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Everyone's Invited

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How are you inviting your students into the learning for each activity? each lesson? each unit? What profound ideas to consider, and that invitation is important for all learners to receive, every day. My favorite ways to engage my mathematicians in the content play directly into the interests of the learners. Sometimes I include a really funny GIF that sparks their curiosity. Other times it’s a pop culture reference or current event that draws them in. Short video clips pique the interest of my students. Or I’ll throw out an interesting or obscure picture to consider. I might pull in some related mathematical expressions to allow students to be purposeful ...
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#ExitTicketGoals

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I would imagine it’s pretty difficult to plan a lesson without a goal in mind. Is it even possible? As educators, we’re constantly thinking about goals. What is the goal of this unit, lesson, activity? Did my students meet their goal? What do I do if they don’t meet today’s goal? What do I do if they show mastery? I believe in the power of backward planning, planning with the end goal in mind. When planning lessons in a unit, it’s useful to keep a copy of the summative assessment nearby. The lessons are the journey to get to the ultimate goal: mastery on the final assessment. Keeping that end goal in mind keeps me on track and moves the students in the ...
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I do. We do. You do. Repeat… * Sigh Breaking away from the traditional-style, gradual release classroom was the best move I ever made for my teaching craft and the mathematicians in my classroom. The gradual release model, I do–We do–You do, has its place in the classroom, and it’s a valid way to deliver your lesson and content to young mathematicians. I definitely have a handful of these lessons throughout the school year. Teaching long division comes to mind. Making a change to a higher level of active learning can open the door toward deeper learning and understanding. One way to promote active learning in your classroom is to break away from ...
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Take a deep breath. They’re anxious too. Except maybe that one﹣looks a little too comfortable already. Ready? Ready. “Mathematicians, welcome to 7th Grade Math!” Genuine smile. Happy soul. There is nothing more critical in teaching a classroom of middle schoolers than setting the tone for your community of scholars. Most days my main goal in teaching middle school math is morphing the wide-eyed, goofy group of tweens in front of me into believing that they are the brilliant, confident scholars that I believe they are. I’ll foster that growth as we build our math community out of respect and high expectations, both of which are vital in this process. ...
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Welcome to the final round of this 4-part post series on how to build productive math discussions into your daily routine. In the first 3 rounds of this post series I shared how to use specific resources found on the web to create math discussions in your classroom. More specifically, the first three posts show you how to Create a moment of   out-loud thinking ( Round 1 ) Create a moment of   controversy . ( Round 2   and   Round 3 ) Create a moment of   Wonder . (Round 4) In this final post I’ll focus less on how to create arguments or math fights and more on a resource that helps create moments of wonder ...
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An expanded Q&A with NCTM President-Elect Trena Wilkerson: What drove you to become an educator? Trena Wilkerson:                    I loved mathematics, but I guess many say that! I also found that I really liked teaching it, making connections, and helping others to make those connections. Finding ways to help students understand (especially those who seemed to struggle with certain ideas in mathematics) is intriguing to me. I taught high school mathematics for eighteen years and found it exciting to work with students across algebra, geometry, calculus, and more. Later I became interested in teacher education and working with preservice teachers, ...
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LET’S GET READY TO RUMBLE!!! Welcome to round 3 of How to start a math fight: Building productive math discussion and discourse into your daily routines. In round 1 of this series I aimed to clarify that a math fight is not a fight, but a phrase centered around students TALKING about their mathematical thinking. From my experience, having students regularly discuss, argue, defend, and justify ideas using mathematics helps them understand topics more deeply. We can create rich discussions in our classrooms by carefully planning three kinds of moments: Create a moment of out-loud thinking ( Round 1 ) Create a moment of controversy ...
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“High school teachers like to close their doors and rule their own kingdoms.  Especially math teachers.  What you’re proposing will never work.”  I heard this often early in my ongoing journey of organizing collaborative professional development for math teachers in my district.  Now, seven years later with student outcomes near the top of state rankings, the same questions come in the past tense, with an echo of incredulity and wonder that teachers actually truly enjoy working together.   Teaching is perhaps the most social of professions.  At every moment, you are orchestrating complex and multi-layered interactions between young people. On your best days, ...
