As a high school math teacher, this question is always on my mind. There are many instances where I can read about how elementary/middle school math teachers engage their students, but find it difficult to find instances where certain strategies work with upper level math students. Manipulatives rule in lower level math content, but finding upper level math manipulatives is very scarce. In fact, thumbing through the latest Nasco Math K-12 (2017, pages 179-184) there are The Hands-On Equation Learning System, Algebra Tiles, and a Pan Algebra Balance. That’s it! There are many flash card systems, posters, workbooks, and other hard copy visuals, but not many manipulatives. The question then begs, how *do* you offer engaging upper level math lessons?

After doing some research, I found several math teachers that utilize some strategies would increase engagement in math class. Jose Vilson list several that I have slowly adopted in my class over the years even before reading about his experiences. When students ask Jose for help on a math problem, he answers them with more questions. (2012) I have done this more in recent times than when I first began teaching over twenty years ago. It has merit and allows me to get a good understanding of a student’s thought processes as they tackle a problem they may not know how to solve. Asking questions gets kids involved and engaged. Another strategy that Jose uses is to have students teach too. (2012) Often times, when many kids have questions at the same time, I plead with students who are done with their assignment to help those that are struggling. I personally feel that students who teach others content become more knowledgeable themselves. They really have to explain carefully their own thought processes and steps to a fellow student that usually have a similar vocabulary, and it works.

Matthew Busick shares some strategies that I don’t utilize at this moment. He states that we should open a lesson with a hook. (2011). Dave Burgess lists a plethora of “hooks” (31, I think) that can be used to engage students in his book, *Teach Like a Pirate*. (2012) This is where innovation comes into play. You have to do the unusual to get attention. I don’t think I have ever “hooked” a class full of students *every* lesson, but it is a good strategy to utilize as often as you can. Another strategy that Matthew uses is to address the “why” during lessons. Often times, I state to my students that the current lesson is in preparation to the next, or it will assist in a future lesson. Not a motivating reason to pay attention to me that day! I need to explain the end result of why we are learning the current lesson. Matthew does incorporate, as I do, many visuals in his lesson. (2012) I constantly tell my students to draw out a problem. Math is *very* visual, and those that teach without this strategy are missing one of the most engaging aspects of learning new content. I believe this is one reason graphing calculators and smartphone graphing apps are becoming more prevalent in math class. I grew up learning upper level math without one (cause they didn’t invent one yet!), and I tell my students how lucky they really are to have such as great tool these days.

References:

Burgess, Dave. Teach Like a PIRATE: Increase Student Engagement, Boost Your Creativity, and Transform Your Life as an Educator. Dave Burgess Consulting, Inc.. Kindle Edition.

Busick, Matthew. (2011). Five Ways to Make Math Lessons More Engaging. Knewton. Retrieved from https://www.knewton.com/resources/blog/teacher-tools/five-ways-to-make-math-lessons-more-engaging/

Nasco Math K-12. (2017). [Printed catalog]

Vilson, Jose. (2012). Engaging Students in Math. Edutopia. Retrieved from https://www.edutopia.org/blog/engaging-students-in-math-jose-vilson

I teach middle school and high school math. I find that it is a lot easier to have more engaging lessons in middle school than high school because of the manipulatives fact. I also often think of how in elementary they have so many more manipulative options to use for their kids and how much more fun their students must have during class. We use the Hands-On Equations system to teach equations before they even start learning how to show their work on paper. Once they have mastered the system, teaching them how to show their work is a breeze. This is the first year I have used the system and I was amazed at how awesome the students do after learning the system. I wish I could’ve used it in the past, but it wasn’t available to me.

I like how you mentioned asking questions gets the kids involved and engaged. I do this all the time, but I never really thought about the fact that it gets them engaged. I just always that was part of the job, but never really thought of the meaning behind it, so thanks for putting that out there. I have my desks in groups of three so students can easily work together. There are usually students with different ability levels in each group, so if I am busy helping a student, I have them help each other if they aren’t already. It’s amazing to see the amount of help students are to each other if they are allowed to be. I know there are many teachers out there who want it quiet during work time, but I think working together, as long as it’s productive and not just giving answers out is a huge asset to the learning process. Obviously there are times when they need to be quietly working if they aren’t being productive working together, but I think if students know the expectations, for the most part the days are going to be productive and helpful for students.

One area I struggle with is hooking students into the lesson. The last time I hooked them on every lesson was in college when I was required too as part of my lesson plan format. I often tell my kids the same thing you do is that they need to know the material for future lessons. Either that or you have a test next week and I agree with you these aren’t much of a reason to be engaged in what is going on in the classroom that day. It should probably be something I start working on for the sake of the students as well as my sanity when I’m trying to get them interested in something without giving them a good reason.

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I really appreciate your comments on the Hands-on Equation System! I have seen something similar in electronic form online and it seems like it would work. I think I will try to get my hands on one to see if it will work for our struggling Algebra 1 kids. I always talk about “moving” terms when solving equations, but I don’t think students really understand what the heck I’m trying to say. 😦 I think having a visual while you do it would make it more concrete for them. Other than this manipulative, I really can’t think of anything else that would be useful in upper level math. Well, a graphing calculator or smartphone app is definitely a great visual tool. In fact, a few of my students downloaded the Desmos app and learned how to use some of the graphing functions. I didn’t even suggest this in my class! It was nice to see them come up with solutions to help them. Well, maybe they are trying to cheat too. 🙂 But I hope they are just checking their answers. Thanks sharing your math experiences!

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Teaching high school math seems like such a challenge. Actually, teaching any subject in high school is terrifying. 🙂 When thinking about student engagement and high school math I couldn’t help but ponder my own experiences. I despised math in high school. In fact, I had to go to summer school to retake algebra 1. But I can’t blame the teachers…I just wasn’t motivated to do math. I think that my lack of motivation or engagement was partially due to the fact that I struggled with math since grade school. Grade school math was even worse than high school math. The 100 problems in 1 minute tests KILLED my confidence. Math was a struggle for me until I was a senior in high school. I took consumer math with Mr. Powell and I loved it. It was learning how to budgeting your money, investing, and paying taxes. I believe that consumer math was so engaging and fun for me because it was based on real life situations. I could use this in the real world! I think that’s the key to teaching math. Find a way to relate it to their life. Make it applicable. “Guess what kids you do need math and this is why….” I love teaching math now, and I think it’s because I had to learn how to make math meaningful to me.

I also agree that it is difficult to engage high school students by using manipulatives. Not a lot of manipulatives are high school appropriate. In fact, the graphing calculator still intimidates me. Drawings are an awesome math tool! I let my kids use dry erase markers on their desks for math time. They think it’s the coolest. 🙂

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I appreciate your honesty about high school mathematics and what a struggle it was. You are NOT ALONE, believe me. I agree that we should be teaching more applied mathematics that students will encounter after graduation. If things go my way next year, I will be able to teach financial math, and statistics. Those are the most useful, in my opinion, classes kids can take. I will definitely like teaching math that kids will not ask, “when will I every use this?” It will be interesting to see how our new math curriculum will mold our students, especially in elementary grades. Thanks for you comment!

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