Math-team-matics Competition

A couple weekends ago, I was able to be a math coach for Rockford’s Math Club at the Math-team-matics Competition at GVSU. Earlier in the year, a group of students decided they wanted to bring the math club back out of retirement, where it has been for the last few years. Their love of math is infectious and inspiring.

As we walked into the competition, one of the students said “I just hope we don’t get last.” For their first ever competition, I would say that was a reasonable goal. Throughout the day, I didn’t get to follow the Rockford math team, but I got to follow Northview. Seeing these students made me remember why I wanted to become a teacher and why I fell in love with math. For an entire day, each of these students put other plans on hold in order to do math. And they had SO much fun. I think that somewhere, along the way, the fun has gotten sucked out of a lot of mathematics classrooms. But, sometime in our lives, every math teacher had that moment where they fell in love with math, with the pure enjoyment of it. We need to bring that back into the classroom.

The students at Grand Valley that day were inspiring, to say the least. But they were also incredibly impressive. The challenges that were thrown at them weren’t easy, but they were able to use their reasoning skills and their creativity to work through the problems. One of my goals as a mathematics teacher is to be able to challenge students and to force them to think creatively and reason their way through problems. Classrooms should be more like this. They should throw problems at students that encourage them to think, to reason, and to be inspired.

As much as I took away from this experience as a teacher, I think the greatest benefit was seeing how happy it made my students to be a part of the competition. They were so excited that I agreed to take them and they were having so much fun all day. Their goal of not placing in last was achieved. They took third! This was such a huge accomplishment for them and I could not be more proud.

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Student voices should be the loudest ones in your head.

Student voices should be the loudest ones in your head.

Too often, teachers are making choices about instruction and content delivery without truly thinking of their students. But, why is that happening? Shouldn’t all teachers be basing their lessons almost entirely on the needs of their students? Student voices should be the loudest ones in your head as you’re planning.

This podcast, by #MichEd host Brad Wilson, highlights what students want, what they’re looking for in school, and what makes them learn best. The majority of students discussed hands-on learning. This type of learning keeps students engaged, interested, and willing to do the work. They need the stimulation in order to retain and understand content. Students also talked about making choices. They want to make choices about topics they work with, pacing of content, peers they are in a group with, and how they demonstrate their knowledge. Isn’t this what teachers have been recently trying to push in the field of education? Why haven’t we just been listening to students?

One of the main points that I found so interesting is that students know how they learn best. As teachers, we shouldn’t take this away from them. We want our students to be skilled in metacognition and self-awareness. If our students understand themselves enough to know how they learn, then we need to let them learn in that way. Now, I know its near impossible in a classroom to let each student learn exactly how they want everyday, but the alternative is not to teach how we want to everyday instead. Teachers should be taking into account the learning styles of students and giving them the opportunity to learn in the way they learn best as often as possible. If the majority of your class consists of hands-on, visual learners, the majority of your lessons should be hands-on and visual. Give students options. They are capable of making decisions and should be encouraged to do so. The podcast highlights many students who know exactly how they learn, and who even noted that other students learn differently from them. If students have choices of how to receive content, we can engage so many more students than by forcing them to learn how we think they should learn.

After all, our whole job is for them. Teaching is all about the student. Their voices should be the loudest we hear.

Ask Questions!

Ask-The-Right-Questions-

One of the most important things I’ve found in teaching so far is the importance of asking meaningful questions to deepen mathematical understanding. I want my students to be mathematical thinkers and to be able to discuss their thinking with me and with their peers. I think that so much of mathematics education has focused on answers and procedures. Instead of that, I want to instill in my students the idea that the journey to get to answers, the thinking, is what doing math is all about. That’s what is important. 

At my latest observation, I asked my coordinator, Jon, to focus on the questions I was asking students and how they can influence the thinking of my students. I wanted to analyze how well my questions were actually inspiring thinking within my students and if I could be more effective at this. 

One of the main realizations we had was how often I was starting questions with “why?” That was even the whole question a lot of times. Though this is a good start to the way I want students to be thinking, it comes off as a bit aggressive. Jon talked about how there are genuine questions we can ask as teachers and how these are often more effective. For example, we ask a lot of questions like “what is the distance formula?” for repetition purposes, but these aren’t genuine questions. We know the answer. Instead, a genuine question would be “how did you think about that?” We don’t know how our students’ thought processes work and having them explain it is what I would want my ideal student to be able to do– to explain, in detail, how they thought about the math involved. 

Another idea we came across was the issue of how to reword questions when students are not responding well. When my students struggled with the answer, it was hard for me to reword it in a different enough way to get them to understand. Then, for time management purposes, I would often give them or lead them into answers that I wanted them to discover or illustrate to me themselves. Having ideas for multiple questions before the lesson will help me to get students to understand what I’m asking. This will take a lot of planning, but will definitely be worth it. 