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Let’s start up round 2 of How To Start a Math Fight: Building productive math discussion and discourse into your daily routines. In Round 1 of this series I clarified that a math fight is centered around students TALKING about their mathematical thinking. From my experience, having students regularly discuss, argue, defend, justify ideas using mathematics helps them understand topics more deeply. We can create these rich discussion moments in our classrooms by carefully planning three kinds of moments: Create a moment of out-loud thinking (Round 1) Create a moment of controversy . (Round 2 & Round 3 ) Create a moment of Wonder ...
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#NCTMontheHill: The Power of Building Relationships   The NCTM Board has embraced and is actively supporting NCTM’s advocacy role. Recently,  Board members made visits to Capitol Hill to meet with their members of Congress to introduce NCTM, share key educational issues and the impact they are having, and work to build relationships.  In short, make a friend.   Almost all ten members of the Board who participated were able to meet with the offices of both their Senators and their Representatives. In addition, every NCTM Board member had at least one meeting where they were able to connect and discuss key issues. On Capitol Hill, members of Congress ...
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Ding Ding! Welcome to Round 1 You may be wondering and saying to yourself: Math Fight? Really? What does that even mean? Come on Jon, you can’t be seriously promoting violence! You’re right, I would never promote violence in the classroom, so let me fill you in on what I mean by a Math Fight. Here is an image that is NOT a Math Fight! Here is an image of a math fight in progress: Here is another math fight What do you notice? To me, a math fight is where two or more students have differing opinions or thoughts and are productively trying to convince each other that they are correct or to convince each other that their ...
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Examples of Effective Modeling Activities Several years ago a friend shared a video with me that changed my perspective on teaching math forever. It was Dan Meyer’s Ted Talk, Math Class Needs a Makeover . Before I had ever heard the term modeling, the concept was lodged in my mind and consequently my practice because of the following clip. After you check it out, let’s take a look at a few tried and true classroom activities on modeling. // Meyer goes on to make five suggestions for implementing these kinds of activities. (I highly recommend watching the entire video!) Use multimedia Encourage student intuition ...
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The Roles of Teacher and Technology: Mathematical Modeling Using Desmos We have many tools in our math teacher toolkits. Need to demonstrate place value? Base ten blocks. Explore area and perimeter? Geoboards. Probability, you say? Out come my cards and dice. The thing is, we don’t expect students to understand place value simply because we handed them the base ten blocks. We don’t expect them to derive formulas for area and perimeter without some guidance with the geoboards. We don’t expect them to grasp probability because we let them play dice and card games for the week. Yet, we often expect students to learn math simply because we hand ...
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Modeling Math Using PhET Simulations I was talking with a former teacher recently, and she commented on how easy it is for today’s teachers to access resources from all over the world. We really are fortunate to live in the age of widespread digital technology. On the other hand, the sheer volume of educational materials out there can be paralyzing! It frequently takes me as long to locate high-quality resources as it does to create my own by the time I filter through the pseudo-educational junk. So when I find something I like, I get excited to share it with other teachers. In this post, I want to tell you about an award-winning resource called PhET ...
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Connecting Charting a Course for Success with Catalyzing Change In his May 2017 President’s Message, NCTM President Matt Larson boldly stated that “ Mathematics education is STEM education .” He argued that mathematical understanding is an essential foundation across all disciplines of  STEM. The Committee on STEM Education of the National Science and Technology Council recently issued Charting a Course for Success: America’s Strategy for STEM Education stating that mathematics is foundational to the development of success across all STEM fields of study. This report outlines a federal strategy for the next five years across the content areas ...
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We know it isn't this... but what is it??? Since a math researcher told me about the work of Richard Lesh, I’ve been reading everything I can get my hands on about modeling in math. One thing I’ve learned is that modeling is a versatile and deceptively simple word! Even the experts use the same word to mean different things in different contexts. (Check out the TCM article, Common Core Confusion about Modeling , for instance!) So first, let’s start with some working definitions. I’m going to focus on two specific types of modeling that I find particularly useful in my classroom: Modeling with Mathematics and Mathematical Modeling.   What is Modeling ...
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When I was a kid, I remember wanting to be helpful. It didn’t matter if it was in the garage, the kitchen, the family room, outside, or elsewhere; I really enjoyed helping with tasks. While I would like to think that it was something inherent, further reflection leads me to believe it had a lot to do with empowerment. From an early age, my parents and extended family wouldn’t have me complete menial tasks. Instead, they involved me directly with the creation/destruction/modification of whatever we were working on at the time. As a way of closing out this mini-series on ways in which parents of middle school students can support and foster their love ...
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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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