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Week 12: Chris Hunter

Blog post: It stuck.


I think this is such an appropriate final blog post for me to respond on; it’s about the advice that will stick with you as you begin your teaching career. So it got me thinking… what advice/learnings am I going to remember forever and take with me into every classroom?

  • Have a sense of humor.
  • Remember that it’s okay to be wrong, and help your students understand that as well.
  • Be yourself.
  • Teach the students, not the subject.
  • Use the grade book to track progress/master of skills so that you are well-informed when assigning letter grades to your students.
  • Encourage mathematical discussion.
  • Break the mold of traditional teaching – give students a chance to come up with the questions, given the answer.
  • Make learning personal.
  • Get to know your students and understand that there are things going on in their lives that may be affecting their school life.
  • Make your classroom a safe and welcoming place.
  • Don’t forget to make time for yourself.
  • Teach students for the society that they will be entering.
  • Never stop reflecting, learning, and evolving your practice.

These are the things that jump to my mind first about what I want to do when I enter my own classroom for the first time. I know that over time and with more interaction with other teachers and other resources this list will continue to grow. I think it’s important to note that a lot of these points are very simple; I don’t want to overthink things. I think that the simplicity of these ideas will go a long way in the classroom and I am excited for what’s to come.

One other thing that has really stuck out to me over the course of my practicum is the idea of teaching students to be mathematicians instead of just to do math. I fell in love with the idea of having students identify what strategies and qualities define a mathematician and have them constantly reflect on how they are developing in those areas throughout the course of the semester. I believe that these skills (be systematic, look for patterns, start small, be persistent, stay organized, describe, seek why and prove, work backwards, etc. ) are arguably the most applicable skills that students can learn in a math class and I have realized that they have become a way of life for myself. I found that I was approaching problems in my real life in ways that I would approach a math problem and so when students ask me why they need to learn something, I will always respond with something along the lines of “while you may not use this specific content in your life, I promise that you will use the strategies you are applying to the solving of the problem to something, sometime in your life.” There’s more to math than just math. And that’s the one thing that will remain with me in every classroom I enter, forever.

Week 11 Response: Andrew Stadel

Blog post: We don’t need no stinkin’ homework


The subject of homework has always been one that I can never agree on a strategy for. I, like, Andrew agree that there should never be incentives offered to do it. I believe this for a few reasons: I would feel more comfortable if the students were completing the practice for the class with access to my help, the students need to learn to take responsibility for their own learning and they should not be rewarded for practice; this defeats the purpose because they need to be able to make mistakes and if they’re being given marks for homework then they will not feel comfortable to do so. I would love to adopt SBG into my practice one day and so I’m open to any ideas to motivate students to do homework and value their learning. The most valuable part of this blog post I found was actually the comments section. Andrew seems to also be struggling with ways to motivate students to do homework (and he only assigns a few questions!) and there were some excellent ideas in the comments section. I absolutely love Dan’s idea of doing peer review of homework the next day. To me this seems like the perfect solution! This is a great way to incorporate assessment as learning, as well! What I love most is that this is a way to motivate students to do homework in a way that is still super beneficial for their learning. This will help students improve their mathematical communication, their reasoning, and so much more. I can’t wait to try this myself!

Week 10 Response: Kate Nowak

Blog post: Review and practice: add em up


I picked this specific blog post because it’s actually one that I read and tried during my own practicum. I knew that my students needed some time to work through review problems in class but wanted to do so in a way that they would feel comfortable working together and stay on task. This activity worked fabulously! It was a nice break from the usual textbook activities (even though I just took the questions from the text) but I was able to differentiate their difficulty level based on which worksheet it fell on. I also loved the idea that students had to check their own answers in a way that didn’t directly tell them what was wrong.. they instead had to go back and discuss the answers with their group and work towards identifying their mistake themselves. When I tried this in my practicum I did encounter a few problems at the start where students kept asking me if their answer was right, but eventually they became more independent with their learning. All in all, this was a fabulous review activity, it was different enough to keep the students on track the whole class, and it really optimized their thinking and review skills. I would definitely do this again!

