Two Approaches to Grouping Students in Mixed-Ability Math Classes

            In this article in Mathematics Teacher, Cassandra Kinder and Corey Webel (University of Missouri/Kansas City) say decisions on how students are grouped in math classes “carry explicit and implicit assumptions about student capability, what it means to work together in mathematics, and the purpose of group work.” A common and well-intentioned practice is grouping students by math ability so that struggling students can get extra support and more-advanced students can take on additional challenges. 

            But there’s been strong pushback on ability grouping, and in 2020, the National Council of Teachers of Mathematics called on schools to stop the practice. “This sorting and ranking,” say Kinder and Webel, “has the potential to exacerbate inequality when policies create different-quality learning opportunities for ‘advanced’ groups and those who are ‘behind’ and need intervention. Students who are placed in ‘low’ groups suffer from lower-quality learning opportunities and are reinforced with negative narratives about their mathematical competence.” 

            With ability grouping “off the table,” ask Kinder and Webel, how should teachers handle classes with a wide range of math achievement? They describe two approaches:

• Hierarchical mixed-ability grouping – Standardized test scores are used to level students (for example high, medium-high, medium-low, and low), students are sorted into groups with a mix of levels, and students then work on grade-level problems, with the higher-achieving students helping their lower-achieving groupmates. There are obvious problems with this approach, say Kinder and Webel: (a) test scores decide who is more or less competent, which preserves ability labels; (b) students who are seen as more proficient are expected to explain the math to their peers; and (c) negative beliefs about math ability may be reinforced for students labeled as “low.”  In short, say the authors, mixed-ability grouping has the same disadvantages as straight ability grouping in that it “supports a general narrative, or story, that sees mathematical ability as innate, mathematics learning as linear, and mathematical competence as the ability to get correct answers without making mistakes.”

• Non-hierarchical grouping – Students are grouped in a variety of ways (working with partners, in small groups, or individually) based on how they solved an initial problem. The teacher:
• Selects a rich task that can be solved in a variety of ways; 
• Provides students individual time to solve the problem; 
• Observes students’ strategies, noting similarities and differences; 
• Groups students keeping the lesson’s math objective in mind. 

The teacher might group students who used a similar strategy and ask them to refine it, or group students who used different strategies and ask them to make connections and debate which is best. Both ways, say Kinder and Webel, “foreground students’ mathematical reasoning and support collaboration and collective sense-making.” The teacher then follows up with whole-class        discussion of how students thought about and solved the problem. 

            Non-hierarchical grouping has significant advantages, the authors believe. It “allows the creation of student groups with targeted support in mind, but those groups are based on the assumption that all students have valuable ideas to contribute to a shared understanding… This approach encourages recognizing differences without describing some students as lacking mathematical understanding. This advances the (productive) narrative that all students are capable and have valuable mathematical ideas.”

“Beyond Mixed-Ability Grouping: What to Consider?” by Cassandra Kinder and Corey Webel in Mathematics Teacher, April 2025 (Vol. 118, #4, pp. 273-279); the authors can be reached at c.kinder@umkc.edu and WebelCM@missouri.edu.

Please Note: This summary is reprinted with permission from issue #1084 of The Marshall Memo, an excellent resource for educators.

Resources for Financial Literacy Education

            In this article in Social Education, Scott Niederjohn and Billie Kowalke (Concordia University Wisconsin) and Kim Holder (University of Tennessee/Chattanooga) make the case for personal finance education in secondary schools and list key topics that should be included: income and careers, money management, credit and debt, saving and investment, risk management and insurance, financial decision-making, consumer protection, and taxes. They suggest these online resources: 

• Council on Economic Education (CEE) – https://www.councilforeconed.org
• Foundation for Economic Education (FEE) – https://fee.org 
• JumpStart Coalition for Personal Financial Literacy – https://www.jumpstart.org 
• Junior Achievement (JA) – https://jausa.ja.org 
• Next Gen Personal Finance (NGPF) – https://www.ngpf.org 

 “The State of Personal Finance Education in the U.S.” by Scott Niederjohn, Kim Holder, and Billie Kowalke in Social Education, March/April 2025 (Vol. 89, #2, pp. 91-96)

Please Note: This summary is reprinted with permission from issue #1083 of The Marshall Memo, an excellent resource for educators.

