xi CHAPTER 1: INTRODUCTION ...1 Conceptual Framework ...2 Rationale ...4 Research Questions ...8 Significance of the Study ...9 Definitions...10 CHAPTER 2: LITERATURE REVIEW ...11 Histor
INTRODUCTION
Homework is an issue that affects not only students and teachers, but also parents
Homework, defined as any tasks teachers assign to students to be completed during non-school hours (Cooper, 1989), is a ubiquitous feature of schooling, and the most common type is instructional Within instructional homework, at least three purposes can be embedded: to practice skills already taught, to prepare students for upcoming lessons, and to extend learning by applying concepts beyond the classroom.
To provide students with an opportunity to practice or review material presented in class (Becker
Epstein (1982) identifies three core purposes of preparatory and bridging activities: (1) activating students' prior knowledge; (2) introducing preparation materials to help students get ready for the new material that teachers will cover in class (Muhlenbruck et al., 1999); and (3) extending and integrating previously learned knowledge and skills so they can be applied to new situations or combined with other concepts (Lee & Pruitt, 1979).
Public views on assigning mathematics homework have been controversial, with parents, students, and teachers often holding divergent perspectives Parents frequently argue that there is too much or too little homework, voicing concerns about workload and balance Students contend that homework infringes on their leisure time and free activities Meanwhile, teachers themselves sometimes misunderstand the purpose of homework, contributing to the ongoing debate about its effectiveness Research by Cooper, Robinson, and Patall (2006) highlights these mixed perceptions and the need for clearer goals behind mathematics homework assignments.
Research shows homework is a valuable extension of in-class mathematics instruction (Henderson, 1996), even as popular media highlight ongoing tensions between parents and schools over assignments (Kralovec & Buell, 2000; Loveless, 2003) Despite these debates, most mathematics teachers view homework as a central part of instructional practice and student learning Evidence indicates that instructional methods shape how students learn, and homework provides an important mechanism for students to actively engage with mathematical concepts beyond the classroom (Cooper, Robinson, & Patall, 2006).
Considering the varying purposes of homework, it is natural to ask whether different homework types influence student achievement in distinct ways However, research linking homework to achievement is limited, and studies that examine the effects of specific homework types are even scarcer To address this gap, this study investigates how homework type as an element of opportunity to learn relates to student math achievement.
The Mathematical Task Framework (MTF), developed by Stein and colleagues within the Qualitative Understanding Amplifying Student Achievement and Reasoning (QUASAR) project, highlights how mathematical tasks shape students’ learning opportunities and the pivotal role teachers play in designing and implementing those tasks As Silver and Herbst (2007) note, teachers’ handling of tasks influences student engagement and, ultimately, students’ opportunity to learn mathematics The framework also distinguishes between the intended curriculum (prewritten content such as textbooks or tasks) and the implemented curriculum (how teachers actually use those materials in the classroom), with Porter (2004) clarifying that the intended curriculum sets standards while the implemented curriculum reflects instructional delivery Researchers commonly apply the MTF to analyze empirical data on the extent of opportunity to learn mathematics that teachers create through task-based instruction, aiming to improve student learning (Stein et al., 1996).
This study adopts the MTF framework as its conceptual basis, mapping the curriculum’s homework types to the tasks described in the curricular materials shown in the MTF figure Lesson coverage refers to how teachers structure and deliver the lessons, while homework assigned encompasses tasks implemented by teachers and, where applicable, by students Student learning is reflected in achievement scores, as illustrated in Figures 1 and 2.
Figure 1 The Mathematical Tasks Framework (Stein, Smith, Henningsen, & Silver, 2000)
Figure 2 The Mathematical Tasks Framework as It Relates to Homework
Within this study, the Mathematical Tasks Framework is adapted for homework so that Phase 3 does not map one-to-one to the third phase of the original framework Consequently, the actual homework assignments completed by students are not known.
This study examined three types of homework problems: basic understanding of concepts, problems that apply concepts, and review problems Opportunity to Learn (OTL) based on lesson coverage relates to teachers’ decisions to assign different types of homework from chapters throughout the textbook, representing Phase 2 (lesson coverage by teachers) of the MTF Teachers may assign none, some, or all of the problems from the lessons taught The percent of each type of homework problem assigned from the available problems corresponds to Phase 3 (homework assignment based on lesson coverage) of the MTF Phase 4 (student mathematics achievement) in the MTF refers to student mathematics learning.
