-answer context at eliciting a relational understanding of the equal sign, but the operations on both sides context was best. Results suggest that textbooks rarely present equal signs in contexts most likely to elicit a relational interpretation—an interpretation critical to success in algebra" (p. 367).

The four middle-school textbook series (Grades 6 to 8) analyzed included:

• Skills-based: Saxon Math (Hake & Saxon, 2004) and Prentice Hall Mathematics (Charles, Branch-Boyd, Illingworth, Mills, & Reeves, 2004)

• Standards-based: Connected Mathematics (Lappan, Fey, Fitzgerald, Friel, & Phillips, 1998) and Mathematics in Context (Romberg et al., 1998).

According to McNeil et al. (2006), "all four textbook series focus on both skills and concepts to some degree; however, [they classified] for the sake of comparison and conciseness" (p. 372).

The caveat to this study is that results might only apply to the four textbook series for grades 6-8 examined.  Educators should examine their own texts for how the equal sign is used.

Morgan, P., Farkas, G., & Maczuga, S. (2015, June 1). Which instructional strategies most help first-grade students with and without mathematics difficulties? Education Evaluation and Policy Analysis, 20(10), 1-22.  DOI: 10.3102/0162373714536608. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4500292/

A major finding from this study is that "First-grade teachers in the United States may need to increase their use of teacher-directed instruction if they are to raise the mathematics achievement of students with MD [mathematics difficulties]."  Such teacher-directed instruction includes "routine practice and drill."  Co-author Paul Morgan discusses major findings from this study in a video posted on YouTube.

National Council of Teachers of Mathematics. (2012, February). Large scale mathematics assessments and high-stakes decisions. https://web.archive.org/web/20230923174257/https://www.nctm.org/Standards-and-Positions/Position-Statements/Large-Scale-Mathematics-Assessments-and-High-Stakes-Decisions/

With regard to large scale mathematics assessments and high-stakes decisions, NCTM stated:

"The results of large-scale mathematics assessments should not be used as the sole source of information to make high-stakes decisions about schools, teachers, and students. High-stakes decisions should also take into account relevant and valid data on classroom-based performance, such as formative and summative assessments of high quality that offer students a range of opportunities to demonstrate their mathematical knowledge. Moreover, educational systems—states, districts, and schools—should be held accountable for providing essential support for high-quality mathematics teaching and learning before teachers and students are held accountable for assessment results." (para. 1)

Nickow, A. J., Oreopoulos, P., & Quan, V. (2020). The impressive effects of tutoring on preK-12 learning: A systematic review and meta-analysis of the experimental evidence. (EdWorkingPaper: 20-267). Annenberg Institute at Brown University: https://doi.org/10.26300/eh0c-pc52

Nickow, Oreopoulos, and Quan summarized findings from 96 experimental research studies since 1980 on preK-12 tutoring interventions of all types.  Per the Abstract, tutoring was defined as "one-on-one or small-group instructional programming by teachers, paraprofessionals, volunteers, or parents."  They found "tutoring programs yield consistent and substantial positive impacts on learning outcomes, with an overall pooled effect size estimate of 0.37 SD. Effects are stronger, on average, for teacher and paraprofessional tutoring programs than for nonprofessional and parent tutoring. Effects also tend to be strongest among the earlier grades. While overall effects for reading and math interventions are similar, reading tutoring tends to yield higher effect sizes in earlier grades, while math tutoring tends to yield higher effect sizes in later grades. Tutoring programs conducted during school tend to have larger impacts than those conducted after school."

Pellegrini, M., Lake, C., Inns, A., & Slavin, R. E. (2018, October). Effective programs in elementary mathematics: A best-evidence synthesis. Baltimore, MD: Center for Research and Reform in Education, Johns HopkinsUniversity. https://web.archive.org/web/20200331134549/http://www.bestevidence.org/word/elem_math_Oct_8_2018.pdf

Pellegrini, Lake, Inns, and Slavin (2018) reviewed research on mathematics achievement outcomes using 78 studies (65 randomized and 13 quaisi-experimental) that evaluated 61 programs in K-5.  "Programs were organized in 8 categories.  Particularly positive outcomes were found for tutoring programs.  One-to-one and one-to-small group models had equal impacts, as did teachers and paraprofessionals as tutors.  Technology programs showed modest positive impacts.  Professional development approaches focused on helping teachers gain in understanding of math content and pedagogy had no impact on student achievement, but more promising outcomes were seen in studies focused on instructional processes, such as cooperative learning.  Whole-school reform, social-emotional approaches, math curricula, and benchmark assessment programs found few positive effects, although there were one or more effective individual approaches in most categories.  The findings suggest that programs emphasizing personalization, engagement, and motivation are most impactful in elementary mathematics instruction, while strategies focused on textbooks, professional development for math knowledge or pedagogy, and other strategies that do not substantially impact students’ daily experiences have little impact." (Abstract section, p. 2)

See the research for all of the programs that were listed in each category, as not all had significant outcomes.  Programs meeting ESSA evidence standards with strong or moderate, the latter noted in parentheses, ratings included:

