Herman + Rasiej Mathematics Initiative
RESEARCH HIGHLIGHTS
Research Update from Yasemin Copur-Gencturk
We are excited to share a synthesis of research findings as a product of Math Initiative research studies led by Yasemin Copur-Gencturk.
Proficiency in Teaching Mathematics Study
The ability to notice important aspects of mathematics instruction. Our paper on teacher noticing, written by Copur-Gencturk and Rodrigues, has been the first large-scale study on teacher noticing. Here’s a sneak peek of our findings!
What are Teachers Noticing?
More than 500 elementary teachers across the U.S. watched brief videos of classroom math instruction. We asked them to list the most significant things they noticed about the math content of the lessons.
Noticing Topic
Noticing Depth
If you are interested in learning more about teachers' noticing, please check Yasemin Copur-Gencturk and Jessica Rodrigues's paper published in 2021:
Content-specific noticing: A large-scale survey...
Problem Solving Findings
Yasemin Copur-Gencturk and Tenzin Doleck
As part of this study, we also examined teachers’ problem-solving strategies. We identified common strategies elementary school teachers used to solve word problems. The two papers written by Yasemin Copur-Gencturk and Tenzin Doleck, inform teacher educators about how teachers deal with mathematics problems and provide insights into teachers' mathematical thinking. Here’s a sneak peek of our findings!
Teachers' Problem Solving Strategies
More than 300 fourth and fifth grade teachers across the U.S. solved four open-ended fraction problems. We examined the strategies that teachers use correctly to solve the problems.
For the problem below, we identified the following common strategies.
Suppose that Max, the Wonder Dog, ate 1/4 of a bag of treats on Sunday. Each night after that, Max ate 3/16 of the bag. How many nights (including Sunday) would it take to finish the whole bag?
Problem Solving
Examples of solutions using the most common strategies for the Max the Wonder Dog Problem.
Sample
Solutions
If you are interested in learning more about teachers' solution strategies in story problems, please check Yasemin Copur-Gencturk and Tenzin Doleck's two papers published in 2021:
Strategic competence for multistep fraction problems ...
Linking teachers' solution strategies ...
Teachers' Knowledge of Fraction Magnitude
Fractions are one of the most, if not the most, challenging topics to teach and learn. In this study, we collected data from more than 600 mathematics teachers in grades 3-7 across the USA. We aimed to examine in-service teachers' knowledge of fraction magnitude by using estimation tasks. Here are some highlights of our findings!
Teachers' Knowledge of Fraction Magnitude
More than 600 mathematics teachers across the U.S. solved the estimation tasks and explain their answers. We analyzed teachers' responses to these two tasks according to the accuracy of their estimations and reasonableness of their estimation.
Estimating the sum of fractions
Estimating the quotient of fractions
Percentage of teachers who provided reasonable estimations for fraction addition and division
Frequency with which teachers used various strategies for estimations
Using fraction magnitude in their estimations.
Rough estimates, not a simultaneous attention to numerator and denominator
Not attending to the fraction as a magnitude (e.g., attending to numerator and denominator as separate quantities)
We also analyzed the alignment between teachers' estimation strategies with the concept of fraction magnitude. If you are interested in learning more about teachers' knowledge of fraction magnitude, please check Yasemin Copur-Gencturk's paper published in 2021:
Teachers' knowledge of fraction magnitude
Mathematics Teachers' Conceptual Understanding of Fraction Operations
Yasemin Copur-Gencturk
Fractions are one of the most challenging topics to teach and learn. This study used a sample of more than 300 elementary school teachers from across the USA. Dr. Copur-Gencturk explored teachers' knowledge of key concepts underlying fraction arithmetic based on their explanations of the two tasks below. You can find some highlights of our findings below:
Teachers' Knowledge of Fraction Operations
More than 300 elementary school teachers in 4th and 5th grades across the U.S. solved these two tasks and explained their answers by using different representations. Dr. Copur-Gencturk analyzed teachers' responses to these two tasks according to the accuracy of their explanations and the kinds of concepts and representations they used in their responses.