Since An Agenda for Action (National Council of Teachers of Mathematics, 1980) called for changes in student mathematics, curriculum design has focused on developing students’ mathematics problem-solving skills The Curriculum and Evaluation Standards for mathematics further reinforced this emphasis, shaping how mathematics is taught and assessed.
School Mathematics, published by the National Council of Teachers of Mathematics (NCTM) in 1989, laid out recommendations for the content to be included in school mathematics, the mathematical skills students should master, and learning goals for each grade band The subsequent publication, Principles and Standards for School Mathematics (PSSM) (NCTM, 2000), refined and clarified those standards, offering a more cohesive framework for instruction, assessment, and curriculum planning In 2001, the No Child Left Behind Act was enacted, strengthening federal accountability and shaping mathematics education across schools.
No Child Left Behind (NCLB) legislation prioritized closing the achievement gap and boosting student achievement for all learners After the release of the Principles and Standards for School Mathematics (PSSM) and the passage of NCLB, many school mathematics curricula were developed and implemented to reflect the recommendations of these standards, with the goal of enhancing student achievement across classrooms.
To boost student achievement, teachers must implement curriculum materials effectively in the classroom Homework allocation is closely tied to how the curriculum is put into practice, yet this area remains highly debated and understudied The conversation extends beyond the quantity of homework to consider the quality and nature of the assignments and their impact on learning.
Homework is an important part of secondary school students’ lives, but it is often viewed as excessive pressure and its value is questioned, with concerns about its impact on mental health and student motivation Yet research summarized by Cooper, Robinson, and Patall (2006) shows a generally positive relationship between homework and student mathematics achievement, suggesting that homework can support learning However, further investigations are needed to identify the specific factors related to homework assignments that most effectively enhance learning outcomes.
Opportunity to learn (OTL) is widely regarded as the single most important predictor of student achievement, according to the National Research Council (2001) Research also shows that homework provides opportunities for learning mathematics beyond classroom instruction (Cooper, Robinson, & Patell, 2006) Because homework is inherently complex, it can produce both positive and negative effects, highlighting the need to examine the role and types of homework in shaping policies and practices However, existing research is limited, with most studies using the amount of homework assigned or completed as a measure of its relationship to achievement, and little attention has been paid to how different types of homework may influence learning outcomes.
LITERATURE REVIEW
Homework has long been a central component of teachers’ instructional practice, yet it remains a controversial topic for parents and schools To determine which types of homework best support student learning, it is essential to examine historical research on the role of homework in the school curriculum and its impact on achievement This synthesis analyzes studies on the relationship between homework and achievement, considers how different homework types create opportunities to learn, and assesses how these factors influence student outcomes The chapter also defines the variables used, explains how these relationships are studied, and introduces historical and modern mediation concepts alongside contemporary statistical methods.
Homework is the most common instructional practice in school mathematics and a constant topic of debate among parents, educators, and policymakers about its necessity, frequency, and the amount assigned to students These questions require not only current and future studies but also an understanding of the origins of these concerns and what researchers have previously found about the impact of mathematics homework on learning This literature review provides a historical perspective on the research surrounding homework, tracing how ideas about its role in math education have evolved and what that history implies for today’s practice and policy.
During the early 1900s, research on homework proposed that assignments increased time spent on academic tasks and helped cultivate self-discipline through memorization, a process thought to support knowledge acquisition Homework was promoted as a powerful learning strategy because memorization could be achieved by completing tasks outside the classroom without direct teacher instruction But this view was soon challenged by researchers who stressed the development of problem-solving skills and questioned learning that relied on memorization alone In the 1920s, two divergent perspectives emerged: homework abolitionists, who argued for eliminating homework altogether, and homework reformers, who sought to reform assignments to foster students' conceptual understanding and genuine interest in learning.