• Tutoring: Math Recovery (moderate), Numbers Count, Catch-up Numeracy, Galaxy Math, Pirate Math, MathCorps, Number Rockets, FocusMATH, Fraction Face-Off, ROOTS
• Programs incorporating technology: DreamBox Learning, Mathematics and Reasoning, SuccessMaker
• Instructional process programs: PAX Good Behavior game (moderate)
• Whole school reform: Center for Data-Driven Reform in Education
• Social-emotional learning: Positive Action
• Math curricula: Math Expressions, Math in Focus
• Benchmark assessments: Acuity (pp. 79-80)

Also see:

Pellegrini, M., Neitzel, A., Lake, C., & Slavin, R. (2021). Effective programs in elementary mathematics: A best-evidence synthesis. Baltimore, MD: Center for Research and Reform in Education, Johns Hopkins University. https://bestevidence.org/category/mathematics/mathematics-elementary/

This is an updated article on this same theme, which reviews research on the achievement outcomes of elementary mathematics programs. "87 rigorous experimental studies evaluated 66 programs in grades K-5. Programs were organized in 6 categories" (p. 2).

Rittle-Johnson, B., & Jordan, N. C. (2016). Synthesis of IES-Funded Research on Mathematics: 2002–2013 (NCER 2016-2003). Washington, DC: National Center for Education Research, Institute of Education Sciences, U.S. Department of Education. https://ies.ed.gov/ncer/pubs/20162003/pdf/20162003.pdf

This report from the IES is highly relevant to math educators.  It lists 28 ways that federally funded research during this time period contributed to what we know on how to teach mathematics and approaches to professional development.  Almost 200 federally funded studies about math learning and teaching were analyzed.  The report is organized into two sections: 1.  Whole Numbers, Operations, and Word Problem Solving in Elementary School (10 contributions), and 2. Fractions and Algebra in Middle School (14 contributions).  The report revealed 4 contributions related to professional development approaches.

Rosen, L. D. (2010). Rewired: Understanding the iGeneration and how they learn.  New York, NY: Palgrave Macmillan. Available: https://amzn.to/3oRYYvd

Rosen's book contains nine chapters and 256 pages:

1. Why tweens and teens hate school
2. Welcome to the iGeneration
3. An explosion of WMDs: wireless mobile devices
4. Multitasking madness
5. Real life or screen life?: the educational opportunities of immersive social networking and virtual worlds
6. Tapping into a very creative generation of students
7. Media literacy among 21st-century kids
8. Concerns, worries, and barriers
9. Rewiring education

Rosen suggested that teachers should begin to use cellphones as tools for mobile learning.  Students should generate original content online as part of learning (e.g., via setting up a MySpace or Facebook page).  They should be taught how to judge the trustworthiness of media sources and use the internet to help provide a global perspective.  Teachers need to teach media literacy so that learners are not just gathering superficial information, but using it to gain deeper understanding.

Also see Michael Koliska's 2011 book review of Rewired: Understanding the iGeneration and how they learn, a professional resource published in the Journal of Media Literacy Education.

Rudner, L., & Schafer, W. (Eds.). (2002). What teachers need to know about assessment. Washington, D.C.: National Education Association. https://www.researchgate.net/publication/237666611_What_Teachers_Need_to_Know_about_Assessment

This 111-page book in pdf format is available free online. You will learn fundamental concepts related to all assessments; essential classroom assessment concepts; and useful concepts and issues pertaining to district, state, and national assessments.  Teachers will learn how to construct multiple choice and performance assessments, how to construct and evaluate scoring rubrics, and read about essential skills for students.  This latter includes improving the quality of student notes, how to study for tests, and how to avoid the traps associated with standardized tests.

Scherer, M. (2001, September). How and why standards can improve student achievement: A conversation with Robert J. Marzano. Educational Leadership, 59(1), 14-18. https://www.ascd.org/el/articles/how-and-why-standards-can-improve-student-achievement-a-conversation-with-robert-j.-marzano

In an era of accountability that has been created by technology and the information explosion, we must be specific about what students must know and be able to do. Marge Scherer, Editor in Chief of Educational Leadership, posed several key questions on how and why standards can improve student achievement in a conversation with Robert J. Marzano, then Senior Fellow at the Midcontinent Research for Education and Learning Institute (McREL, https://www.mcrel.org/). Marzano's comments fell into three categories: a manageable number of standards, a change in our record-keeping system that does not increase teacher clerical work, and the need for a repertoire of instructional strategies. Highlights follow.

Step one toward implementing standards is to cut the amount of content addressed within standards by about two-thirds. The sheer number of those standards is the biggest impediment to their implementation. Someone at the district or school level has to cut down the content to essentials related to standards. This would give teachers ample time to cover the essential knowledge in the time allotted and provide them with room to supplement that content. Schools and teachers are looking to state departments of education for guidance.

In addition to trimming standards, a monitoring system is needed that allows tracking of student progress on specific standards. Marzano suggested a change from our grading practices to standards-based grading. This would require a change in record keeping and the use of rubric scores or percentage scores on specific standards that were covered in a course. Administrators have to set up a record-keeping and monitoring system that is easy for teachers to use, if they expect teachers to implement standards. Over time, you would plot student progress on specific standards. Those patterns are more reliable and valid than a single score from a year-end test. Getting feedback on student progress as often as possible, at least once a year, is absolutely essential to the teaching and learning process.

