Engagement in Mathematics — It’s not Easy!

•February 16, 2012 • Leave a Comment

How do we get our students engaged in mathematics?

I think that’s a winning question for sure. There’s no short, simple answer here. We certainly know how not to engage our students in mathematics: lecturing with a few examples and then assigning some repetitive bookwork ought to do the trick. The problem is, however, that this is what so many teachers are used to doing. This is what is comfortable. It’s not easy to branch out and do something different – especially when that different thing isn’t guaranteed to work. As teachers we are making ourselves vulnerable to failure by trying something different. This approach has “worked” for years, so why fix something that isn’t broken? I argue that the system is broken, however, and that it does need fixed. This teaching style does not entice students to learn. So, how can we avoid this?

I don’t think there’s a simple answer to this, either, but I think there are things we can do to help. We need to be willing to fail, though; willing to make ourselves vulnerable. It’s alright if we’re not right every time (we tell our students this, too, so why shouldn’t it be true for us?). First and foremost, I think we need to allow our students to take control of their own learning. We cannot allow them to be mindless listeners (is it really considered listening if it’s mindless?), but must rather make them into interactive learners. Thus we are dismissing the idea that they are the student and we are the teachers and we hold all of the truths. we don’t. The truths can, however, be discovered. Our students can discover them.

I’m not suggesting that we abandon all forms of lecture and set students loose, but I am suggesting that there are ways to better engage our students by allowing them to take control of their own learning. In my book, step one in this greater control is minimizing bookwork. I believe there are good textbooks out there. I believe there are far more bad textbooks out there. More often than not, students don’t learn what they need to from textbook questions. We can’t, however, just cut out bookwork because that doesn’t benefit anyone. I am working on replacing bookwork in my classroom. I am designing lessons that are intended to be partially worked on in class, but mostly completed as homework. My lessons should make my students think about what math actually means. There’s more challenge and more ownership. I think I hold my students to an unrealistically high standard. But why not? Why should they be limited by my low expectations of them? Thus I am designing challenging lessons that I believe my students can complete with the proper support – lessons that engage them and challenge them to take control of their own learning.

I have 5 lessons uploaded on my previous post. Take a gander. Do you think they actually do what I claim? Feedback and discussion more than welcomed.


New Lessons!

•February 14, 2012 • 1 Comment

“OK class, for homework tonight I want you to complete 1-30 odds,” the teacher tells her groaning students. We’ve all been there. It’s not fun, it’s not engaging, and I dare to even say it’s not worthwhile. As a student I, someone who excelled at and even enjoyed mathematics, hated this. As a teacher, I want to avoid this. Now don’t get me wrong, I don’t judge you if you do it. It’s not easy to come up with things that are engaging and mathematically worthwhile for students.

As a student in the Honors College at GVSU, I need to do an individual senior project. I had pretty much complete control over what I wanted to do. Most students opt to do a research project or something similar. I decided to create math homework. In order to avoid assigning excessive bookwork that no one likes, I am working on creating lessons that can be assigned as homework. The lessons focus on a higher order of thinking and students will definitely need support, so I imagine allowing some time for each assignment to be worked on in class, but a majority of the assignments I envision being done as homework. That’s not to say that they are inappropriate for groupwork or classwork, but just that I envision them replacing bookwork.

That being said, I could use any feedback you’d be willing to give. Thus far I have 5 lessons. The lessons are all very similar in structure, but I’m working on varying my tasks in the remaining lessons. So here’s what I want from you:

Engagement — are these actually engaging to students?

Mathematical merit — are they worth my students time? Will they learn something from them?

Anything else — strengths, weaknesses, I’ll take anything.


Math in the Real World  

Functions — What’s in a Name?

How Much Cashback?

Where do you Belong?

Lines All Around Us!

Note: Lessons are not intended to be taught in the order written

Plugging Away!

•January 27, 2012 • Leave a Comment

So I’ve “finished” lessons 2 and 3. I completed them myself and thought they were engaging, but the problem is I like math. I’d even say that I love math. So would these be engaging to my students?

After a friendly nudge from my professor (@mathhombre), I stopped worrying about what my students know and don’t know. Why should they be limited by my low expectations for them? I understand I can’t start asking them to prove the Squeeze Theorem (my homework for the week), but I can ask them to explore without limits.

So, if you would be so kind, any feedback would be greatly appreciated! Anything positive (You’re a genius! These are great!), anything negative (How do you expect to be a math teacher when you added 2 + 2 wrong in the solutions?!), anything in between (eh. They’re better than bookwork, but will they actually engage students?). Maybe some of those things are a little extreme, but seriously, ANY feedback would be graciously accepted!


Lesson 02 — What’s in a Name? Functions

Lesson 03 — How Much Cashback?

Lesson 01!

•January 16, 2012 • Leave a Comment

Lesson 01 — Representations of Functions (Pdf)

I have completed my first lesson! Sort of. Since this project is all about 1) making super awesome activities for students and 2) me growing as a teacher I would really appreciate any feedback anyone has!

I am particularly interested in if this will be engaging to students, but I am open to feedback of all sorts.