Six Misconceptions About Psychological Safety

            In this Harvard Business Review article, Amy Edmondson (Harvard Business School) and Michaela Kerrissey (Harvard T.H. Chan School of Public Health) say psychological safety has been widely recognized as a key factor in teams’ creativity, morale, and performance. But a number of distortions and misconceptions have led critics to say it needs to be tossed out as another flawed management fad. Edmondson and Kerrissey address these one at a time: 

• Misconception #1: Psychological safety means being nice. The idea is that you shouldn’t say what you really think unless it’s positive. But safety and comfort are not the same thing. “Wanting to be nice, people avoid being honest and, whether they realize it or not, collude in producing ignorance and mediocrity,” say Edmondson and Kerrissey. “Teams that don’t surface hard truths perform worse than those that do.” Effective teams give permission to be candid, take interpersonal risks, ask questions, disagree, admit mistakes, and distinguish between being nice and being kind. “Nice is the easy way out of a difficult conversation,” say the authors. “Kind is being respectful, caring, and honest.” 
• Misconception #2: Psychological safety means getting your way. A healthcare executive said a colleague didn’t support his idea in a meeting and that made him feel psychologically unsafe. What nonsense, say Edmondson and Kerrissey. Leaders need to hear what people think and not be emotionally fragile. “It’s helpful to think of psychological safety not as a gift for one participant but rather as an environment for the whole team.” Of course leaders shouldn’t tolerate bullying, harassment, disrespect, or unethical conduct. 
• Misconception #3: Psychological safety means job security. When Google laid off 12,000 people in 2023, one employee stood up at a town hall meeting and said this went against the company’s commitment to psychological safety. But that policy didn’t guarantee there wouldn’t be layoffs, say Edmondson and Kerrissey. In fact, by feeling safe to stand up and speak out, the employee was validating the policy.
• Misconception #4: Psychological safety will undermine performance. Some leaders believe embracing psychological safety will make it difficult to address weaknesses and hold people accountable. But this is a false dichotomy, say the authors; top performance requires both high standards and psychological safety. Leaders need to cultivate a climate in which candor is the norm; otherwise, “people hide information to save face or to be agreeable or both. And teams fall easily into groupthink – where members don’t want to disrupt what they erroneously assume is a consensus.” 
• Misconception #5: Psychological safety should be a mandated policy. “We can’t mandate psychological safety any more than we can mandate things like trust and motivation,” say Edmondson and Kerrissey. “You can’t pull a lever and make it happen.” In fact, trying to mandate psychological safety is likely to result in people keeping leaders in the dark about things they don’t want to hear. Psychological safety is built in a group’s interactions, and is fostered when leaders consciously use three tools: messaging honestly about challenges the team faces; modeling being a good listener, asking good questions, and showing that it’s okay not to know all the answers; and mentoring colleagues with feedback on group norms.
• Misconception #6: Psychological safety requires a top-down approach. “It’s true that what leaders do matters,” say Edmondson and Kerrissey. “But ultimately, psychological safety is built by everyone – at all levels… In small but important ways, everyone influences the environment. Anyone can call attention to the need for input or ask questions to draw others out, and anyone can respond to others in productive rather than punitive ways… By showing interest in other people’s ideas and concerns, team members can reinforce their peers’ voices and help establish a productive learning climate.” 

            Edmondson and Kerrissey conclude with suggestions on how to build on these insights to foster and reinforce a team’s psychological safety: 

• Frequently say what your team is trying to accomplish, why it matters, and how everyone plays a key role. 
• Improve the quality of team conversations. “That entails asking good questions, listening intently, and pushing for closure,” they say. 
• Institute structures for sharing reflections and tracking progress. “What matters,” say Edmondson and Kerrissey, “is the discipline of offering honest appraisals of what’s going on with the work (performance against goals) and of the team climate and quality of interactions.” 

 “What People Get Wrong About Psychological Safety” by Amy Edmondson and Michaela Kerrissey in Harvard Business Review, May/June 2025

Please Note: This summary is reprinted with permission from issue #1083 of The Marshall Memo, an excellent resource for educators.

Different Feedback Strategies to Meet Individual Teachers' Needs

            In The Learning Professional, author/leadership coach Keith Young and district director of student services Judith Mendoza Jimenez suggest three levels of feedback based on teachers’ needs and levels of experience: rapid response, moderate engagement, and expansive intervention. 