Research at McREL identified classroom practices that generally lead to achievement gains. These include:

• identifying similarities and differences
• summarizing and note-taking
• receiving reinforcement for effort and recognition for achievement
• doing homework and practicing
• using nonlinguistic representations
• learning cooperatively
• setting objectives and receiving feedback
• generating and testing hypotheses
• using cues, questions, and advanced organizers.

Schoenfeld, A. H. (2002). Making mathematics work for all children: Issues of standards, testing, and equity. Educational Researcher, 31(1), 13-25. https://www.researchgate.net/profile/Alan-Schoenfeld-2/publication/242539746_Making_Mathematics_Work_for_All_Children_Issues_of_Standards_Testing_and_Equity/links/02e7e528dae5ee9c63000000/Making-Mathematics-Work-for-All-Children-Issues-of-Standards-Testing-and-Equity.pdf

Schoenfeld discussed four conditions necessary for providing high quality mathematics instruction for all students: high quality curriculum; a stable, knowledgeable, and professional teaching community; high quality assessment that is aligned with curricular goals; and stability and mechanisms for the evolution of curricula, assessment and professional development.

It has taken time for curricula to be developed and implemented that is aligned to 1989 NCTM Principles and Standards, and more time for hard data based on large-scale implementations to be collected on their effectiveness.  In terms of the current state, Schoenfeld stated that the body of data indicates the following (p. 16):

1. "On tests of basic skills, there are no significant performance differences between students who learn from traditional or reform curricula.
2. On tests of conceptual understanding and problem solving, students who learn from reform curricula consistently outperform students who learn from traditional curricula by a wide margin.
3. There is some encouraging evidence that reform curricula can narrow the performance gap between Whites and under-represented minorities."

Schoenfeld presented data from Pittsburgh Public Schools to illustrate effectiveness of reform curricula, and noted reform experiences in Michigan and Massachusetts.

He stated that "teaching is a profession more in name than in reality", which is "a national outrage and a national pathology" (p. 16).  The reason for this stems from the need for more training, the typical expectation being that "one year of teacher training will prepare candidate teachers to take on full responsibilities of the classroom" and that once in the field "the vast majority of teachers have minimal opportunities for professional growth" (p. 16).

There are at least two large-scale assessments aligned with NCTM Principles and Standards.  These are New Standards Mathematics Reference Examination and a standards-based assessment developed by the Mathematics Assessment Resource Service (MARS).  See:

• Briars, D., & Resnick, L. (2000, August). Standards, assessments -- and what else? The essential elements of standards-based school improvement (CSE Report 528). Los Angeles, CA: National Center for Research on Evaluation, Standards, and Student Testing.  https://cresst.org/wp-content/uploads/TECH528.pdf   [This report discusses the Pittsburgh Public Schools experience and the New Standards Reference Examination for Mathematics and has examples of content.]

• Ridgway, J., Crust, R., Burkhardt, H., Wilcox, S., Fisher, L., & Foster, D. (2000). MARS report on the 2000 tests. San Jose, CA: Mathematics Assessment Collaborative.

Siegler, R., Carpenter, T., Fennell, F., Geary, D., Lewis, J., Okamoto, Y., Thompson, L.m & Wray, J. (2010, September). Developing effective fractions instruction for kindergarten through 8th grade: A practice guide (NCEE #2010-4039). Washington, DC: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education.  https://ies.ed.gov/ncee/wwc/PracticeGuide/15

This practice guide is intended for teachers in K-8 to help their learners gain proficiency in understanding and problem-solving with fractions.  "This document uses the term fractions rather than rational numbers. The term fractions refers to the full range of ways of expressing rational numbers, including decimals, percentages, and negative fractions" (p. 7).  The following five recommendations are included.  Each is accompanied by examples on how to carry out the recommendation:

1. Build on students’ informal understanding of sharing and proportionality to develop initial fraction concepts.
2. Help students recognize that fractions are numbers and that they expand the number system beyond whole numbers. Use number lines as a central representational tool in teaching this and other fraction concepts from the early grades onward.
3. Help students understand why procedures for computations with fractions make sense.
4. Develop students’ conceptual understanding of strategies for solving ratio, rate, and proportion problems before exposing them to cross-multiplication as a procedure to use to solve such problems.
5. Professional development programs should place a high priority on improving teachers’ understanding of fractions and of how to teach them.

Stepanek, J. (2000). Mathematics and science classrooms: Building a community of learners. It's just good teaching. Northwest Regional Education Laboratory Math and Science Center. https://educationnorthwest.org/sites/default/files/06.00.pdf

Stepanek has several chapters, but among them are three models for collaborative learning (democratic, caring, and ecological) and group process skills and strategies to eliminate stratification in groups.

Trends in International Mathematics and Science Study (TIMSS, formerly the Third International Mathematics and Science Study). TIMSS information is located at the National Center for Educational Statistics.  For math, there is a sampling of questions (Dare to Compare) that appeared on prior TIMSS and National Assessment of Education Progress Exams: https://nces.ed.gov/timss/.

