Category: Math


With all of the continued discussion over the importance of teaching algebra, I felt compelled to share some thoughts. It seems to me the conversation is centered around the wrong topic. Instead of asking if algebra is relevant (of course it is),  we should be asking, “Is the way we are teaching algebra relevant?”

Algebra, or any other math strand for that matter, is relevant to building well rounded, successful citizens. The content isn’t the problem… the pedagogy is. The problem is found in classrooms where the students sit silently, listening to the teacher deliver his or her math knowledge while demonstrating a series of algorithmic steps. Those teachers then require the students to follow exactly the same steps when solving equation after equation after equation. It’s how most of us experienced math – direct instruction, then 25 or so problems using the steps just demonstrated. Heaven forbid, you miss a step or in a moment of true rebellion, solve the problem in a different way. My own children have been forced to follow this stifling way of learning math. One weekend, my oldest son brought home a packet of 80 problems for his algebra 2 class. Since he was able to solve them without all of the steps the teacher required, he did so. (He’s a rebel.) His grade on that assignment…a 54%. Why? The reason I was given when I asked was that he didn’t show all of his work. Yes, he did. His work just required fewer steps.

One of the most frustrating things I experienced as a teacher was when parents would tell me they had horrible math experiences in school, yet they were upset when I didn’t teach their children the same way they had experienced. Math hasn’t changed. Math instruction needs to. Teachers need to stop expecting students to “do math” and start letting them experience math.

A few years ago, my school system transitioned to a student centered, problem focused approach to teaching math. We moved from the traditional algebra 1-geometry-algebra 2 sequence to an Integrated Math sequence. Since I had already been using this approach in my class, I was thrilled. Others were not. The role of the teacher was expected to change. No longer the “sage on the stage,” teachers were encouraged to introduce problem situations, then allow students to work together to reach conclusions.  I loved it and so did my students. Don’t get me wrong, it was difficult for them at first. Students are good at working side by side, but many students need to be explicitly taught how to have productive mathematical discourse. It was up to me to teach them, through questioning how to discuss math. The teachers who embraced this pedagogy saw great results. Teachers were questioning students and students were asking probing questions of each other. They were searching for answers and quickly realized that many paths can lead to the same solution. Math became relevant. One question became obsolete, “Why do I have to know this?” Students were free to explore mathematical ideas. They solved real world problems and in doing so, actually learned some algebra.

As a math teacher, I began every year by challenging myself to help the students assigned to me fear math less, take more risks and see how math is and will be relevant to them regardless of the path they choose. We need to change the conversation. Let’s stop spending so much time arguing whether or not algebra is necessary and spend some time discussing what’s happening in math class.

All. By. My. SELF! When my middle child was three years old, those were his favorite words. He was experimenting with his independence and wanted to do everything by his self. He was quick to announce to anyone who would listen that help was not needed. Why is it that we teachers do the same thing? We feel we must do everything all by ourselves. We talk about how our students need to learn to collaborate, yet do we model that skill? Are we really doing all we can to learn from each other and help each other grow?

Last summer while at ISTE in Philadelphia, I attended a session led by Will Richardson. During his presentation, he discussed the importance of educators connecting and collaborating with each other. He stated that if we are not sharing the best of ourselves then we really aren’t doing anything to counteract all the negativity directed toward our profession. His comments really caused me to think about my own habits. When I am designing work for my students, I typically go to the web and see what I can find that others have already done. I had to stop and ask myself how much I was giving back. I’m thankful there are teachers out there willing to share the best of their ideas. I am now trying harder to do the same.

During my transition to a 1:1 environment this year, one of the challenges I faced was how to effectively integrate technology into a math classroom. I was determined to use the laptops I now had access to as more than word processing tools. I just wasn’t sure how to do that. So, I went to my favorite PD and lesson planning tool…Twitter. Sure enough, little by little, I began to find math teachers willing to share their best. I’ve found lessons and ideas created by other teachers. Sometimes I add to them or otherwise adapt them to meet the needs of my students, and sometimes I use them just as they are. I am thankful to these educators for their willingness to share.

We don’t have to do this alone. In these days when teachers are constantly under attack, we must support each other, build each other up, and do our best to not let anyone feel they are all by themselves. Are you sharing your best? If you aren’t, I hope you will!

Here are some of the best I have found… Yummy Math, Utah Education Network, Adams County School District 50, Bridgeport School System, Ohio Resource Center, Curriki. There are so many more. Please share some you have found!

Just ask the children

Earlier this week I was part of a team that led professional development for all of the secondary math teachers, some EC & ESL teachers and a handful of administrators in our district. The session was the first of three that are meant to prepare our staff as we move toward implementation of the Common Core State Standards next school year. For this first session, we decided to focus on the standards themselves and the mathematical practices that are part of the CCSS. As an introduction to the practices, the groups of teachers and administrators were asked to respond to the following: “Write a few words or phrases that describe an excellent mathematics classroom.” We allowed them a few minutes to discuss, then we asked them to share out. The responses were pretty much as we predicted. Many mentioned motivation, students listening and working together, students trying and not giving up too easily. Some mentioned technology. Almost all focused on student behaviors.

After all of the groups had shared, we revealed that the three of us who were facilitating the discussion, had asked our students to respond to the same prompt. We shared a few of the student responses. (The complete list of responses can be found here http://goo.gl/6WYtc) The reaction of the teachers was interesting to watch. Some were surprised, some were shocked. Some couldn’t believe students could so clearly articulate what they felt an excellent mathematics classroom should look like. While many of the teacher responses focused on student behaviors, most of the student responses focused on the learning environment. Almost all of the students mentioned working in groups, collaboration, or teamwork. Practice 3 states that mathematically proficient students “justify their conclusions, communicate them to others and respond to the arguments of others.” In addition, this same practice says, “Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.” It is interesting to me that what the CCSS says we NEED to do in order to produce mathematically proficient students is exactly what the children are telling us they WANT to do in math.

The content is important. The standards are necessary. However, the learning environment we establish is what leads to student engagement and thus learning. We say we want the children involved in their learning, yet we remain convinced we know what the best learning environment is. If we really want to know what an excellent mathematics (or any other) classroom looks like, we just need to ask the children!