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Bringing Up The F Word With Your Middle Schooler By now, students in middle school have been exposed to the F-word. It has been used by their classmates for a few years now, and slowly but surely, it has stirred up more and more trouble. After all, the general consensus around the word in society is rather negative. Yep, people all over the world avoid the F-word at all costs... Fractions. Whew. OK. I said it. Did that cause a visceral reaction? Did you clutch your chest, leaning back in your chair as you read it? Maybe it wasn’t that dramatic, but there are countless students across the country, and adults taking care of them when they ...
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I’m going to avoid the rhetorical question of “Have you ever argued with a kid in middle school?” because, well, it seems as though the ability to disagree is woven into teens, especially those in middle school. Is that a bad thing? Sure, I don’t want my students, or my own children, constantly forming opposition to my requests, expectations, or ideas. However, there is a difference between defiance and disagreement and we need to do a better job of nurturing the latter as a way of mitigating the former. By nature, human beings are curious, inquisitive, and cautionary. When we get into a situation that is unfamiliar, we make assumptions. When those ...
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“Ugh, really? Math ? Pffff, c’mon. Can we talk about anything else?” - Most middle schoolers any time a parent tries to bring up something math-y  How many pipes do you see? How did you count them up? Can you think of a different way to approach that stack? This picture, taken on a drive home with the kids in the back of the car, brought forth a ton of great ideas. For me, I took the stack and cut it up into pieces, then found a length and width to determine an area. You didn’t do that? Great! What was your approach? How about your child’s? There’s something enjoyable about working with students in the middle grades. Their candid ...
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When I was a child (back in the 1980s), my friends and I loved playing a guessing game called Guess Who ?  In this game, one person chose a character and the other person had to ask yes or no questions to determine which character was chosen.  Desmos has created a math version of this, Polygraph . I often use Polygraph with my students at the beginning of a unit, when I am introducing a topic.  Shown below is the Polygraph I used with my 7th-grade accelerated group at the beginning of our Transformations unit.  Students are shown an array of choices. One student picks a choice that the other students must ask yes or no questions to identify. ...
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Let’s look at the labor demand expected in US by 2030. McKinsey Global Institute recently published a report about automation in the US and its effect on the job market. It shows that there will be a drop in demand for labor with secondary or less education (due to Artificial Intelligence, robots, and other automation), and a jump in demand for a college-educated workforce. Therefore, teachers will be expected to continue to make a push for college readiness to fulfill the market demand. However, according to The Nation's Report Card only 25% of students performed at or above proficient level in math on the most recent assessment. Another report says, ...
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My Favorite No One of my go-to and favorite activities is the error analysis task of My Favorite No.  Originally created by Leah Alcala from Berkeley, California, this is a task that I use often with my students.   I have often looked through my Activity Builder (AB) answers and have seen some creative, but incorrect answers from my students.  In looking through the answers, I find one that I can tell what the student was thinking and what misconception they have regarding the topic.  I take a screenshot of the solution and the question that it answers and use it as a question for the class to discuss. In the Point Collector AB , one ...
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The Dashboard In my last post, I introduced one of my favorite Desmos activities, Point Collector: Lines.  When I run this activity with my students, the Teacher Dashboard allows me to augment/pace the activity to create opportunities for discussion in my class.  While my students are working, often in groups of two to three at a computer, I walk around my classroom while I am glancing at the Dashboard - this allows me to interact with the students while checking on their progress and understanding of the activity.   Parts of the Dashboard The dashboard consists of the list of students, slide previews, and three teacher buttons: Anonymize, ...
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This blog is for  The Virtual Conference on Mathematical Flavors . I am honored to be a keynote. The discussion below is based on what I consider to be my seminal work as researcher and educator. Unpacking the mathematical experiences of Black boys is a "flavor" that we must be intentional about if we are serious about equity work. Bilal's Story Bilal is an eighth-grade Black boy who has been successful with school mathematics and school in general. Bilal stated that mathematics is an easy subject for him to learn because he likes mathematics and he loves the challenge of problem solving. In fact, he credits his father for helping him develop a love for ...
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Why Desmos? My classroom is a noisy one - full of discussions, debates, and even arguments.  This is not how it always was. When I first started teaching, my desks were lined up in rows and students worked quietly on problems after being shown a lesson on the board.  We would go over the problems the next day in class and this pattern would repeat - day after day. Luckily enough, a couple of years ago, I attended a Bay Area Math Project Conference that was led by Dan Meyer .  Dan showed us a website on which we were able to draw a function that related time versus a man’s height when he was shot out of a cannon.  There were oooohs and ...