Walters, K., Smith, T., Leinwand, S., Surr, W., Stein, A., & Bailey, P. (2015, November). An up-close look at student-centered math teaching: A study of highly regarded high school teachers and their students. Quincy, MA: Nellie Mae Education Foundation.  https://www.nmefoundation.org/publications/an-up-close-look-at-student-centered-math-teaching/

This case study of 22 highly regarded high school teachers and their students in six New England states and New York was conducted by researchers from The American Institutes of Research (AIR), with support from the Nellie Mae Education Foundation.  The team examined student-centered math instruction to "provide rich descriptions of how the approach [played] out in several classrooms, taking into account how teachers’ personal philosophy and the school’s instructional context might influence their practice. The case study also provided insights into students’ perspectives on different approaches to mathematics instruction. Second, the researchers [looked] across a larger sample of classrooms to determine the effects of varying degrees of student-centeredness on students’ engagement with learning and their problem-solving skills" (Executive summary, p. 3).

The researchers developed and then applied an analytic framework with four types of learning opportunities in mathematics. In student-centered mathematics learning environments, students have meaningful opportunities to:

• Use mathematical reasoning to understand the “why” as well as the “how.”
• Communicate their thinking and critique the reasoning of others.
• Make connections between and among mathematical concepts and real-world concepts.
• Engage and persevere in solving complex mathematical problems.

Data sources included videos of lessons, weekly instructional logs, teacher interviews, and student focus groups.

Key findings on student outcomes:

• Students in math classrooms led by highly regarded teachers feel very positively about their teacher and the class. However, students with highly regarded teachers who implement more student-centered approaches to math instruction report that they find the content more interesting and meaningful.
• Students in more student-centered math classrooms report being more engaged in how much they are learning and how interested they are in the material, compared to students in less student-centered classrooms.
• Students in more student-centered math classrooms showed higher growth on a test of problem-solving skills than students in less student-centered classrooms.

As a summary of student-centered instructional practices of teachers, findings were reported on orchestration of discussion and instructional tasks, as follows.

Orchestration of discussion:

• Focus on the “why” as well as the “how.”
• Encourage students to justify and explain their solution strategies.
• Encourage students to critique the mathematical reasoning of others.
• Support students by advancing, but not taking over, their thinking as they engage in productive struggle with mathematics.
• Elicit and make connections between different mathematical ideas and/or approaches to the same problem.

Instructional tasks:

• Focus on the “why” as well as the “how.”
• Allow for multiple entry points and solution methods.
• Challenge students to reason about mathematics by looking for patterns, making conjectures, conducting explorations, examining connections between and among mathematical concepts, and justifying mathematical solutions.
• Make explicit the connections between mathematics and real-life experiences.
• Encourage the use of different tools, including technology, to explore mathematics and solve mathematics problems.
• Provide collaborative opportunities for students to communicate about and critique each other’s mathematical reasoning.  (Executive summary, p. 6)

Two conclusions stand out among those provided: "Highly abstract mathematical concepts can be presented in student-centered ways, with positive outcomes for students."  And, "Teaching philosophy and instructional context may affect how strongly and consistently teachers enact student-centered approaches." (Executive summary, p. 7).

Wagner, T. (2003, November 12). Beyond testing: The 7 disciplines for strengthening instruction. Education Week, 23(11), 28, 30. https://www.tonywagner.com/news/beyond-testing  Also see https://www.edweek.org/ew/articles/2003/11/12/11wagner.h23.html

Tony Wagner, co-director of the Change Leadership Group (CLG) at Harvard University's graduate school of education, reported on strategies used for improving teaching in districts that have dramatically raised the level of student achievement for the lowest quartile of students, including those from the most at-risk populations. He discussed seven practices, which the CLG identified, that appear to be central to any successful instructional-improvement effort.  All of these might not be implemented at once, some must come before others, but none can be skipped.  Quoting his words:

• The district creates an understanding and a sense of urgency among teachers and in the community for the necessity of improving all students' learning, and it regularly reports on progress. Data are disaggregated and are transparent to everyone. Qualitative data (for example, from focus groups and interviews), as well as quantitative data, are used to understand students' and recent graduates' experience of school.

• There is a widely shared vision of what good teaching is, which is focused on rigorous expectations, the quality of student engagement, and effective strategies for personalizing learning for all students.

• All adult meetings are about instruction and are models of good teaching.

• There are well-defined standards and performance assessments for student work at all grade levels. Both teachers and students understand what quality work looks like, and there is consistency in standards of assessment.

• Supervision is frequent, rigorous, and entirely focused on the improvement of instruction. It is done by people who know what good instruction looks like.

• Professional development is primarily on-site, intensive, collaborative, and job-embedded, and is designed and led by educators who model the best teaching and learning practices.

• Data are used diagnostically at frequent intervals by teams of teachers, schools, and districts to assess each student's learning and to identify the most effective teaching practices. There is time built into schedules for this shared work.

Wenglinsky, H. (2002, February 13). How schools matter: The link between teacher classroom practices and student academic performance. Education Policy Analysis Archives, 10(12). https://epaa.asu.edu/index.php/epaa/article/view/291

Wenglinsky found that teacher classroom practices have a significant effect on student achievement. Additionally, high-quality professional development focusing on higher-order thinking skills and diversity issues does appear to strongly influence classroom practice. Teacher quality and classroom practice can have an effect on student achievement equal to or exceeding that of socioeconomic status (SES) of students.

