Essential Questions for Middle Grade Math: Middle Grade Math Progress

Grade 6: Students understand ratio concepts and use ratio reasoning to solve problems (Common Core State Standards for Mathematics).

Grade 6: Students use reasoning about multiplication and division to solve ratio and rate problems about quantities. Students solve a wide variety of problems involving ratios and rates (Common Core State Standards for Mathematics).

Grade 7: Analyze proportional relationships and use them to solve real-world and mathematical problems. (Common Core State Standards for Mathematics).

Grade 7: Students extend their understanding of ratios and develop understanding of proportionality to solve single- and multi-step problems. 

State adoption of rigorous math standards that prioritize depth, coherence and rigor

Grade 6: Students apply and extend previous understandings of multiplication and division to divide fractions by fractions. (Common Core State Standards for Mathematics).

Grade 6: Students compute fluently with multi-digit numbers and find common factors and multiples. (Common Core State Standards for Mathematics).

Grade 6: Students apply and extend previous understandings of numbers to the system of rational numbers. (Common Core State Standards for Mathematics).

Grade 6: students use the meaning of fractions, the meanings of multiplication and division, and the relationship between multiplication and division to understand and explain why the procedures for dividing fractions make sense. (Common Core State Standards for Mathematics).

Grade 7: Students apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. (Common Core State Standards for Mathematics).

Grade 7: Students develop a unified understanding of number, recognizing fractions, decimals (that have a finite or a repeating decimal representation), and percents as different representations of rational numbers. (Common Core State Standards for Mathematics).

Grade 8: Students know that there are numbers that are not rational, and approximate them by rational numbers. (Common Core State Standards for Mathematics).

Teaching Fractions: Help students understand why procedures for computations with fractions make sense. (What Works Clearinghouse, Developing Effective Fractions Instruction).

Teaching Fractions: 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. (What Works Clearinghouse, Developing Effective Fractions Instruction).

Teaching Fractions: Professional development programs should place a high priority on improving teachers’ understanding of fractions and of how to teach them. (What Works Clearinghouse, Developing Effective Fractions Instruction).

State adoption of rigorous math standards that prioritize depth, coherence and rigor 

Grade 6: Students apply and extend previous understandings of arithmetic to algebraic expressions. (Common Core State Standards for Mathematics).

Grade 6: Students reason about and solve one-variable equations and inequalities. (Common Core State Standards for Mathematics).

Grade 6: Students represent and analyze quantitative relationships between dependent and independent variables. (Common Core State Standards for Mathematics).

Grade 6: Students understand the use of variables in mathematical expressions. They write expressions and equations that correspond to given situations, evaluate expressions, and use expressions and formulas to solve problems. (Common Core State Standards for Mathematics).

Grade 7: Students use properties of operations to generate equivalent expressions.

Grade 7: Students solve real-life and mathematical problems using numerical and algebraic expressions and equations.

Grade 8: Students work with radicals and integer exponents (Common Core State Standards for Mathematics).

Grade 8: Students understand the connections between proportional relationships, lines, and linear equations (Common Core State Standards for Mathematics).

Grade 8: Students analyze and solve linear equations and pairs of simultaneous linear equations (Common Core State Standards for Mathematics).

Grade 8: Students define, evaluate, and compare functions (Common Core State Standards for Mathematics).

Grade 8: Students use functions to model relationships between quantities (Common Core State Standards for Mathematics).

Grade 8: Students use linear equations and systems of linear equations to represent, analyze, and solve a variety of problems.
(Common Core State Standards for Mathematics).

Grade 8: Students grasp the concept of a function as a rule that assigns to each input exactly one output. (Common Core State Standards for Mathematics).

Algebra I: Students are able to see structure in expressions. They interpret the structure of expressions and write expressions in equivalent forms to solve problems. (Common Core State Standards for Mathematics). 