• Rapid response – Many classroom issues can be addressed quickly, say Young and Jimenez, “without the need for extended sit-down feedback sessions.” For example, during a classroom visit, an observer might prompt the teacher to check for understanding or focus on disengaged students by whispering to the teacher, handing them a note, or sending a text. “I didn’t have to wait until the end of the day to learn what the students needed,” said a teacher who appreciated the quick feedback. [Here’s a detailed discussion of real-time coaching.] 

            Another approach is having a brief feedback chat in the corridor immediately after an observation. An elementary principal found these informal conversations built rapport and helped teachers make minor instructional tweaks. Similarly, a district administrator observing a school’s faculty meeting pulled the principal aside and unobtrusively suggested a way to get input from reluctant colleagues. 

• Moderate engagement – “Some feedback needs more than a quick chat,” say Young and Jimenez, “structured enough to get into detail, yet flexible enough to fit into a busy school day.” Novice teachers might be asked to co-teach a lesson with a seasoned colleague, actively engaging with a new teaching idea without having to take full responsibility for the lesson, then debriefing afterward. Administrators might also orchestrate peer observation cycles to get teachers into each other’s classrooms and spread effective practices. 

            “It was powerful to see my colleague handle the same challenges I face – and to learn from their solutions,” said one teacher. “I also realized I need to plan my complex thinking questions in advance because improvising them during the lesson rarely worked for me.” 

            Another moderate engagement strategy is teachers recording videos of lessons and reviewing them afterward with an instructional coach. This is like athletic teams looking at game videos, say Young and Jimenez, “allowing educators to see missed opportunities, analyze strategies, and plan for improvement.” 

            For very proficient teachers who seldom need corrective feedback, the best approach might be to have them coach themselves based on rubrics, classroom videos, or an analysis of their students’ work. One experienced art teacher reviewed her students’ portfolios at the end of a semester and made a number of changes in pedagogy, lesson pacing, and scaffolding. 

• Expansive intervention – Longer, more in-depth coaching can help teachers develop new practices, improve student engagement, perhaps confront biases. An Arizona science department head engaged in a semester-long, twice-a-week coaching cycle with a novice teacher to plan lessons, observe classroom dynamics (especially student-led labs), and debrief after each classroom visit. “It wasn’t just about tweaking a lesson here or there,” said the teacher. “It was like a deep dive into everything – how I pressed my students, how I understood the standards, how I communicated during the lab, even how I handled their mistakes. I went from feeling overwhelmed to watching my students own their learning.” 

            Another idea is “ramble chats” – extended walk-and-talk conversations in which an instructional coach and an effective teacher talk informally about curriculum, pedagogy, and student learning – without the constraints of a formal agenda. “This type of feedback,” say Young and Jimenez, “proves well-suited to teachers who are either highly experienced or highly self-reflective or, ideally, both. The open-ended and time-consuming nature of these conversations fosters deep reflection and creative problem solving.” 

            The goal of this kind of differentiated support, conclude Young and Jimenez: “a professional learning culture where every individual feels seen, supported, and inspired to make changes – from quick adjustments to deep transformations. That kind of continuous improvement is possible when we reimagine feedback as not just a tool for addressing deficiencies, but as a catalyst for growth, innovation, and empowerment.”  

“3 Essential Feedback Categories for Inspiring Educator Growth” by Keith Young and Judith Mendoza Jimenez in The Learning Professional, February 2025 (Vol. 46, #1, pp. 34-37)

Please Note: This summary is reprinted with permission from issue #1079 of The Marshall Memo, an excellent resource for educators.

Graphic Novels About Immigration

             In School Library Journal, Brigid Alverson recommends these graphic novels on the joys and challenges of the immigration experience: 

• Speak Up, Santiago! A Hillside Valley Graphic Novel by Julie Anta, illustrated by Gabi Mendez, grade 3-7
• Uprooted: A Memoir About What Happens When Your Family Moves Back by Ruth Chan, grade 3-
• How to Draw a Secret by Cindy Chang, grade 3-7
• History Comics: Ellis Island, Immigration, and the American Dream by Felipe Galindo Feggo, illustrated by Tait Howard, grade 4-9
• Just Another Story: A Graphic Migration Account by Ernesto Saade, grade 7 and up
• This Land Is Our Land: A Blue Beetle Story by Julio Anta, illustrated by Jacoby Salcedo, grade 8-12
• Unaccompanied: Stories of Brave Teenagers Seeking Asylum by Tracy White, grade 10 and up

 “Coming Home” by Brigid Alverson in School Library Journal, March 2025 (Vol. 71, #3, pp. 47-49)

Please Note: This summary is reprinted with permission from issue #1078 of The Marshall Memo, an excellent resource for educators.

How Instructional Leadership Teams Can Catalyze Effective Practices

(Originally titled “How Teacher Teams Can Transform School Practices”) 

            “The time is ripe for faculty-wide conversations around strengthening instructional practice,” says New York City principal M-J Mercanti-Anthony in Educational Leadership. This is important, he believes, because many teachers are unaware of recent research findings and continue to use outmoded and, in some cases, discredited practices with their students. 

            Mercanti-Anthony lists four reasons why the best thinking on teaching and learning is not being implemented more widely: 

• Teacher and administrator training programs have gaps, especially in cognitive science. 
• Educators’ egos are caught up in their work, and feedback can be taken personally.
• Schools’ egg-crate culture often prevents highly effective practices from being shared.
• Many teachers are wise to the “faux discovery” process: they’re asked to try out a new practice and gather data, only to learn they’re being manipulated into adopting it. 

How can principals address these impediments and foster sincere, productive discussion of best practices? 

            Mercanti-Anthony believes the key is good use of a school’s instructional leadership team (ILT). Members should be recruited based on their capacity and willingness to explore the research, take a fresh look at teaching and learning in the school, and commit to weekly meetings. It must be clear that other groups in the school will deal with discipline policies, the bell schedule, planning school events, and test data, allowing the ILT to be laser-focused on instruction. A step-by-step roll-out of an ILT’s work over time:

• Studying the science of how people learn – Mercanti-Anthony suggests that the ILT spend several months exploring often-untapped research findings, including:
• Retrieval practice;
• Spaced review;
• Interleaving;
• Connecting abstract concepts with concrete examples;
• Building metacognitive skills so students self-monitor and learn from mistakes;
• Asking questions that get students thinking deeply and elaborating. 

During this exploration phase, some ILT members may begin experimenting with new ideas in their classrooms.  

• Choosing one strategy – The ILT organically chooses a strategy to introduce to the faculty – for example, putting retrieval practice to work with the “brain dump” plan. “ILTs should resist the temptation of introducing more than one strategy at a time,” says Mercanti-Anthony. 

• Taking the practice to scale – To get the idea widely adopted, the key is peer-to-peer discussion groups, lesson study teams, and teachers visiting classrooms trying the new practice. 

• Repeating – Once the initial strategy is launched, the ILT chooses another, studies it in depth, and follows the same dissemination strategy. 

            If the ILT follows these steps, says Mercanti-Anthony, colleagues won’t see subsequent ideas as “one more thing.” He sees this as a multi-year process, “providing resources, suggestions, and assistance in keeping the process moving forward.” 

“How Teacher Teams Can Transform School Practices” by M-J Mercanti-Anthony in Educational Leadership, March 2025 (Vol. 82, #6, pp. 28-34)

Please Note: This summary is reprinted with permission from issue #1078 of The Marshall Memo, an excellent resource for educators.

The Art and Science of Interactive Readalouds

 (Originally titled “A Better Way to Read Aloud”) 

            In this Educational Leadership article, Douglas Fisher and Nancy Frey (San Diego State University and Health Sciences High and Middle College) say that reading aloud to students has great potential for learning – if it’s done well. Here are the key factors they noticed when they observed and interviewed 25 highly effective grade 3-8 teachers: 

• A well-chosen text that will capture students’ interest and address a learning need; 
• Preparing and practicing beforehand to formulate questions and be able to read fluently;
• Establishing a clear purpose with students – a concept or skill they will learn;
• Reading with accuracy, correct pronunciation, appropriate rate, fluency, expression, phrasing, and enthusiasm;
• Engaging students with facial expressions and hand gestures;
• Discussing the text before, during, and after the readaloud – ideas, the author’s style and choice of words, key vocabulary, predictions;
• Connecting the text to reading and writing that students are doing – for example, writing a letter to one of the characters in the story or comparing the text to something else students have read. 

For primary-grade students, Fisher and Frey suggest the additional element of print referencing – drawing attention to letters, words, punctuation, and print concepts like left-to-right directionality. 

 “A Better Way to Read Aloud” by Douglas Fisher and Nancy Frey in Educational Leadership, March 2025 (Vol. 82, #6, pp. 10-11)

Please Note: This summary is reprinted with permission from issue #1077 of The Marshall Memo, an excellent resource for educators.