In addition, he noted aspects of teacher quality that are related to student achievement when class size and SES are taken into account. In particular, the following five variables are positively associated with achievement:

• Teacher major
• Professional development in higher-order thinking skills
• Professional development in diversity
• Use of hand-on learning in classrooms
• Focus on higher-order thinking skills

Wiens, P. D., Zizzi, C., & Heatwole, C. (2022). Instructional grouping theory: Optimizing classrooms and the placement of ranked students. Educational Practice and Theory, 44(1). doi: 10.7459/ept/44.1.02. https://www.ingentaconnect.com/contentone/jnp/ept/2022/00000044/00000001/art00002

Wiens, Zizzi, and Heatwole investigated two common approaches to grouping students: "an approach where students are grouped based on their aptitude and a cross-sectional approach where equal groups are formed and comprised of students of varied aptitudes. Instructional Grouping Theory is the study of how selection strategies impact the learning of group members. Using a non-biased, mathematically centric analysis, [they] found that a liked-skilled tiered grouping strategy is preferable to a cross-sectional grouping strategy when the goal is to facilitate the learning of all students. In addition, [they] found that a higher teacher-to-student ratio provides further benefit when analyzing the potential for facilitated learning" (Abstract section).

The University of Rochester News Center (2022, September 6) provided additional commentary on this research in What is the best way to group students?

Williams, T., Kirst, M., Haertel, E., et al. (2010). Gaining Ground in the Middle Grades: Why Some Schools Do Better. Mountain View, CA: EdSource. https://files.eric.ed.gov/fulltext/ED508674.pdf

Williams, Kirst, Haertel, et al. from EdSource and Stanford University conducted survey research in the 2008-09 school year, which involved 303 middle grades schools in California. The team surveyed 303 principals, 3752 English Language Arts (ELA) and math teachers in grades 6-8, and 157 superintendents of the districts and charter management organizations that oversee the schools.  They analyzed the reported district and school practices, correlating them with California's spring 2009 standardized test results in ELA and math in grades 6, 7, and 8 taken by approximately 204,000 students in their sample.  The study is significant for documenting the range of traditional and newer policies and practices that are in place in those middle schools and for identifying which of those practices and policies differentiated higher-performing schools from lower-performing schools with similar student populations on standards-based tests.  Findings have implications for practices that might be incorporated in other settings, which lend themselves for achievement and better standardized testing results independent of student background.

The following are some of the major findings noted in the Narrative Summary of this study:

• An intense schoolwide focus on improving academic outcomes most distinguishes higher- from lower-performing middle grades schools.  Effective practices include (1) setting measureable goals for improved student outcomes on standards-based tests, including for interim benchmark tests. (2) There's a shared school mission to prepare students academically for the future.  This includes strong regular communication on the importance of middle school achievement in preparation for high school and future goals.  Instruction and curricula are designed so that learners leave middle school with strong foundational academic and study skills, are on track to pass the California High School Exit Exam, and are ready to take on courses required for college entrance. (3) Adults are held accountable and responsible for improved student outcomes, and (4) the school expects students and parents to share responsibility in student learning.  This latter includes requirements and contracts for parent participation.

• In higher-performing schools, curricula and instruction are closely aligned with state academic standards.  Effective practices include (1) implementation of standards-based curricula and instructional practice that is tight and coherent.  ELA and math teachers use the adopted curriculum programs daily.  Teachers report collaborating frequently to discuss curriculum pacing, scope and sequence; to develop common benchmarks and assessments; to discuss how common benchmarks and assessments relate to instruction; and to break-down state content standards into prerequisite student skills. (2) Cohensive policies and strategies are implemented to further strengthen student learning of ELA and math in grades 7 and 8.

• Higher-performing schools use assessment and other student data extensively to improve student learning and teacher practice.  Data are used throughout the year in higher-performing schools, rather than just a few times a year as seen in lower-performing schools.  Effective practices include (1) strong district support for using assessment data.  For example, the district provides a computer-based system to enable school staff members to access and review student data, and has standards-based benchmark tests available for each grade and subject that it expects schools to administer.  (2) Facility with and frequent use of assessment data indicates a changing role of principals in higher-performing schools.  There is a culture shift to focus on student outcomes.  Teachers report frequent use of assessment data to evaluate individual student achievement, achievement by subgroups, and to set goals; help students see steady and measureable progress in their learning; identify and correct gaps in their instruction; and analyze student assessment data to identify effective instructional practices.  They frequently administer benchmark assessments, diagnostic assessments, and classroom-based assessments.

• Higher-performing middle grades schools emphasize early identification and proactive intervention for student academic needs. Among effective practices (not exhaustive) are a comprehensive range of required and voluntary strategies to intervene for students who are two or more years below grade level or who are in danger of failure for the current year.  The range of required intervention strategies includes such things as extra instructional time during the school day, perhaps in place of an elective; short-term interventions that run concurrent with class; intervention outside of the regular school day; required intersession or summer courses.  Voluntary academic intervention for those at risk for failure in the current year might take the form of academic support during nonclassroom time (e.g., after school or during lunchtime); programs like Advancement Via Individual Determination (AVID); and an online or intervention program.  Teachers report using differentiated instruction for individuals or groups and flexible student groups during class time.

• Every role in a professional community of educators is important to making gains in middle grades student outcomes.  This includes practices by teachers, principals, and superintendents.  Examples of best practices include useful professional development of teachers, a considerable amount of common planning time per month in 7th and 8th grade for ELA and math teachers.  The report elaborates further on specific findings regarding key players in the professional community.