TASK 1
To capture teachers' conceptual understanding of fraction operation: Addition
TASK 2
To capture teachers' conceptual understanding of fraction operation: Division
Percentage of teachers' responses to fraction addition and division tasks
Incorrect
Sample Responses for
Addition Operation
Partially Correct
Sample Responses for
Division Operation
Incorrect
Partially Correct
Correct
Correct
The analysis also included the concepts and representations teachers used at each level of explanation:
If you are interested in learning more about teachers' conceptual understanding of fraction operations, please check Yasemin Copur-Gencturk's paper published in 2021:
Teachers' conceptual understanding of fraction operations
Mathematics Teachers' Implicit Race- and Gender -Biases
Yasemin Copur-Gencturk, Ian Thacker, Joe Cimpian, & Sarah Lubienski
Mathematics teachers can significantly affect students’ perceptions of their mathematical ability and future career choices. Hence, it is important for teachers’ assessments of students’ mathematical abilities to be free from bias. Still, most research conducted on teacher bias has failed to discern whether teachers are biased or if their assessments of their own students’ abilities are based on valid evidence not captured by researchers.
Teachers' Bias Against the Mathematical Ability of Female, Black, and Hispanic Students
In this experiment, 390 mathematics teachers evaluated 18 mathematical solutions to which gender- and race-specific names were randomly assigned. Dr. Copur-Gencturk and colleagues analyzed teachers’ evaluations of 18 mathematical solutions to which gender- and racespecific
names had been randomly assigned.
Names Assigned to Students' Work
The Same Student Work Assigned Different Names
Here are some highlights of our findings:
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Teachers displayed no detectable bias when assessing the correctness of students’ solutions;
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However, they perceived White students’ ability to be higher, especially relative to Black and Latina girls
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Surprisingly, non-White teachers displayed greater bias favoring White-sounding names.
If you are interested in learning more about teachers' bias against the mathematical ability of female, black, and Hispanic students, please check Yasemin Copur-Gencturk and her colleagues' paper published in 2019:
Teachers' bias against the mathematical ability...
The Answer Lab from Morgan Polikoff
Educational leaders need to make tough decisions all the time. Often, these decisions could be informed by research, but rarely does this actually happen. The Answer Lab is changing this. Dr. Polioff and his colleagues take questions directly from policymakers and find the right experts to answer them using the newest and best evidence. Hard questions. Clear answers. On a timeline that work. Here are some briefs that may interest you:
QUESTION/Brief 3: What is the best way to provide professional learning to teachers when they lack key content knowledge in mathematics?
Heather C. Hill, Harvard University
Studies of past standards-based reforms suggest that less knowledgeable teachers may transform investigation-based tasks into direct instruction, represent subject matter as facts and procedures rather than as disciplinary principles and practices, stymie student thinking, or even deliver inaccurate content. For this likely-substantial population of teachers, the learning demands of standards-based reform are steep.
To date, scholars have explored two strategies for addressing this problem:
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One focuses on improving teachers’ subject matter knowledge directly, in hopes that better knowledge will support higher-quality enactment of the new standards. However, studies over the past decade reveal that professional development intended primarily to improve teachers’ content knowledge did not consistently promote improved student outcomes.
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The second strategy involves tackling teachers’ content knowledge challenges indirectly, through the curriculum materials used in the classroom. Specifically, STEM programs that feature teacher learning about new curriculum materials see larger positive student impacts than programs that feature only teacher professional development or curriculum materials alone.
Additional Recommendations:
First, recent analyses show that some professional development delivery formats seem especially effective.
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Professional development that took place in a summer workshops was slightly more effective than programs that took place at other times.
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Programs drawing multiple teachers from the same school, rather than just one or two teachers per school, were also more effective.
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Programs saw better effects when they featured a meeting after the start of program implementation; these meetings allowed teachers to troubleshoot problems, consult with one another, and talk with a coach or facilitator familiar with the program.