My final “grow” moment from this lesson was about addressing student misconceptions. When students come up with ideas that are incorrect, but common (and understandable), I have a hard time knowing how to respond. I know that saying “no” in any part of my response is something I don’t want to do. This has a lot to do with my opinion that students who hear the word “no” will shut down and not listen to any of the rest of my response. For example, in this particular lesson, I had asked students which side was the hypotenuse and how they knew. One of my students responded and said “I know that side is the hypotenuse because it’s the one that’s diagonal.” My response in the moment was “yeah, but, actually, it doesn’t always have to be. We know it’s the hypotenuse because it’s across from the right angle.” I immediately regretted saying the “yeah, but…” part because I don’t want my students to be confused. Jon and I talked about saying something like “that’s really interesting! Let’s look at this,” showing them an example of something that disproves their idea. In this way, we are not shooting students down, not giving them incorrect ideas, and clearing up misconceptions (that much of the class shared.) 

Now what? 

In the future, I want to be conscious of the ideas that we discussed. Firstly, I want to change my question starters and begin asking more genuine questions. I think my students will really respond better to questions about their thinking, rather than “why?” Why questions seem to be looking for the mathematically correct answer of why, which isn’t my goal at all. So, I want to focus more on the goal I have and which questions seem to be getting there. Second, I want to plan, plan, plan. I want to plan multiple questions that address the big ideas of the lesson and how to get students to be able to answer them. This will take practice and experience, but I’m enthusiastic to start trying. Last, I want to spend a minute or two actually addressing misconceptions. I don’t want to just tell them why something is wrong, I want to show them. I want my students to see exactly why the hypotenuse is not always the diagonal line in order to better understand and retain that information. I think all of these things will help me to increase the mathematical thinking of my students. ‘Cause, after all, it’s the journey that’s important, right? 

 

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Pythagorean Theorem with Jellybeans

Pythagorean Theorem with Jellybeans

As I began planning for my unit on the Pythagorean Theorem, one important element kept striking me as vitally important–getting my kids up, moving, engaged, and interested. Eight-graders have a hard enough time sitting still and paying attention as it is, even without the added bonus of having to do it while learning math. Since the Pythagorean Theorem can be applied so widely to real-world scenarios, I wanted to utilize this privilege to its full extent.

 

This activity, found on the website of the National Council of the Teachers of Mathematics, is perfect for my students. The activity allows students to develop the Pythagorean Theorem through discovery of their own learning. It encourages students to test out scenarios, form conjectures, test these conjectures, and, ultimately, form the Pythagorean Theorem. It has the added bonus of students being able to play with candy. I believe that my students will enjoy the activity, and will greatly benefit from discovering the mathematics on their own. The Pythagorean Theorem is a vital concept throughout algebra, so students need a developed understanding of the ideas at hand.

 

Pythagorean Theorem with Jellybeans also incorporates a lot of the CCSS Standards for Mathematical Practice. Firstly, students must be able to make sense of the problem of finding a relationship between the squares drawn on sides of a right triangle and persevere in solving this problem. Second, students must reason abstractly. They will move between contextualizing variables to decontextualizing information fluently to represent a physical relationships in the form of a rule or conjecture. Third, they will critique the reasoning of others and develop arguments about their conjectures. They will be able to provide input on the conjectures of their group members and be able to make conjectures of their own. Fourthly, students will use the tools given to them to model the relationship mathematically. Fifth, they will use these tools strategically (and not eat the Jellybeans until they’re finished). Sixth, they will attend to precision to ensure that the conjecture they construct is accurate. Seventh, they will find a pattern between the squares on a right triangle and make use of this structure by developing a universal rule. Finally, after testing their conjectures, they will express reasoning in repeated regularity.

 

Rarely does an activity touch on all of the SMP, but I think this example is a great one. I’m excited to be able to try this in my class and (hopefully) see a change in the level of engagement and excitement in my kids as a result.

Middle School Mathematics

I have officially begun my Teacher Assisting semester. In just three days in the classroom, I can honestly say that I have never felt more at home. I’ve wanted to be a teacher my entire life, and it’s amazing to see how confident I am that this is what I want to do for the rest of my life. One of the most important things I’ve taken away from this past week is that my reluctance to teach middle school has diminished. I had always thought that I wanted to teach high school and swore I would never teach middle schoolers. Despite my beliefs, I am honestly starting to love the middle school atmosphere. The students are honest, intelligent, and just coming into their own as self-regulating learners. I think it is absolutely inspiring how influential middle school mathematics teachers are. They bridge the gap between elementary and high school math content and have the opportunity to produce students who love mathematics. This past week in my placement has definitely opened my eyes to what I want to pursue in the future as a teacher.