Across the 1930s and 1940s, many school districts eliminated homework for grades K–6, viewing it as ineffective and a distraction from other student activities In the post–World War II era, homework reformers argued that U.S students lagged behind their international peers, especially in mathematics, and that homework practices contributed to this gap They turned to research to reshape the educational discourse on homework, promoting new pedagogical aims that emphasize meaningful, activity-based problems rather than rote repetition of textbook material Gill and Schlossman (2000) urged educators to move beyond a simplistic judgment of homework as wholly good or bad and to redefine its rationale and content, steering away from drill on in-class lessons Concurrent reforms also sought policy and scheduling changes to regulate the organization, quantity, pacing, and burdens of homework on students and their families.
& Schlossman, 2000, p 33) The central mission of such reform called for “learning by doing”,
“educating the whole child”, and “child-centered learner driven education” (Gill & Schlossman,
2000) This perspective directly resulted in an increase in the amount of homework assigned (Cooper & Valentine, 2001)
In the 1960s and 1970s, psychologists argued that homework could burden students and infringe on time for social, recreational, and creative activities, potentially affecting mental health and contributing to a reduction in homework in many schools Then, in 1983, A Nation at Risk linked insufficient homework to weaker mathematics performance in the United States, prompting a renewed emphasis on achievement and higher educational standards As a result, some schools began assigning more homework at earlier grade levels, including kindergarten, signaling a shift toward greater homework requirements to drive academic outcomes.
2006) In 2001, No Child Left Behind called for mandatory annual testing to close the achievement gap in schools which also resulted in increased homework assignments (Kohn,
2006), especially mathematics homework Nevertheless, public concerns from parents and social media about homework being a stress factor for students still remain a challenge for schools and educators (Cooper et al., 2006)
Historical perspectives on homework have shifted under public influence and reform movements, and homework remains a heated topic of debate among educators and parents Therefore, researchers need a thorough understanding of the nature of homework assignments and their direct and indirect effects on student achievement This understanding is essential for guiding the proper structuring of school policies and instructional practices, because homework should ultimately be designed to enhance student mathematics achievement.
As one aspect of opportunity to learn, research on homework has generally shown a correlation between homework and student achievement (Cooper, 1989; Cooper, Robinson, & Patall, 2006) Although measures of homework vary, some using amount and others using frequency or types of homework, such correlation between homework and achievement is generally found to be positive
Cooper (1989) conducted a meta-analysis of 120 empirical studies on the effects of homework using studies conducted between 1960 and 1987 He concluded that there were three different types of studies on homework and achievement The first type investigated the achievement level of students who were given homework with those who were not given homework to determine if the existence of homework is a factor in achievement Such studies were normally conducted in a controlled environment with predetermined students of similar background and similar levels of prior knowledge being randomly assigned to two groups Most studies of this type showed that homework being assigned generally had a positive influence on student achievement (Foyle, 1984, 1990; McGrath, 1992; Finstad, 1987, Meloy, 1987; Townsend,
Research from 1995 indicates significant grade-level differences in the relationship between homework and achievement as measured by standardized tests High school students with assigned homework scored significantly higher on standardized tests than peers in the same grade who had no homework, while middle-grade students with homework performed moderately higher than those without homework.
Cooper, Robinson, and Patall (2006) analyzed homework–achievement studies from 1987 to 2003, grouping experimental studies that used random assignment and controlled whether homework was assigned, and found that most studies reported a positive effect of homework on mathematics or language arts achievement (Finstad 1987; Foyle 1990; McGrath 1992; Townsend 1995) However, these studies have limitations: controlled-environment designs with assigned homework often used similar test items, so students not assigned homework did not practice those items, which compromises the results; standardized assessments as posttests measure only immediate effects and cannot capture long-term effects without accounting for other factors in the controlled setting A second type of study compared homework completed outside school with in-class homework and generally found that supervised homework had a stronger influence on achievement than unsupervised work, especially in elementary schools, though the correlation was not significant for middle and high school students, illustrating a strong grade-level effect The final type examined the relationship between time spent on homework and achievement, reporting significant correlations and sometimes aiming to establish causality in mathematics, though Cooper (1989) concluded a correlation exists but none of these studies isolated the role of different types of homework on achievement.