Many thanks,



•January 9, 2012 • Leave a Comment

I spent 4 days last week immersing myself into Algebra I classes. As I began this project, I realized that I didn’t know a lot about what Algebra I students are like. After 4 days in the classroom, I think my biggest obstacle is going to be expecting too much from my students. Where is the realistic line of what they know and what they are capable of and what they don’t know or can’t do? I found in my four days at CPHS we went over the equation for slope each day. The students as a whole still didn’t know it concretely by the end of the week. My other major concern is getting students to care about what I’m teaching them. With so many other things going on in their lives, why should they care about math class? Why should they do their math homework? It seems as though this visit that was supposed to answer my questions has just left me with many more.

My original goal with these activities was to allow exploration and discovery. My observations have made me think that my students may need more structure. My intent is, however, to foster a more creative approach to learning mathematics in my classroom. I think that I need to establish this environment from the beginning and teach my students to be more independent. I need to encourage my students to speak up when they think they’re right and when they think they’re wrong. I need to let them know that every answer is valuable, even when wrong. I also need to teach them that it’s ok to struggle and ok to be wrong, they just need to try different things. It’s not that easy though. I will be combating years of spoon fed information and structured activities. Thus I still need some structure in my activities or I don’t think my students will put forth effort.

I think my time in the classroom showed me more about classroom management that what students are actually capable of. I think next time I visit I will have a chat with some students and figure out what they think is engaging and what they are capable of doing. I think that the students aren’t dumb, just unmotivated.

Now that I’ve sufficiently rambled about nothing for a bit I suppose I am finished. I am keeping plugging away at these lessons. I’m hoping they are something students will be more interested in.

Relating to Students

•December 7, 2011 • Leave a Comment

“Effective teaching involves in depth knowledge of both the students and the subject matter”

                        — Gloria Ladson-Billings, ­The Dreamkeepers, page 125

 A couple of weeks ago one of my professors, Rebecca Walker, let me borrow Gloria Ladson-Billings’ The Dreamkeepers: Successful Teachers of African American Teachers. After sitting down and talking with Rebecca about my senior project for a bit we got to talking about relating to students (as I was having a hard time developing lessons for imaginary algebra I students; I didn’t know what algebra I students were like). As my ultimate goal is to end up teaching in Boston, she suggested I started thinking about making my lessons culturally relevant to African American students because it is likely I will end up teaching a classroom consisting mainly of African American students. Previous to reading Dreamkeepers, I had the mindset that my students are students no matter if their skin color is black, white, green, or blue. As I read the book this idea slowly unraveled. It’s opposite of everything I’ve been taught in my life to ignore skin color, but the ideas really struck me, and they really make sense. I need to know my students in order to make problems that are interesting and engaging to them. Engaging their culture and lifestyle is more likely to be interesting to them. Moreover, by trying to draw their home lives and interests into the classroom I am not only making the material relevant, but showing them that I respect them. I respect their culture and their interests. I think that there is value in what they like and what they do. Coming from a middle class white family I really have no idea what my Boston students will like, so it’s difficult to come up with these culturally relevant problems. I am, however, slowly researching and trying to educate myself further. For now I have observations set up in my high school the first week back from winter break and I plan on getting to know some students and hopefully developing activities interesting to them that can be transferred and used in Boston.

It’s Only the Beginning!

•November 17, 2011 • Leave a Comment

I knew this was going to be hard but it’s turning out to be much harder than I had originally anticipated. First I had this wonderful idea for a lesson and got almost an entire student page finished only to look back at my standards and realize that the lesson didn’t fit the objectives at all. My first go around I was asking students to come up with examples. Although I think that’s a very valuable skill it didn’t align with my standards so I took a step back and started coming up with some examples on my own. No worries, I saved the “mistake” lesson because it should come in handy later. If not for this project, I can definitely in my classroom.

After that little mishap I worked on actually coming up with real world situations that could be modeled by different families of functions. It’s actually quite difficult. I worked with square root functions in my teaching high school math class a few semesters back so I decided to start there. During that class I wrote a unit plan on the square root function (not something I’m that proud of today, but we all have to start somewhere). I remember writing a problem about a referee on a soccer field. I decided to adapt that problem for this project. I need a little help seeing as it is only my first problem in my first lesson.

Now that I was on track with my topic, I needed to try to think of questions that would challenge and engage my students while allowing them to grow as mathematicians. I could think of several questions I could ask about the diagonal of the soccer field, but what questions are engaging? What questions are relevant? And what questions are actually going to help my students learn? Writing the questions is a lot harder than I originally thought. Sure I can mimic the type of questions I’ve been asked my whole life, and I love math, so they’re good, engaging questions, right? Wrong. I know that the questions I think are fun aren’t necessarily fun to my friends. To illustrate my point – I got a little tipsy and started doing optimization problems a couple weeks ago. To me, yeah that was a great time. That doesn’t mean I’m going to ask my students to do those problems. I was working on 1-30 odds. So, what do my students find interesting? This is quite difficult with hypothetical students. It is also difficult to assess what my students know and what they are capable of when I don’t have any. Is my wording effective? Are my questions clear? Can you realistically complete the question? I can quickly see my need to find students and teachers to interact with in order to write these lessons.

All of this and I’m not even half way done writing lesson 1. It’s going to be a long semester! But, I am definitely up for the challenge. Especially if it means I’m going to be a better teacher in the end.

  • Remember your objective
  • Try to challenge and engage your students
  • Make your questions meaningful
  • Assess what your students know and what they are capable of
  • Keep questions in their Zone of Proximal Development
  • Don’t give up!