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High quality evidence suggests that intensive coaching experiences can bring about strong improvements in teacher practice and modest improvements in student outcomes.
Lynch, K., Hill, H. C., Gonzalez, K. E., & Pollard, C. (2019). Strengthening the Research Base that Informs STEM Instructional Improvement Efforts: A MetaAnalysis. Educational Evaluation and Policy Analysis, 0162373719849044.
If you are interested in learning more about the best way to provide professional learning to teachers when they lack key content knowledge in mathematics, please check Brief#3.
QUESTION/Brief 6:
How Can Teachers Help Students Who Lack Foundational Math Skills But Have Been Passed Into Advanced Math Classes?
Alan Schoenfeld, U.C. Berkeley
Under the best of circumstances, the students in any class have a wide variety of strengths and weaknesses, so teaching can seem like a balancing act. At times, due to intentional or unintentional policies, we find a substantial percentage of students lacking what we would consider foundational skills.
What Doesn't Work: The “obvious” solutions don’t always work:
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“doubling up” on math prep .... increase failure rates
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within-class differentiation ... increases differences in student performance
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a focus on “missing” skills in mathematics ... ignores the possibility that students often learn core ideas in the context of problem solving
What Does Work:
One of the very useful things to come out of an equity-oriented approach is the concept of “group worthy math problems”
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have multiple entry points
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allow for multiple solutions
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different students might approach the task in different ways
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all students profit from comparing and contrasting solutions and showing how they connect
Teaching for Robust Understanding
A key to making all of this work is establishing discourse structures in class that involve students being active participants in sense making. Doing so involves a shift in perspective, from “What should teachers do” to “How are students experiencing instruction, and what kind of sense making are they doing?”
If you are interested in learning more about how teachers can help students who lack foundational math skills but have been passed into advanced math classes, please check Brief#6.
QUESTION/Brief 9:
What are the best approaches for teaching mathematics to newcomers to the U.S. who are English learners?
Marta Civil, University of Arizona
Zandra de Araujo, University of Missouri
Carlos LópezLeiva, University of New Mexico
Erin Sylves, Fairfax County Public Schoolss
MarÍa del Rosario Zavala, San Francisco State University
Our focus in this brief is on students who are new arrivals to the United States and are emergent English speakers, known as “newcomers.” The term “newcomers” encompasses a diverse group of students.
Within this group we distinguish two very different subgroups:
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students who had regular access to formal schooling prior to their arrival in the U.S.
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students who did not have regular access to a formal school system or whose education was interrupted by war, famine, and other traumatizing events prior to their arrival to the U.S.
We have organized evidence for teaching newcomers in mathematics into three sections: course placement, ideas for instruction, and collective responsibility.
Placement:
When newcomers first arrive, it is important to understand what they already know about mathematical concepts and procedures. Ideally someone who is familiar with the students’ community and speaks their language should conduct a diagnostic interview to assess students’ knowledge and understanding of mathematics.
Properly placing students and ensuring they have access to needed courses is essential to future success in school as well as for making a living in the United States.
Instruction:
Looking across the growing body of literature examining effective mathematics instructional practices for English learners, we provide the following principles for teaching mathematics with English Learners:
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English Learners should work on challenging mathematical tasks and be provided with support to access the tasks.
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English Learners need opportunities to communicate about mathematics using multiple modalities and resources (orally, writing, drawings, gestures, manipulatives and tools, home languages).
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English Learners need scaffolding strategies that help them engage in and make sense of mathematical tasks while developing their learning of English
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English Learners bring cultural, linguistic, and mathematical resources to the classroom
Building Community:
To nurture and learn from newcomer families and communities, multiple approaches are necessary. Educational leaders need to embrace the mathematics education of newcomers as a two-way process: teaching and learning from students and their families.
If you are interested in learning more about the best approaches for teaching mathematics to newcomers to the U.S. who are English learners, please check Brief#9.
If you are interested in learning more about the Answer Lab and reading more briefs, please check the Lab's website: