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Thank You!

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Thank you! It has been a great honor and a humbling experience to serve as president of the National Council of Teachers of Mathematics. As I said in my first president’s message, NCTM is its members—a community of professionals committed to ensuring that each and every student learns significant mathematics in equitable environments. I believe that statement more firmly today than ever before. I have had the wonderful opportunity, while attending NCTM conferences and Affiliate meetings, to meet many of you. Every time I do, I come away energized and encouraged for the future of our profession after witnessing not only your positive energy and commitment to ...
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After my son had collected candy at a parade he wanted to eat some.  I told him he could choose one thing from his bag. He chose a clear zipper bag with 2 packages of Starburst in it.  Each package contained 2 Starburst. He chose one, but he actually got to eat 4 candies. If you are familiar with Christopher Danielson ’s work, you have most likely had conversations around units and the variety of units that can exist in one situation, like the example above.  If not, I will discuss his book How Many and the hashtag #unitchat in a future post. It wasn’t until the past few years, however, that I realized there is more to it than just ...
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As a Learning Support teacher, I look for opportunities to connect student thinking to in order to design small group lessons, and adjust my instruction based on their thinking. My role as a Grade 1 Learning Support is typically to push-in to support three classes. At times, however, we decide as a team to identify a small group for short-term intervention work. We did just that on our current unit: Basic Facts & Place Value. Keeping the two Mathematics Teaching Practices highlighted below in mind ( Principles to Actions ), I started our small group work with an exploration. Elicit and use evidence of student thinking. Effective teaching of ...
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As part of our series on implementing a Badging system , we've explored sample tasks and student responses centered around Math, Equity, and Culture and Data Representation .  Because the main purpose of these badges is to encourage middle school students to "fall in love" with mathematics, in the final segment I want to examine a topic strand that makes it easy for students to love and appreciate math:  Math and Beauty .    The name of this topic strand is purposefully vague.  Math and Beauty topics could center around the beauty of mathematics in nature.  They could also represent artists' attempts to make mathematical beauty apparent in their creations.  ...
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So far in this series I've introduced you to the concept of "Badges" (what I call my free-choice activities that are designed to engage kids in how mathematical concepts are used outside of a math classroom) and we've explored one of the topics within my Badging system, activities centered around Math, Equity, and Culture .  Today, we will investigate another topic strand, focused on Data Analysis and Representation . I worry that too often in Middle Grades we focus on Algebra preparation so students are ready for the Algebra -> Trigonometry -> AP Calculus progression that we (and their college counselors...) hope to be their high school experience.  ...
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Next month at our Annual Meeting in Washington, NCTM will release and have an enhanced conference strand on Catalyzing Change in High School Mathematics: Initiating Critical Conversations. I want to thank the writing team, particularly the chair Karen Graham, for bringing Catalyzing Change to publication. I also want to thank all the reviewers, many of whom saw multiple drafts, as well as the NCTM Publications staff who ensured the book was ready by the Annual Meeting. Member feedback was critical at every step of the process. Catalyzing Change seeks to initiate critical conversations around the following challenges: Explicitly broadening the purposes ...
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Too often students see the math that they're learning in school as disconnected from life, impotent to have real meaning and purpose outside of its own confines.  After my last introductory post on the reasons to implement a Badging system , I want to take you through a couple of opportunities I've given my students to see math work in a civic sense.  These badges I've collected fall under a heading I've entitled Math, Equity, and Culture and show mathematics used in powerful ways to those students interested in societal issues. First, I took an old ABC news article about the Electoral College written by mathematician John Allen Paulos and I asked ...
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By Evgeny Milyutin and Lisa Meyer Put yourself in a students’ shoes for a minute. Imagine that throughout your whole life, the only language you’ve heard or spoken is Spanish. You’re from a rural town in Honduras, the only home you know, and then at age six your family moved to the USA. Once there, you were signed up for 1s t grade at the local elementary school, and you were thrown right into an English-speaking classroom. While at school, you received some English language support, but what you heard all day long at school is English. Take another look, you used to love math class in Honduras; yet, in your American classroom you feel bored, exhausted ...
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I want my middle school students to be successful in mathematics, but I also want them to fall in love with mathematics.  Some students are naturally inclined to really enjoy "traditional" mathematics; they are efficient and accurate at arithmetic, easily notice patterns, or might enjoy trying to solve new problems that stretch their knowledge base.  Other students, however, don't feel that same connection to traditional school mathematics.  It might be due to a lack of success in past math classes or a familial disdain for mathematics passed on from their parents, but there exists in every middle school students who are not inclined to love the type of ...
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Why Teach Mathematics?

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As a teacher of mathematics, you have no doubt had multiple students ask what is actually a very complicated question: “Why do I have to learn this?” At one time or another, perhaps while grinding through a series of context-free symbolic manipulation exercises, nearly every one of us has struggled to provide our students with an answer they, and/or we, find satisfactory. But the student “why?” question raises an equally important, but less often-asked question: “Why do we teach math?” Francis Su, past president of the Mathematical Association of America, has argued that this is a very important question because how we answer it strongly influences who we ...
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My Favorite Routines

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Demonstrate kindness Challenge yourself and smile Learn from your mistakes What will I try differently this year? What went well last year? What didn’t go well? How can I get my students to understand ______ better? My personal reflections led to me to make changes in my teaching, such as asking my students to reflect often, revamping my assessment practices, and incorporating more activities focused on building empathy. After trying so many new ideas every year, I find there are a few that I revisit and establish as tradition in my classroom. I’m going to share with you my favorite activities I use to improve classroom culture and student learning. ...
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Calendar Time Must Die

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I spend a lot of time in early childhood classrooms, and, as the headline suggests, I have gotten to a point where I cannot sit through one more moment of Calendar Time. It is difficult to select what makes me most crazy about this practice: ● Is it that too often Calendar Time takes up prime instructional real estate -- those precious morning minutes when children are fresh and ready for a new day? ● Is it that PreK learners, who have been doing Calendar Time daily for months, still shout out every potential answer to the question “What day is it today?” ● Maybe it is the way so many children put their heads in their hands or turn to poke at their ...
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Gaining New Perspectives

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To build empathy Follow their thinking, not yours Be patient, listen Examine the dot card above (You may recognize this from Jo Boaler’s Week of Inspirational Math activities). How many dots do you see? How did you count them? Did you see the arrangement of five dots found on the face of a six-sided die with one additional dot on the left and right side? Did you see the outer six dots forming a hexagon with one dot in the middle? What does this activity teach us about how we think? Dot talks, along with number talks and pattern talks, demonstrate how students see and engage with images, words, and ideas differently. These routines ...
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Sometimes, even with the best-made plans, the research indicates that some students are forced off the path to mathematical success by structural or systemic barriers that exist in some schools (Jilk 2014). Two of these structural obstacles are student and teacher tracking. Student tracking is the placement of students into qualitatively different and in some cases dead-end mathematics course pathways. Student tracking is insidious because these dead-end pathways are not mathematically meaningful and do not prepare students for any continued study of mathematics. NCTM officially reframed its equity statement to focus on Access, Equity, and Empowerment, ...
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“It was fun to watch the "ah-ha" moments because you could see the connection they made through the successful problems they'd solved and their explanations.” - former 8th grade student. Even though my classes experience the same lesson, I often remind my students that they will each take something different away each day. Regardless of where their understanding is, I want students to understand how capable they all are in learning mathematics. To help students recognize their growth, I have them study their mistakes, analyze all their assessments at the end of each semester, and take reassessments to demonstrate their new understanding. In my ...
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In a previous blog , we outlined NCTM’s history of engaging the mathematics education community on issues at the intersections between culture and mathematics, as well as works critiquing school mathematics and mathematics education using critical theories. In a 2017 Journal for Research in Mathematics Education article, Dr. Luis Leyva highlighted the intersecting nature of whiteness and gender as contributing to racialized and gendered spaces that produce inequities in mathematics education. There is a significant body of research literature examining school mathematics as a political act that challenges the ways in which mathematics education is framed. ...
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Getting correct answers does not support conceptual understanding. We need to shift away from the practices of rewarding students whose learning style and personality are compatible with algorithms, following steps, and getting-answers. Getting answers does not support conceptual understanding - these students do not achieve true understanding or depth of knowledge on which they can build and connect ideas.   We need to build depth of knowledge that goes beyond answer-getting, as highlighted by Phil Daro ( http://serpmedia.org/daro-talks/ ). A student’s ability to memorize an algorithm and answer a question correctly does not indicate conceptual ...
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It always makes me sad when I go into primary grades classrooms during mathematics and see slumped shoulders, bowed heads, and even tears. In many ways, I find it entirely improbable that as a society we’ve been able to put together two things as inherently joyful as children and mathematics and create shockingly large amounts of boredom and misery. In some ways, this is really quite an achievement. My commitment to bringing joy into mathematics classrooms comes from two places. The first is a recognition that comes out of theories of learning that children learn best when they are engaged and are not stressed. For example, we know that not only do timed ...
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“Through learning how to lead and guide someone else's learning I found that I had a lot to learn as well, so I think my knowledge and understanding of how to teach, listen, ask questions to help make connections, and be patient all while working with a group or team (more than one person at a time) has improved.” - Former 8th grade student. Reflections are powerful tools for personal, social, and academic development. I ask my students to reflect on their learning and behavior at least once a week. By reflecting often, they strengthen their capacity to identify their strengths, acknowledge their areas for growth, plan ahead, develop empathy, and improve ...
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One of the questions I am frequently asked goes something like this: “What do you think about acceleration?” The question is often asked in the context of teachers working with parents who want their child to skip grade level work or entire courses so they can get into the next grade or course more quickly. The parental goal more often than not is to ensure their child can complete calculus in high school. As a school district math curriculum administrator, I faced “acceleration pressure” from parents nearly weekly. Should we support acceleration? This question, like many questions in mathematics education, does not have a binary answer. The answer is “it ...
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