Algebra I: Students perform arithmetic with polynomials and rational expressions. They perform arithmetic operations on polynomials, understand the relationship between zero and factors of polynomials, use polynomial identities to solve problems, and rewrite rational expressions. (Common Core State Standards for Mathematics). 

Algebra I: Students create equations that describe numbers or relationships

Algebra I: Students can reason with equations and inequalities. They understand solving equations as a process of reasoning and explain the reasoning, solve equations and inequalities in one variable, solve systems of equations, and represent and solve equations and inequalities graphically. (Common Core State Standards for Mathematics). 

State adoption of rigorous math standards that prioritize depth, coherence and rigor 

Grade 6: Students solve real-world and mathematical problems involving area, surface area, and volume. (Common Core State Standards for Mathematics).

Grade 6: Students build on their work with area in elementary school by reasoning about relationships among shapes to determine area, surface area, and volume. (Common Core State Standards for Mathematics).

Grade 7: Draw, construct and describe geometrical figures and describe the relationships between them. (Common Core State Standards for Mathematics).

Grade 7: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. (Common Core State Standards for Mathematics).

Grade 7: Students continue their work with area from Grade 6, solving problems involving the area and circumference of a circle and surface area of three-dimensional objects. (Common Core State Standards for Mathematics).

Grade 8: Students understand and apply the Pythagorean Theorem. (Common Core State Standards for Mathematics).

Grade 8: Students solve real-world and mathematical problems involving volume of cylinders, cones and spheres. (Common Core State Standards for Mathematics).

Grade 8: Students use ideas about distance and angles, how they behave under translations, rotations, reflections, and dilations, and ideas about congruence and similarity to describe and analyze two-dimensional figures and to solve problems. (Common Core State Standards for Mathematics).

State adoption of rigorous math standards that prioritize depth, coherence and rigor 

Grade 6: Students develop understanding of statistical variability. (Common Core State Standards for Mathematics).

Grade 6: Students summarize and describe distributions. (Common Core State Standards for Mathematics).

Grade 6: Building on and reinforcing their understanding of number, students begin to develop their ability to think statistically. (Common Core State Standards for Mathematics).

Grade 7: Use random sampling to draw inferences about a population. (Common Core State Standards for Mathematics).

Grade 7: Draw informal comparative inferences about two populations. (Common Core State Standards for Mathematics).

Grade 7: Investigate chance processes and develop, use, and evaluate probability models. (Common Core State Standards for Mathematics).

Grade 7: Students build on their previous work with single data distributions to compare two data distributions and address questions. (Common Core State Standards for Mathematics).

Grade 8: Students investigate patterns of association in bivariate data. (Common Core State Standards for Mathematics).

State adoption of rigorous math standards that prioritize depth, coherence and rigor 

Students enjoy math. Students demonstrate interest, liking, or enjoyment of mathematics as well as affective reactions to mathematics. (Mathematica, High Quality Measures).

Students feel a sense of belonging. Students feel connected to the math learning content and activities and being an accepted, respected, and valued math learner. (Mathematica, High Quality Measures).

Students see the value and importance of math. A student’s perception about the importance of doing well on mathematics and usefulness of mathematics for many aspects of daily life or fulfilling future goals (Mathematica, High Quality Measures).

Students demonstrate self-efficacy and confidence. A student’s perception of their ability to successfully complete a specific math task, which can vary by task. Math confidence is a student’s global assessment of their math ability (Mathematica, High Quality Measures).

Students demonstrate a growth mindset. A student’s belief that math abilities can be developed and improved through hard work, practice, good strategies, and input from others (as opposed to the belief that math abilities are fixed, stable, and unable to change) (Mathematica, High Quality Measures).

Students demonstrate an interest in math education and career. A student’s interest in using and pursuing math beyond the classroom in their future education and career (Mathematica, High Quality Measures).

Students express interest in the pursuit of STEM education and career (Mathematica, High Quality Measures).