More recent studies (Davis & Jordan, 1994; Hill, 2003; Peng & Wright, 1994; Thomas, 2001; Thomas, 2002) have examined homework’s role in achievement using multivariate analysis models that account for multiple factors Drawing on data from the National Education Longitudinal Study of 1988 (NELS) and subsequent follow-up studies of the same cohort of middle school and high school students, these investigations offer insights into various elements that may affect achievement, with homework as one of the factors considered The most common measure of homework in these studies is the amount of homework assigned or completed by students, typically captured as frequency or duration Overall, these studies report a positive effect of the amount of homework on achievement However, they did not include exogenous factors such as socio-economic status or gender, because the data were not collected in a controlled environment.
Several studies that controlled for variables such as prerequisite knowledge used multivariate analyses to examine the relationship between homework and achievement (Brookhart, 1997; Cool & Keith, 1991; Fehrmann, Keith & Reimers, 1987; Foyle, 1990; Cooper, Lindsay, Nye & Greathouse, 1998; Hendrix, Sederberg & Miller, 1990; Olson, 1988; Smith, 1990; Smith, 1992; Wynn, 1996; Portes & MacLeod, 1996) These studies generally found a positive association between the amount of homework assigned and student achievement, but they did not establish causality (Cooper et al., 2006) Many of these investigations relied on simple bivariate correlations between homework time and achievement scores and did not control for other variables that might influence the relationship Across these analyses, a significant correlation between time spent on homework and achievement emerged, although such correlations were not significant for elementary students.
Although many studies have examined the relationship between homework and achievement, researchers have not reached consensus on how teachers assign homework or its effectiveness in improving student achievement There is limited literature on homework types and their impact on student outcomes Nevertheless, homework is often seen as part of the opportunity to learn mathematics that teachers provide for students Related literature on the opportunity to learn in the context of homework assignments should be considered to better understand how homework relates to learning.
Homework and Opportunity to Learn
Opportunity to learn (OTL) explains differences in student achievement, a concept that originated with Carroll’s 1963 model of school learning as one of its five core constructs Carroll defined OTL as the amount of time available for a student to learn a specific task, while Husén (1967) offered an alternative view, viewing OTL as the overlap between mathematics that is taught and the mathematics content actually tested Building on both perspectives, researchers have integrated Carroll’s time-based view with Husén’s content-coverage perspective to develop various OTL frameworks for their studies (Robitaille & Travers, 1992; Winfield, 1987).
Stevens (1993) identified an Opportunities to Learn (OTL) framework that links teacher instructional practices to student learning and gained wide recognition among educators The framework comprises three core variables: content exposure and coverage, content emphasis, and quality of instructional delivery Content exposure and coverage measure both the time students spend on learning and the depth of instruction they receive Content emphasis links the documented content coverage within the implemented curriculum to the selection of assessments—whether for basic skills instruction or beyond—and, consequently, to the types of homework assigned Finally, quality of instructional delivery describes how instructional practices influence students’ academic achievement.
The construct of OTL has also appeared in studies organized by the International
METHODS
This chapter outlines the research design, sample, and measures used to analyze the mediation effects of homework types on the link between opportunity to learn (OTL) and students’ mathematics achievement OTL is defined as the circumstances that allow students to engage in and devote time to academic tasks (National Research Council, 2001, p 333) In this study, OTL is assessed through two indicators: teachers’ actual lesson coverage and teachers’ reports of item coverage on posttests, capturing both instructional delivery and posttest opportunities The analysis investigates the extent to which different homework types mediate the influence of OTL on students’ math achievement, including the impact of teacher-perceived OTL measured by posttest opportunity to learn on achievement.
This study investigates the extent to which different types of homework mediate the impact of opportunity to learn (OTL) on students’ mathematics achievement OTL is examined from two angles: actual lesson coverage and teachers’ perceived opportunity to learn the mathematics assessed on the posttest The study seeks to answer questions about the mediating role of homework in the OTL–mathematics achievement relationship, specifically how various homework types and the two OTL perspectives influence posttest performance.