Woodward, J., Beckmann, S., Driscoll, M., Franke, M., Herzig, P., Jitendra, A., Koedinger, K. R., & Ogbuehi, P. (2012). Improving mathematical problem solving in grades 4 through 8: A practice guide (NCEE 2012-4055). Washington, DC: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education. https://ies.ed.gov/ncee/wwc/PracticeGuide/16

Woodward and colleagues provided five recommendations for improving mathematical problems solving in grades 4-8 and discussion of the research supporting the following:

1. Prepare problems and use them in whole-class instruction.
2. Assist students in monitoring and reflecting on the problem-solving process.
3. Teach students how to use visual representations.
4. Expose students to multiple problem-solving strategies.
5. Help students recognize and articulate mathematical concepts and notation.

Recommendations 2 and 3 are supported by "strong" evidence, according to research reviewed for this practice guide.

Zhang, Q., Sun, J., & Yeung, W. (2023, April). Effects of using picture books in mathematics teaching and learning: A systematic literature review from 2000-2022. Education Research, 11(1), e3383. https://bera-journals.onlinelibrary.wiley.com/doi/10.1002/rev3.3383

Zhang, Sun, and Yeung reviewed 16 empirical studies from 2000–2022 "regarding the use of picture books in mathematics instruction, in order to investigate their effects on mathematics learning in students."  "Most of the selected studies targeted early mathematics education, with only a minority addressing secondary education."  Findings revealed that "various approaches are available for the integration of picture books into mathematics teaching, having various positive effects on student attitudes toward mathematics, as well as their academic performance and mathematical representation ability. The reported inhibiting factors for teachers using picture books in teaching included a lack of pedagogical knowledge and confidence, time constraints, resource constraints and doubts regarding the expected outcomes. Conversely, the enhancing factors included early educational stage (especially the pre-school level), perceived pedagogical benefits, desire to improve teaching and enabling social norms." (Abstract section)

 

 

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Technology Integration

 

 

Battista, M. T. (1998). Computer environments that engender students’ construction of mathematical ideas and reasoning: A constructivist perspective. Paper presented at the ENC Technology and NCTM Standards 2000 Conference. Arlington VA, June 5-6, 1998. https://web.archive.org/web/20140925143322/http://mathforum.org/technology/papers/papers/battista/battista.html

Brodersen, R. M., & Melluso, D. (2017). Summary of research on online and blended learning programs that offer differentiated learning options (REL 2017–228). Washington, DC: U.S. Department of Education, Institute of Education Sciences, National Center for Education Evaluation and Regional Assistance, Regional Educational Laboratory Central. https://ies.ed.gov/ncee/rel/Products/Publication/3832

Carrol, T. G. (2000). If we didn't have the schools we have today, would we create the schools we have today? Contemporary Issues in Technology and Teacher Education, 1(1), 117-140. https://citejournal.org/volume-1/issue-1-00/general/article1-htm/

Carroll included discussion of the classroom of tomorrow and six reasons why the web has won.

Cheung, A., & Slavin, R. (2011, July). The effectiveness of educational technology applications for enhancing mathematics achievement in K-12 classrooms: A meta-analysis. Baltimore, MD: Johns Hopkins University, Center for Research and Reform in Education. https://bestevidence.org/tech_math_apr_11_2012/

Cheung and Slavin included "74 qualifying studies, with a total sample size of 56,886 K-12 students" in this meta-analysis.  Three categories of educational technology were reviewed: Computer managed learning (via the program Accelerated Math); Comprehensive models that included both computer assisted instruction (CAI, e.g., via programs Cognitive Tutor and I Can Learn) and non-CAI activities in math instruction; and Supplemental CAI technology for individualized CAI to supplement traditional instruction (e.g., via programs Jostens, PLATO, Larson Pre-Algebra, and SRA Drill and Practice).  "Findings of the review indicate that educational technology applications produce a positive but small effect (ES=+0.16) on mathematics achievement. In particular, supplemental CAI had the largest effect, with an effect size of +0.19. The other two categories, computer-managed learning and comprehensive models, had a much smaller effect size, +0.09 and +0.06, respectively."

 

 

Delgado, P., Vargas, C., Ackerman, R., & Salmeró, L. (2018, November). Don't throw away your printed books: A meta-analysis on the effects of reading media on reading comprehension. Educational Research Review, 25, 23-38. https://www.researchgate.net/publication/330854760_Don't_throw_away_your_printed_books_A_meta-analysis_on_the_effects_of_reading_media_on_reading_comprehension

Delgado and colleagues conducted a meta-analysis of research from 2000-2017 comparing the reading of comparable texts on paper and on digital devices.  The rational of the study was due to "the increasing dominance of digital reading over paper reading" and the resulting critical need to gain "understand of the effects of the medium on reading comprehension."  They "included studies with-between participants (n=38) and within-participants designs (n=16) involving 171,055 participants.  Both designs yielded the same advantage of paper over digital reading."  The effect size was significant (ES=+.21).  Significant influencing factors included "(1) time frame: the paper-based reading advantage increased in time-constrained reading compared to self-paced reading; (2) text genre: the paper-based reading advantage was consistent across studies using informational texts, or a mix of informational and narrative texts, but not on those using only narrative texts; (3) publication year: the advantage of paper-based reading increased over the years. Theoretical and educational implications are discussed." (Abstract section)

Delgado and colleagues noted that digital reading is an integral part of education.  Future research might look at the influence of the type of device (e.g., desktop computers, hand-held devices) and the effect of scrolling, as this latter was "found to be a possible obstacle to comprehension during digital reading" (p. 35).  They concluded that "ignoring the evidence of a robust screen inferiority effect may mislead political and educational decisions, and even worse, it could prevent readers from fully benefiting from their reading comprehension abilities and keep children from developing these skills in the first place" (p. 36).