Use visual representations to illustrate math concepts. Students can benefit from exploring math concepts through the use of visual representations, such as number lines, diagrams, and percent bars (IES, Strategies to engage students and transform the middle school math experience).

Teachers can use visual representations, such as manipulatives and area models, to help students understand core concepts about computational procedures related to fractions and why they work (IES, Strategies to engage students and transform the middle school math experience).

Combining visual representations with concrete representations, such as hands-on manipulatives, also can help students transition to more abstract representations of math concepts. For instance, teachers may use three-dimensional objects that can be touched and manipulated (i.e., base 10 blocks, fraction tiles) to make the underlying math concepts more visible (IES, Strategies to engage students and transform the middle school math experience).

Use real-life connections to give meaning to word problems. This strategy can help students understand abstract math processes, such as fractions and other rational number concepts (IES, Strategies to engage students and transform the middle school math experience).

Connecting instruction to everyday experiences is a strategy to help students master more complex math concepts. Teachers can engage students by presenting math problems with real-world contexts that are familiar and meaningful to them (IES, Strategies to engage students and transform the middle school math experience).

Use student discussion to build math engagement and understanding. (IES, Strategies to engage students and transform the middle school math experience).

Create space for students to reflect on their problem-solving process. Small-group activities can allow students to articulate the process they used to solve a problem and the reasoning for each step. By engaging with peers to share, compare, and discuss their approaches to solving problems, students build skills in communicating their thinking and learn new approaches to solving problems. (IES, Strategies to engage students and transform the middle school math experience).

Encouraging students to use clear and concise mathematical language in verbal and written explanations can help students build deeper understandings of math concepts and gives teachers an opportunity to check for understanding. (IES, Strategies to engage students and transform the middle school math experience).

Use computational thinking to build confidence in math. Computational thinking refers to problem-solving strategies that help students approach unfamiliar problems. These strategies encourage student inquiry and emphasize understanding concepts instead of memorizing formulas to deepen mathematical learning. By providing middle school students with concrete strategies for approaching math problems, teachers can help build students’ confidence in and increase their engagement with math. (IES, Strategies to engage students and transform the middle school math experience).

Engagement and achievement through Computational Thinking (ENACT) program in Milwaukee Public Schools (Institute of Education Sciences).

Teachers should explicitly teach students that academic abilities are expandable and improvable in order to enhance girls’ beliefs about their abilities. Students who view their cognitive abilities as fixed from birth or unchangeable are more likely to experience decreased confidence and performance when faced with difficulties or setbacks. Students who are more confident about their abilities in math and science are more likely to choose elective math and science courses in high school and more likely to select math and science-related college majors and careers. (What Works Clearinghouse, Encouraging Girls in Math and Science).

Teachers encourage students to view intelligence and mathematical ability as qualities that can be developed through effort and perseverance. Research indicates that when teachers adopt a growth mindset, student achievement improves, particularly among girls, English language learners, and economically disadvantaged students. Sharing neuroscience findings about brain plasticity and emphasizing that mistakes are opportunities for learning can help students embrace challenges and persist through difficulties (Crawford, 2018).

Teach students that working hard to learn new knowledge leads to improved performance. (What Works Clearinghouse, Encouraging Girls in Math and Science).

Remind students that the mind grows stronger with use and that over time and with continued effort, understanding the material will get easier. (What Works Clearinghouse, Encouraging Girls in Math and Science).

Teachers should provide students with prescriptive, informational feedback regarding their performance. Prescriptive, informational feedback focuses on strategies, effort, and the process of learning (e.g., identifying gains in children’s use of particular strategies or specific errors in problem solving). Such feedback enhances students’ beliefs about their abilities, typically improves persistence, and improves performance on tasks. (What Works Clearinghouse, Encouraging Girls in Math and Science).

Provide students with feedback that focuses on strategies used during learning, as opposed to simply telling them whether they got an answer correct. This strategy encourages students to correct misunderstandings and learn from mistakes. (What Works Clearinghouse, Encouraging Girls in Math and Science).