OTL, measured by lesson coverage, positively influences mathematics achievement across Pre-Transition Mathematics, Transition Mathematics, and related courses, with the largest impact in Pre-Transition Mathematics and a meaningful, yet smaller, effect in Transition Mathematics The findings suggest that higher lesson coverage under OTL supports the development of foundational concepts and skills that carry into more advanced topics, underscoring the value of ensuring sufficient coverage within each course level For educators and curriculum designers, this means prioritizing thorough lesson coverage when implementing OTL, monitoring coverage as a key instructional metric, and adjusting pacing to align with the specific demands of Pre-Transition and Transition Mathematics to maximize student achievement.
Algebra? b How does OTL as measured by posttest OTL influence mathematics achievement in Pre-Transition Mathematics, Transition Mathematics, and Algebra?
2 To what extent do different types of homework influence the impact of OTL measured by lesson coverage on student mathematics achievement measured by 3 posttests in each of
Pre-Transition Mathematics, Transition Mathematics, and Algebra?
This study investigates the extent to which different homework types influence the impact of Opportunity to Learn (OTL) on student mathematics achievement during the Pre-Transition period, with OTL measured by teacher perceptions on each posttest The analysis focuses on how teacher-rated OTL on posttests moderates the relationship between homework type and the corresponding posttest mathematics scores, offering insights into how variations in homework design affect learning outcomes.
Mathematics, Transition Mathematics, and Algebra?
The results indicate that the mediation effects of homework types on mathematics achievement differ according to how OTL is measured Specifically, when OTL is indexed by lesson coverage, certain types of homework show a stronger indirect association with mathematics achievement via OTL than when OTL is indexed by posttest measures Conversely, other homework types reveal distinct mediation patterns under the posttest-based OTL metric, suggesting that the same homework design can influence achievement differently depending on the OTL indicator used These findings highlight that the operationalization of OTL shapes the observed indirect pathways from homework to achievement, and they imply that both researchers and practitioners should use multiple OTL indicators to capture the full mediating role of homework For practice, it suggests tailoring homework design to the OTL measurement approach and interpreting mediation results with the measurement method in mind.
This study conducts a secondary analysis of data from evaluations of the University of Chicago School Mathematics Project (UCSMP) secondary mathematics curricula, namely Pre-Transition Mathematics (PTM) in the 2006–2007 school year (1st Edition, Field Trial Version), Transition Mathematics in the 2005–2006 school year (3rd Edition, Field Trial Version), and Algebra in the 2005–2006 school year (3rd Edition, Field Trial Version) Pre-Transition Mathematics (Year 1) combines arithmetic with statistics, geometry, and algebraic thinking, and it uses algebra to describe generalizations, solve simple equations, and write formulas, as described by Thompson, Senk, and Yu.
Transition Mathematics (Year 2) acts as a pre-algebra text with substantial geometry integrated into algebra, creating a solid bridge between topics Algebra (Year 3) covers a broad spectrum of functions, including exponential functions, and interweaves statistics and geometry with algebra to enrich understanding These courses target students in grades 6–8, with PTM students typically in grade 6, and although Algebra is intended for grade 8, some learners use it in high school The Third Edition of the secondary materials, developed between 2005 and 2008, preserves effective features from previous versions while adding active learning, cooperative group work, and technology enhancements.
UCSMP curriculum materials share a core structure across a broad range of mathematics topics, emphasizing learning through reading and answering questions tied to the text They embed problem-solving and real-world applications throughout to help students relate mathematics to authentic contexts, with technology serving as a tool for understanding and exploration Instruction follows a modified mastery approach, supported by problem sets that balance practice of skills, properties, uses, and representations of concepts after each lesson.
Each lesson of these three textbooks contains four types of homework problems for students to complete:
• Covering the Ideas questions focus on basic concepts within the lesson, with many problems being similar to those actually found within the lesson’s examples
• Applying the Mathematics questions extend the concepts or integrate them with previously learned concepts so students can apply ideas in new contexts
• Review questions provide opportunities for students to continue working on important concepts in subsequent lessons and chapters, based on a modified mastery approach within the UCSMP curriculum
Exploration questions expand learning by offering extensions and investigations beyond the core concepts, as Thompson, Senk, and Yu (2012, p 6) explain UCSMP advises teachers to assign most, if not all, of the problems in these homework categories, with exploration questions as the stated exception (Thompson, Senk, & Yu).