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How can we promote mathematics play in more classrooms? What is within our power to make playfulness a norm in maths class? To be honest, there is no special magic necessary here. The strategies offered will not be especially new or profound. However, their effectiveness can be thought of as directly proportional to the commitment of teacher leaders to implement them consistently and with fidelity. Truthfully, it will take courage to disrupt the status quo. First, we must become adept at planning with play in mind in our own classes and/or schools. Playful mathematics still puts student learning at the forefront of lessons. Through the use of multiple measures, ...
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Why? Why should students engage in the study of mathematics? For a satisfactory grade? To graduate from high school and subsequently receive admission into a “good” college? If these were sufficiently motivational, we would likely not even be asking this question in the first place! We should engage students, and consequently re-engage as necessary, in maths because we want to flourish as human beings. Francis Su reminds us that mathematical study builds virtuous basic human qualities and desires, such as hopefulness and perseverance, perceptive insight, joy and a sense of justice through play, truth-seeking, appreciating beauty--all resulting in the ...
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"Galileo Galilei once said: 'Mathematics is the language with which God has written the universe.' Too bad most schools are awful at helping us become fluent in  Universe ." Math-Explorable Explanations In a dream world of some maths teachers, students could play mathematics for its own sake, with childish whimsy of heart, and explore countless possibilities for discovery in our universe. Unfortunately, many of the established systems in education impede this dream from becoming a reality in classrooms. In truth, accountability is necessary due to maths’ unique potential to propel or squelch students’ future educational and career endeavors . Therefore, ...
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Other professions play, why shouldn't we? The idea of work being commensurate with play is not novel. Many a professional athlete, musician, etc., regularly interchange these two words when speaking of their craft. Football players’ ultimate goal is to play and, hopefully win, the Superbowl. A famous rapper once commented he had reached one of his dreams to play his music at the 20,789-seated Madison Square Garden. Similarly, Carnegie Hall is a site where classical music enthusiasts regularly experience energy and awe as they listen to a musician who has likely worked her whole life to play a favorite piece in this prestigious venue. Actors receive ...
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In my last post , I ended with a proposition made by John Van de Walle: “ The traditional whole-number algorithms for addition, subtraction, multiplication, and division should no longer be taught in schools.” Instead, he argued that alternative and/or invented strategies should be encouraged and supported because they are: number-oriented, rather than digit-oriented, flexible, rather than rigid, “left-handed” rather than “right-handed” (starting with the biggest place value first), student-centered, rather than teacher-directed, and focused on number sense and mental math (Van De Walle, 2004). In order to support alternative ...
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If you have been following this blog series you now know more about units coordination , how it relates to fractions , and where it shows up in middle school concepts .  So how do we help students progress in their ability to coordinate units? One thing I have learned from the amazing work of Christopher Danielson is that the best prompts will simply open a dialogue.  In his book How Many ? , he offers pictures to start a conversation about just that.  As the teacher’s edition (which I highly recommend) states, we need to put discussion about unit relationships “front and center for examination and discussion” (40).  These conversations ...
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I advocate for more equitable and just classrooms, schools, and schooling. This work must be addressed at multiple levels of the educational system (e.g., see Aguirre, Mayfield-Ingram, & Martin, 2013, Wager and Stinson, 2012), but in all of the work that I do I always try to highlight the importance of honoring and building on the brilliance of young children’s thinking. Despite decades of evidence, some adults (teachers, administrators, parents, etc.) are surprised, and often a little incredulous, at the idea that young children can understand complex mathematical concepts and even invent strategies to add, subtract, multiply, and divide without ...
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Don’t you love when students have an “aha” moment?  What about your own “aha” moments? I still remember the first time I taught inequalities with algebra tiles and finally understood why the inequality symbol needs to be switched when multiplying or dividing by a negative number.   I have had many “aha” moments since being introduced to units coordination and the work of Anderson Norton and Amy Hackenberg through the US Math Recovery Council .  Incorporating this work into my classroom has been transformational for my thinking.  Here are just a few ways my thinking has shifted. The first blog post in this series introduces an assessment ...
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If you found my first post explaining units coordination with whole numbers helpful, this post will give you the details from my experience working with fractions and how impactful it is to students when understanding units coordination. Fraction problems like this are typical in my 7th-grade classroom: Is ½ of ⅘ more or less than ⅘?   If ½ pound costs $3.50, what is the price per pound? In all fraction problems, there exists one whole of which the fraction is part.  By middle school, most students have the part-whole understanding that ½ is one out of 2 parts of the whole unit.   If a student is struggling with the second question above, ...
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A refresher from my last post:  I am a Learning Support teacher in G1, and along with the G1 teaching team, I look for opportunities to use and elicit evidence of student thinking to in order to design small group lessons, and adjust my instruction based on their thinking. My current small group continued the Basic Facts & Place Value unit. Following the lessons from Days 1-4 (see NCTM Blog Post ), I met with one of our instructional coaches to talk through planning my next instructional steps. We looked at the following areas: Teaching Focus : What math teaching & learning questions do you have about the first few lessons - what are ...
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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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