Provide students with positive feedback about the effort they expended on solving a difficult problem or completing other work related to their performance. (What Works Clearinghouse, Encouraging Girls in Math and Science).

Avoid using general praise, such as “good job,” when providing feedback to individual students or an entire class. (What Works Clearinghouse, Encouraging Girls in Math and Science).

Make sure that there are multiple opportunities for students to receive feedback on their performance. (What Works Clearinghouse, Encouraging Girls in Math and Science).

Teachers should expose girls to female role models who have achieved in math or science in order to promote positive beliefs regarding women’s abilities in math and science. Even in elementary school, girls are aware of the stereotype that men are better in math and science than women are. Exposing girls to female role models (e.g., through biographies, guest speakers, or tutoring by older female students) can invalidate these stereotypes. (What Works Clearinghouse, Encouraging Girls in Math and Science).

Invite older girls and women who have succeeded in math- or science-related courses and professions to be guest speakers or tutors in your class. (What Works Clearinghouse, Encouraging Girls in Math and Science).

Assign biographical readings about women scientists, mathematicians and engineers, as part of students’ assignments (What Works Clearinghouse, Encouraging Girls in Math and Science).

Call attention to current events highlighting the achievements of women in math or science. (What Works Clearinghouse, Encouraging Girls in Math and Science).

When talking about potential careers, make students aware of the numbers of women who receive advanced degrees in math- and science-related disciplines. (What Works Clearinghouse, Encouraging Girls in Math and Science).

Provide girls and young women with information about mentoring programs designed to support students who are interested in mathematics and science. (What Works Clearinghouse, Encouraging Girls in Math and Science).

Encourage parents to take an active role in providing opportunities for girls to be exposed to women working in the fields of math and science. (What Works Clearinghouse, Encouraging Girls in Math and Science).

Create a classroom environment that sparks initial curiosity and fosters long-term interest in math and science. Teachers can foster girls’ long-term interest in math and science by choosing activities connecting math and science activities to careers in ways that do not reinforce existing gender stereotypes and choosing activities that spark initial curiosity about math and science content. (What Works Clearinghouse, Encouraging Girls in Math and Science).

Embed mathematics word problems and science activities in contexts that are interesting to both boys and girls. (What Works Clearinghouse, Encouraging Girls in Math and Science).

Provide students with access to rich, engaging relevant informational and narrative texts as they participate in classroom science investigations. (What Works Clearinghouse, Encouraging Girls in Math and Science).

Capitalize on novelty to spark initial interest. That is, use project-based learning, group work, innovative tasks, and technology to stir interest in a topic. (What Works Clearinghouse, Encouraging Girls in Math and Science).

Encourage middle and high school students to examine their beliefs about which careers are typically female-oriented and which are typically male-oriented. Encourage these students to learn more about careers that are interesting to them but that they believe employ more members of the opposite gender. (What Works Clearinghouse, Encouraging Girls in Math and Science).

Connect mathematics and science activities to careers in ways that do not reinforce existing gender stereotypes of these careers. (What Works Clearinghouse, Encouraging Girls in Math and Science).

Teachers should provide opportunities for students to engage in spatial skills training. Spatial skills training is associated with performance in mathematics and science. (What Works Clearinghouse, Encouraging Girls in Math and Science).

Recognize that children may not automatically recognize when spatial strategies can be used to solve problems and that girls are less likely to use spatial strategies than boys. Teach students to mentally image and draw spatial displays in response to mathematics and science problems. (What Works Clearinghouse, Encouraging Girls in Math and Science).

Require students to answer mathematics and science problems using both verbal responses and spatial displays. (What Works Clearinghouse, Encouraging Girls in Math and Science).

Provide opportunities for specific training in spatial skills such as mental rotation of images, spatial perspective, and embedded figures. (What Works Clearinghouse, Encouraging Girls in Math and Science).