Building on prior work (2012), this study confines its scope to three areas—conceptual ideas, the application of mathematics, and review questions—because these are the types of homework problems teachers commonly assign on a regular basis Focusing on these elements targets typical classroom tasks and provides insight into how students engage with core mathematical concepts, apply procedures, and prepare through review items.
This study uses subsets derived from a larger dataset collected during UCSMP's evaluation of its secondary materials Although the broader evaluation included participants using both UCSMP materials and comparison textbooks, this study includes only teachers and students who used UCSMP textbooks.
To align with the most common instructional purposes for homework problems identified in the literature review, I restricted the sample to teachers and students using the UCSMP curriculum, thereby controlling for the types of homework problems examined Non-UCSMP materials were excluded because teachers and students who used those materials did not necessarily have access to homework problems serving the same purposes as those in the UCSMP curriculum.
Three distinct course samples were analyzed, with each student contributing to only one evaluation study After analyzing data within each sample, the three studies were compared to determine whether the findings were consistent across studies Standardized pretest scores were used to control for prerequisite mathematics knowledge before students began studying the curriculum Posttest scores—drawn from standardized tests and UCSMP staff‑developed assessments—measured achievement The final sample size in each course (PTM, TM, and Algebra) was determined by including only UCSMP students who completed all pretests and posttests in these courses and who stayed with the same teacher, along with that teacher’s colleagues who taught these students.
Teacher data were collected from three sources: teacher questionnaires, opportunity-to-learn (OTL) forms for the posttest, and teachers’ chapter evaluation forms OTL was assessed from two separate perspectives: teacher-reported lesson coverage and teacher-reported opportunity to learn the content of the posttest items We expected there to be differences in the final results of the mediating effects of homework types when OTL was defined by lesson coverage versus by posttest-item content, with these two definitions analyzed separately.
Three homework types served as mediating variables: covering ideas, applying mathematics, and review These mediators were measured by the percentage of available problems of each type that teachers assigned to their students, calculated based on problems in the lessons taught A limitation of the study was the lack of information on students’ completion of these homework problems.
RESULTS
Providing students with the opportunity to learn mathematics has been a central focus for improving achievement in school mathematics This study investigates the extent to which different types of homework influence the impact of opportunity to learn mathematics on student achievement, using data subsets from the University of Chicago School Mathematics Project (UCSMP) and involving students who studied within its framework.
Pre-Transition Mathematics, Transition Mathematics, and Algebra taken as the sample
This study examined whether homework types—covering core ideas, applying mathematics, or reviewing material—mediate the influence of opportunity to learn, as measured by teachers’ lesson coverage or teachers’ perceived opportunity to learn the content, on posttest items across three mathematics courses.
This quantitative study used path analysis to examine mediation effects, with three types of homework problems treated as mediators Bootstrapping with 10,000 resamples was employed to estimate the indirect effect and determine its significance, with bias-corrected confidence intervals providing the inferential criteria.
Opportunity to Learn Measured by Lesson Coverage, Questions Assigned, and
Opportunity to Learn Content on Posttest Items
For Pre-Transition Mathematics, 13 teachers participated in the study Table 1 reports the opportunity to learn (OTL) as measured by lesson coverage and by teachers’ reported posttest OTL The data indicate that OTL measured by lesson coverage in the Pre-Transition setting was recorded and summarized in Table 1.
Mathematics had more variability, ranging from 41% to 90%; OTL percentages measured by posttest OTL were consistent among teachers, ranging from about 80% to 100% for all three posttests
Teacher Provided OTL Measured by Lesson Coverage and by Teachers’ Reported Posttest OTL for Pre- ‐Transition Mathematics
Table 2 reports each teacher's homework coverage, and the data reveal substantial variability in the types of homework problems assigned by PTM teachers, with review problems markedly less frequent than those aimed at covering ideas or applying mathematics.