Finster, M., Decker-Woodrow, L., Booker, B., Mason, C. A., Tu, S., & Lee, J. (2023). Cost-effectiveness of algebraic technological applications. Journal of Research on Eduational Effectiveness. https://www.tandfonline.com/doi/full/10.1080/19345747.2023.2269918

Finster and colleagues presented their "cost-effective analysis (CEA) of three algebraic technological applications, across four conditions: From Here to There (FH2T), Dragon Box 12+ (DragonBox), Immediate Feedback and Active Control."  The study used an "analytic sample of 1,850 middle school students across 9 schools, 34 teachers, and 127 classes."  Overall, the study demonstrated "the efficiency of FH2T and DragonBox as low-cost interventions for improving students’ algebraic performance and addressing the nation’s decline in mathematics." (Abstract section)

Furenes, M. I., Kucirkova, N., & Bus, A. G. (2021). A comparison of children’s reading on paper versus screen: A meta-analysis. Review of Educational Research. https://doi.org/10.3102/0034654321998074

Per the press release from the American Educational Research Association (2021, March 9), this analysis revealed that "Digital Picture Books Harm Young Children's Learning--Unless the Books Have the Right Enhancements."

The authors' examined "the inconsistent findings across experimental studies that compared children’s learning outcomes with digital and paper books.  [They] quantitatively reviewed 39 studies reported in 30 articles (n = 1,812 children) and compared children’s story comprehension and vocabulary learning in relation to medium (reading on paper versus on-screen), design enhancements in digital books, the presence of a dictionary, and adult support for children aged between 1 and 8 years. The comparison of digital versus paper books that only differed by digitization showed lower comprehension scores for digital books. Adults’ mediation during print books’ reading was more effective than the enhancements in digital books read by children independently. However, with story-congruent enhancements, digital books outperformed paper books. An embedded dictionary had no or negative effect on children’s story comprehension but positively affected children’s vocabulary learning. Findings are discussed in relation to the cognitive load theory and practical design implications." (Abstract section)

Johnson, J., & Toms Barker, L. (eds.). (2002). Assessing the impact of technology in teaching and learning: A sourcebook for evaluators.  Ann Arbor, MI: Institute for Social Research at the University of Michigan. https://www.researchgate.net/publication/242507859_Assessing_the_Impact_of_Technology_in_Teaching_and_Learning

This 184 page sourcebook, available for free in PDF format online, provides an overview of measurement issues in seven areas as well as examples of measures used in current projects.  It would be of value to evaluators who are assessing the role of technology in American education.  The areas include learner outcomes in the cognitive and affective domains and in adult education, teacher outcomes related to changed pedagogy and improving technology skills, technology integration, and disseminating the lessons of technology projects.  The first chapter on learner outcomes in the cognitive domain, for example, includes the merits and difficulties of using standardized tests, tailored tests, and authentic assessments in the evaluation of educational projects.

Kerrey, B., & Isakson, J. (2000, December 19). The power of the Internet for learning: Moving from promise to practice. Washington, DC: Web-Based Technology Commission. https://eric.ed.gov/?id=ED444603

This final report of the Web-based Technology Commission contains over 100 pages and was presented to the President and the Congress of the United States in December, 2000. Among the contents are discussions of access to broadband technologies; professional development and how technology can enhance teaching; correcting the paucity of research and development; online content; removing regulatory restrictions to e-learning; privacy, protection, and safety; funding for e-learning, and the call for national action.

Kleiman, G. M. (2000, April-June). Myths and realities about technology in K-12 schools. Leadership & the New Technologies, 14. https://www.sfu.ca/educ260/documents/myths.pdf

Glenn Kleiman of The Center for Online Professional Education discussed the realities surrounding five myths that relate to computer availability in schools, goals and best practices for computer use in classrooms, teacher implementation stages for effective use, district technology plans, and equity and the digital divide.  The message is that short term solutions will not work.  The key is not how many computers are available, but, in his words, "how we define educational visions, prepare and support teachers, design curriculum, address issues of equity, and respond to the rapidly changing world" [Online].

Rakes, C., Ronau, R., Bush, S., Driskell, S., Niess, M., & Pugalee, D. (2020, November). Mathematics achievement and orientation: A systematic review and meta-analysis of education technology. Educational Research Review, 31, article 100337. https://www.sciencedirect.com/science/article/abs/pii/S1747938X19301800

Rakes and colleagues investigated the effects of ed tech on mathematics achievement and orientation (i.e., beliefs, attitudes, and preferences).  Analysis was made on 123 effect sizes from previous studies.  Most of the studies (82%) focused exclusively on procedural understanding.  Commenting on the research, Zhang of Johns Hopkins University (2020, September 29) noted, "Meta-analysis results showed that ed tech in mathematics class has statistically significant but very small effects on achievement (ES = +0.11) and orientation (ES = +0.13). However, after further adjustment for publication bias, these very small effects were gone. Therefore, researchers are inconclusive about ed tech’s effects on student outcomes."