Regularly assess students’ perception of math and their ability to solve challenging problems

Number Talks are a 10-15 minute mental math routine created by Ruth Parker and Kathy Richardson in the early 1990s to engage students in meaningful mathematical discourse and sense-making as well as transform the culture of the classroom to one of inquiry and curiosity. (Mathematics Education Collaborative).

Boost participation & gauge understanding with tech-enhanced questions. Offer students the choice to respond to closed-ended questions using traditional thumbs-up/thumbs-down gestures, or leverage technology with online polls or interactive whiteboards. Embrace technology and use online polls or interactive whiteboards to encourage participation in closed-ended questions. This allows everyone to respond anonymously, fostering inclusivity and reducing student anxiety. Bonus: Real-time data visualization on these platforms can give you immediate feedback on student understanding, allowing you to adjust your lesson plan as needed. (National Council of Teachers of Mathematics).

Make math fun and reflective. Games and activities are a fantastic way to engage students in math. But to maximize learning, take it a step further! After the game, incorporate a “thinking reflection” activity. Ask powerful questions that prompt students to explain their reasoning and problem-solving strategies. (National Council of Teachers of Mathematics).

Emphasize engagement and productive struggle in learning. Base the success of your lessons on the extent of students’ engagement with ideas rather than their immediate happiness. Encourage your students to embrace and navigate the struggle inherent in the learning process. (National Council of Teachers of Mathematics).

A key component of the district’s vision for excellent math instruction is fostering a growth mindset and building students’ confidence in math.

The percentage of eighth graders scoring proficient or higher on their state’s math assessment. If eighth-grade scores are unavailable, we suggest using scores from seventh grade, or sixth grade if seventh is not available. Data should also be disaggregated by student gender, race, ethnicity, disability status, homeless enrolled status, foster care status, and economic status.(StriveTogether, Cradle-to-Career Outcomes Data Guides: Middle Grade Math).

Percent of 4th and 8th graders proficient in reading and math on NAEP. (Council of the Great City Schools).

Algebra I completion rates for credit by grade 9. (Council of the Great City Schools).

Students that completed Algebra I or equivalent in seventh, eighth, or ninth grade disaggregated by gender, race, ethnicity, disability status and economic status. (Council of the Great City Schools).

Eighth grade math achievement on NAEP (National Assessment of Educational Progress) in the most recent year, disaggregated by gender, race, ethnicity, disability status, language status, and economic status. (Council of the Great City Schools).

Trends in eighth grade math achievement on NAEP (National Assessment of Educational Progress) over time, disaggregated by gender, race, ethnicity, disability status, language status, and economic status. (Council of the Great City Schools).

Lessons should start with checks for understanding. Teachers can figure out what skills and understandings are prerequisites for the new concept they’re starting to introduce, and then give students a couple of questions that would allow them to show their knowledge—or demonstrate that they have unfinished learning. Then, teachers can develop a task or mini-lesson to shore up that prerequisite skill, and make explicit its connection to the new learning. For example, teachers could review the basics of linear functions and how to plot them on a graph right before introducing slope-intercept form. (EdWeek, Algebra 1 is a Turning Point).

Teachers check for understanding using targeted, just-in-time support instead of remediation (i.e. having students repeat entire units from 8th grade math before moving on to Algebra 1 content). Remediation can be demotivating and can push students who are struggling further behind by limiting their access to grade-level content. (EdWeek, Algebra 1 is a Turning Point).

Teachers can show multiple representations for new concepts, for example, drawing explicit connections between the way a linear function looks written as a mathematical expression, the way it looks as a graph, and real-world examples a student might encounter. (EdWeek, Algebra 1 is a Turning Point).

The number line doesn’t have to stay in 8th grade: Algebra teachers can continue to plot radicals, exponents, and fractions if students are having a hard time conceptualizing their magnitude. For example: The idea that the square root of 16 is the same as 4 is the same as 2 squared can feel really abstract to students, 
but plotting numbers like these at the same point on a number line can help them better understand. (EdWeek, Algebra 1 is a Turning Point).