Seven teachers participated in the Transition Mathematics study The Opportunity to Learn (OTL) was measured through lesson coverage and teachers’ posttest OTL reports, as shown in Table 3 Results indicate that OTL based on lesson coverage ranged from 56% to 92% for Transition Mathematics, while OTL measured from posttests varied more, with content coverage on the two multiple-choice posttests ranging from 70% to 92% for Posttest 1 (IAAT) and 55% to 100% for Posttest 2 (Algebra/Geometry Readiness Test), and only 41% to 76% for the problem-solving posttest. -**Support Pollinations.AI:** -🌸 **Ad** 🌸Powered by Pollinations.AI free text APIs [Support our mission](https://pollinations.ai/redirect/kofi) to keep AI accessible for everyone.
Number and Percent of Question Types Assigned by UCSMP Pre-Transition Mathematics
Teachers Based on Lessons Taught
The percentage shown represents how many homework problems of each type were actually assigned relative to the total number of problems possible for that type within the lessons taught It is calculated by dividing the actual count of assigned problems of a given type by the total possible problems of that type This provides a clear measure of the coverage of each problem type across the taught lessons.
Table 4 reports the homework coverage for each TM teacher, highlighting substantial variability in the types of homework problems assigned Specifically, review homework is considerably less prevalent than problems that cover ideas or apply mathematics, with one teacher assigning only 27% of the review tasks and another assigning 91%.
Six teachers participated in the Algebra study, and Table 5 reports the variability of OTL as measured by lesson coverage and teachers’ posttest OTL OTL by lesson coverage for Algebra ranged from 47% to 100% With the exception of two teachers, teachers generally reported posttest OTL for at least 90% of posttest 1 items For posttest 2, teachers’ reported OTL ranged from 67% to 100%, and for the problem-solving test, OTL ranged from 7% to 100%.
Teacher Provided OTL Measured by Lesson Coverage and by Posttest OTL for Transition Mathematics
Number and Percent of Question Types Assigned by UCSMP Transition Mathematics Teachers Based on Lesson Taught
Note: The percentage for each type of homework problem is calculated by dividing the actual number of assigned problems of that type by the total number of possible problems of that type in the lessons taught This method presents the share of workload allocated to each problem type within the taught curriculum.
Table 6 presents each teacher’s homework coverage and highlights substantial variation The data show that review homework was the least consistently assigned, with one teacher covering 83% of review problems and another only 2% Coverage for ideas problems ranged from 48% to 100%, and coverage for applying mathematics problems ranged from 25% to 99%.
Teacher Provided Opportunity to Learn Measured by Lesson Coverage and Teachers’ Reported Posttest OTL for Algebra
Number and Percent of Question Types Assigned by UCSMP Algebra Teachers Based on Lesson Taught
The percentage for each type of homework is calculated by dividing the actual number of assigned problems of that type by the total number of possible problems of that type in the lessons taught, and then multiplying by 100 to express the result as a percent.
Impact of Two Types of OTL and Achievement (Research Question 1)
The first research question examines how opportunity to learn (OTL) influences mathematics achievement across different mathematics courses, focusing on OTL as measured by lesson coverage Specifically, it asks how lesson coverage—an indicator of OTL—affects students’ mathematics achievement in Pre-Transition Mathematics and in Transition Mathematics, and whether the effect differs between these course levels The findings aim to clarify the relationship between instructional pacing, curriculum coverage, and student performance, providing actionable insights for curriculum design and teaching practices to improve math outcomes.
Mathematics, and Algebra? b How does teachers’ reported posttest opportunity to learn influence mathematics achievement in Pre-Transition Mathematics, Transition Mathematics, and
The Impact of Lesson Coverage as OTL (Part A)
Part A of Research Question 1 examined the relationship between OTL (Opportunity-To-Learn), as measured by lesson coverage, and mathematics achievement across Pre-Transition Mathematics, Transition Mathematics, and Algebra To address this, nine regression analyses were conducted in which OTL (lesson coverage) served as the predictor of mathematics achievement, as measured by three posttests within each course In every regression, a standardized pretest score was included as a covariate to control for prior achievement The approach aimed to determine whether greater lesson coverage predicts higher posttest performance across the three mathematics courses.
Pre-Transition Mathematics There were 287 students who took all the pretests and posttests, who used the UCSMP Pre-Transition Mathematics curriculum, and who stayed in the same class with the same teacher throughout the study