Ray, B. (2005). Mining what we know about handheld computers: A review of the [anecdotal] evidence. The Turkish Online Journal of Educational Technology, 4(2), article 1. http://www.tojet.net/articles/v4i2/421.pdf

According to Beverly Ray (2005) who reviewed the literature on handheld computers, "The empirical evidence suggests that the integration of handheld technology into the K-12 classrooms promotes 1) teacher productivity and 2) student-centered learning. However, despite a wealth of empirical and anecdotal evidence there is no research base to support these assertions. Further research supporting their effectiveness, however, remains to be done" (p. 5).

Reyes, I., Wijesekera, P., Reardon, J., Elazari, A., Razaghpanah, A., Vallina-Rodriguez, N., & Egelman, S. (2018). “Won’t Somebody Think of the Children?” Examining COPPA Compliance at Scale. Proceedings on Privacy Enhancing Technologies, 2018(3), 63–83.  https://petsymposium.org/2018/files/papers/issue3/popets-2018-0021.pdf

Reyes, Wijesekera, Reardon, Elazari, Razaghpanah, Vallina-Rodriguez, and Egelman (2018) indicated that users of children's apps that have been certified as being COPPA (Children's Online Privacy Protection Act) compliant should be aware that such certification does not necessarily mean that the certified-app does a better job at safeguarding privacy of personal data than a non-certified app.  Their study focused on Android apps available on Google Play.  "Based on [their] automated analysis of 5,855 of the most popular free children’s apps, [they] found that a majority are potentially in violation of COPPA, mainly due to their use of thirdparty SDKs" (p. 63). SDK means Software Development Kit.  Reyes et al. included the list of seven companies in the COPPA Safe Harbor Program, which provide certifications that materials are COPPA compliant.  Among those are iKeepSafe, kidSAFE, and TRUSTe.

Wallace, A. (2013, October 25). CIPA: 10 years later, there is still confusion. Tech & Learning Magazine: Features.  https://www.techlearning.com/news/cipa-10-years-later-there-is-still-confusion

Andrew Wallace tackled the confusion that still exists among those who are required to interpret the Child Internet Protection Act (CIPA) and implement it.  Stating CIPA requirements in a nutshell:

School Districts must:

• Use a “technology protection measure” to block images that are: child pornography, obscene, or harmful to minors.
• Determine, with community input what content (visual or written) is inappropriate for minors.
• Adopt an Internet safety policy that applies to both students and staff.
• Teach students how interact on email, social networking sites, and in chat rooms.
• Deliver instruction with a focus on cyberbullying.
• Monitor in school use of the Internet. (Wallace, 2013, Quick Facts section)

Wells, J., & Lewis, L. (2006, November).  Internet access in U.S. public schools and classrooms: 1994-2005 (NCES 2007020). U.S. Department of Education. Washington, DC: National Center for Education Statistics.  https://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=2007020

John Wells and Laurie Lewis presented survey findings (no survey in 2004) on school connnectivity, student access to computers and the Internet, technologies and procedures to prevent student access to inappropriate material on the Internet, teacher professional development on how to integrate the use of the Internet into the curriculum, and use of the Internet to provide opportunities and information for teaching and learning.

Weston, M. E., & Bain, A. (2010). The end of techno-critique: The naked truth about 1:1 laptop initiatives and educational change. Journal of Technology, Learning, and Assessment, 9(6). https://ejournals.bc.edu/index.php/jtla/article/view/1611

Weston and Bain analyze and respond to "a generation of criticism leveled at 1:1 laptop computer initiatives."  They present "a review of the key themes of that criticism and [offer] suggestions for reframing the conversation about 1:1 computing among advocates and critics.  Efforts at changing, innovating, and reforming education provide the context for reframing the conversation.  Within that context, [they] raise questions about what classrooms and schools need to look and be like in order to realize the advantages of 1:1 computing.  In doing so, [they] present a theoretical vision of self-organizing schools in which laptop computers or other such devices are essential tools" (Abstract section).

Willard, N. (2002). Keeping kids safe online. Education World. https://www.educationworld.com/a_tech/tech119.shtml

The Child Internet Protection Act requires districts to monitor student use of the Internet and to implement technology-based measures to protect against student access to online content that may be harmful to minors. Willard noted four core components for a comprehensive plan to address online safety and Internet use by districts:

• A focus on the educational purpose with Internet use limited to activities that support education, enrichment, and career development;

• Education about safe and responsible use, which is included in the ISTE standards developed for students, teachers, and administrators;

• Supervision and monitoring that are age appropriate and based on circumstances of use;

• Discipline that not only is appropriate to circumstances of misuse, but also educates students on standards for use.

May 8, 2023 Note: Willard also noted that districts that want to have blocking in place should consider the use of the Internet Content Rating Association system.  However, ICRA was discontinued in 2010 per Wikipedia.  For internet safety consider the resources at the Family Online Safety Institute.

 

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