Teachers can be explicit about the connections between word problems and the equations meant to solve them, teaching solution methods for different types of problems. (EdWeek, Algebra 1 is a Turning Point).

Group practice allows teachers to listen to students’ thought processes. Teachers can listen in to group conversations—asking guiding questions to explore a student’s thinking, reinforcing the use of mathematical language, and addressing any misunderstandings in the moment. (EdWeek, Algebra 1 is a Turning Point).

In math, a focus on relationship building and social-emotional learning isn’t an extra; it’s integral to students’ academic success. If students don’t feel comfortable saying they don’t understand, if they aren’t willing to tackle a challenging problem or share their ideas in a group, then they won’t be able to get the practice they need to achieve fluency, or ask the questions that can lead to deep conceptual understanding. (EdWeek, Algebra 1 is a Turning Point).

Give all students access to grade-level content. Helping students master challenging work with appropriate support keeps them on track, so that they’re prepared for higher level math and can succeed in the courses they need for graduation. And it can also build their confidence. (EdWeek, Algebra 1 is a Turning Point).

The Local Education Agency (LEA) aligns curricular selection, professional learning and instructional support (like coaching) to rigorous math standards

Middle school is a critical time to capture students’ interest in math. Middle school math teachers can boost students’ engagement and confidence in math by using student-focused instructional strategies and teaching computational thinking skills. When students learn to believe in their own math skills at school, they carry that confidence in math and in other STEM (science, technology, engineering, and math) topics for a lifetime. (IES, ENACT Math).

Teachers use student-focused instructional strategies Student-focused instructional strategies help all students see themselves as important contributors to the classroom community, which in turn supports students’ self-confidence with math and builds student engagement in math. (IES, ENACT Math).

Teachers provide opportunities to use computational thinking skills Computational thinking skills are problem-solving strategies that students learn to help them approach unfamiliar problems. These strategies encourage student inquiry and focus on deepening mathematical understanding of concepts instead of memorizing rules. These strategies also help students develop skills and mindsets that unlock pathways into high-wage, in-demand fields. (IES, ENACT Math).

Teachers instruct students in computational thinking skills: Pattern recognition (i.e. looking for ways that problems or situations are similar or different); Abstraction (i.e. identifying and representing the important information in a problem or situation); Decomposition (i.e. breaking a complex problem into smaller parts that are easier to address); Debugging (i.e. finding and fixing mistakes to improve one’s work); Algorithms (i.e. developing and using systematic, step-by-step approaches to problems). (IES, ENACT Math).

Teachers employ student-focused instructional strategies Connecting math problems to real situations in students’ lives; Encouraging students to try different strategies for problem solving; Discussing more than one way to solve a problem; Communicating that students are bringing valuable ideas and work to the classroom; Providing opportunities for raising student voice in every lesson. (IES, ENACT Math).

Teaching Computational Thinking Skills: Modeling using computational thinking skills for students; Creating opportunities for students to use computational thinking; Building students’ confidence in using computational thinking; Helping students make their thinking visible. (IES, ENACT Math).

State adoption of rigorous math standards that prioritize depth, coherence and rigor 

The Local Education Agency (LEA) adopts rigorous math standards that prioritize depth, coherence and rigor.

One increasingly popular approach to improving students’ math skills is “algebra for all,” which encourages more students to take algebra and at earlier ages. The best study of this approach, using evidence from Charlotte, North Carolina (see “Solving America’s Math Problem,” Winter 2013), shows that pushing students into course work for which they are ill prepared actually harms their subsequent academic achievement. (Education Next, A Double Dose of Algebra).

A potentially promising alternative to “algebra for all” is “double-dose” algebra, in which struggling students are given twice as much instructional time as they would normally receive. Researchers found positive and substantial longer-run impacts of double-dose algebra on college entrance exam scores, high school graduation rates, and college enrollment rates, suggesting that the policy had significant benefits that were not easily observable in the first couple of years of its existence. The benefits of double-dose algebra were largest for students with decent math skills but below-average reading skills, perhaps because the intervention focused on written expression of mathematical concepts. (Education Next, A Double Dose of Algebra).

Researchers found that ninth graders assigned to “double-dose algebra”—an algebra class plus a second class designed to bolster algebra skills—were more likely to stay in, and complete, college compared to similar students who did not take double-dose algebra. However, when students were placed in double-dose classes with much-lower-skilled peers the program had no effect. (PNAS, Effects of double-dose algebra on college persistence and degree attainment).

Double-dose algebra shows real promise for helping median-skill students in Chicago neighborhood schools to gain math skills, take more college-preparatory math classes, achieve more years of schooling, and earn college degrees. The success of the double-dose approach is consistent with evidence of a similar successful intervention in college—offering a remedial course along with a core math course (e.g., statistics) to those who do not meet the minimum math requirement. (PNAS, Effects of double-dose algebra on college persistence and degree attainment).

In 2015, the California Legislature passed a new law-the California Mathematics Placement Act to address widespread concern over equity in the math placement process. The law is aimed at improving the measurement of student performance (creating a more fair, transparent, and objective math placement process) in order to move more students successfully through the high school curriculum. The law requires districts to include certain practices, such as relying on multiple objective measures in placement decisions, using student performance data to ensure equity and efficacy, and ensuring the consistency of placement policies between elementary and high school districts. (PPIC, Math Placement in California’s Public Schools).

Large numbers of students who took Algebra in eighth grade have often been required to repeat the course in high school, even though many were considered proficient on algebra tests, one California study found, noting that students of color were more likely to meet that fate. One possible explanation was that the majority of districts relied on parental requests, which could increase access to advanced math courses for more privileged students. As a result of these concerns, California legislators passed a law on math placement intended to address disparities as students transition from middle school to high school. (Just Equations, Math Misplacement).

Research on postsecondary placement may hold key lessons for K-12 schools. Postsecondary research has shown that placement reforms are most effective when paired with math pathway reforms. Even for students who aren’t fully prepared, evidence has demonstrated clearly that supporting them to succeed in college-level courses is a more effective way to boost math achievement than assigning them to remedial sequences. (Just Equations, Math Misplacement).

Numerous studies have demonstrated that far more students ultimately succeed in college-level math courses if they’re allowed to enroll in them and receive just-in-time support. Beginning in 2018, the 23-campus California State University system embarked on an extensive reform, eliminating the use of placement tests and banning remedial courses for entering students. In the past, one out of every 17 Latinx students and one out of every 11 African American students were “disenrolled” after failing remedial courses. Under the new policies, all entering students begin their math sequence at the college-level, though they may be referred to “corequisite” versions that provide just-in-time support. In its first year of implementation, college-level math courses were taken by eight times as many students who would have been deemed “not ready” in prior years. And the pass rate in those courses even went up slightly. In eliminating remedial courses and providing co-requisite support, CSU didn’t just change how it placed students, it also changed the math sequences themselves. (Just Equations, Math Misplacement).

A 2017 California law bars community colleges from placing students in remedial courses unless evidence shows that doing so will boost their success in college-level math. (And given what existing research says, there is rarely justification for placing students in remedial courses.) The law has led to significant increases in student enrollment in and passage of college-level math courses, across racial and ethnic groups, according to a recent report by the Public Policy Institute of California. However, the report also noted that equity gaps in math completion remain, particularly for Black students. (Just Equations, Math Misplacement).

Improving the transition between eighth and ninth grade ideally requires considering inequities in students’ middle school math opportunities, given that only some students have access to accelerated options, which too often predetermines their high school trajectories. As the postsecondary reforms illustrate, high schools need to focus not just on placement, but on the quality and variety of the math pathways students ultimately can pursue. (Just Equations, Math Misplacement).