Week 9 Response: Matt Vaudrey

Blog post: Teacher 4 a Day- Reflection


This post immediately caught my eye because it just sounded like a totally awesome lesson. And after reading his post about it, I definitely cannot wait until the day I can do this in my own classroom! Letting your students be “teacher for a day” accomplishes so much in one assignment. This activity really made me think of what PDP has done in shaping my own ideas about math and how students interact with it. I know that I have come so far in my own mathematical understanding while I have gone through the process of planning a lesson and to be able to give me students the same opportunity definitely excites me. I always knew that I was “good” at math, but teaching it has shown me deeper understandings into the concepts than I ever could have gotten as just a student. This is the perfect activity to go alongside bloom’s taxonomy, because it activates that highest order of thinking. Students need to evaluate the needs of other students and the work that they are going to present them and create a lesson that will accomplish their learning goals. It also gives students an excellent opportunity to participate in peer evaluation not only in their exit slips that they had to include but also in the other students’ presentations. I can’t wait to try this out!

Week 8 Response: Julie Reulbach

Blog post: I Speak Math


So this week I’m having trouble picking a single blog post to respond to, because I’m not sure that I agree with a lot that Julie is writing about. So instead I’m just going to respond to her posts as a whole, because I find that they all followed the same type of path, anyway. I went searching and searching through her blog to find some cool activities that I could critically examine and imagine implementing in my own classroom, but everything I found seems to just be more fun ways of having students complete problem drills, for lack of a better word. I got excited when I saw her idea for math stations (I love the idea of math stations: students are working at their own pace, they’re collaborating with their peers at the same station, they’re moving around the classroom, you can differentiate the levels of difficulty..) but Julie’s math stations were made up of worksheets cut into pieces. In my opinion, that is simply assigning them a worksheet but making them move around to answer it. They are working at their own pace which is great, but I don’t see a high level of differentiation in these tasks, the problems are so procedural that there is no collaboration needed, and it’s just bland. If you were going to do math stations, each station should have a unique and open ended problem that has the students sitting at the station really grappling with each others ideas, and then an open class discussion for a wrap up on what everybody discovered. Another cool addition to that would be to have problems with new concepts worked out on these stations, and have the students try to make sense of it themselves and teach themselves and each other.

Another activity that I came across was her Draw It game. In this game students are racing to answer the questions projected on the board in their given space. I was watching the video and noticed that there were two girls racing to draw and label the area of a parallelogram. By the time the one girl got it right, the other one hadn’t even finished drawing a parallelogram. How do we know that she knows what that is? How can we help her to better understand? Was it just time pressure that messed her up? The problem was never addressed, because the other girl had put the right answer up on the board. Point for that team, next contestants, next question, done. Perhaps this would be a good activity to use for preparation for a review class so that you have an idea of what students need to work on, but I’m a little concerned as to how and what would happen to the students who go up there for their turn and have no clue how to answer the questions.

I also read a lot about quizzes and tests and summative assessments and I want my classroom to be drowning in formative assessment. I want my students to stop caring about collecting marks and I want to ease them into the world of learning for what it is. I think that classroom time shouldn’t be spent drilling students. Nor should I be assigning them 30 questions on one concept out of the textbook. I want them to embrace the struggle that is playing with mathematics in my classroom. I would be more than happy to provide them with some extra questions if they feel that they need to brush up on the procedural before jumping into a rich problem, but I think that needs to be their call. I want to teach them problem solving, not step memorization.

Week 7 Response: Geoff Krall

Blog post: Developing a taxonomy of problems: Not all problems are implemented equally


I absolutely love Geoff’s idea of creating a taxonomy of problems and I think that this is a really great idea to tie into all of the things that we learned during our assessment class with Peter Liljedahl. I think that this definitely goes hand in hand with tracking the progress of the students by skill and classifying our questions and this taxonomy helps us to create the problems that we can use to get to that point where we can track their progress. I absolutely love the idea of problem based learning and think that it gives the students a great sense of ownership of the learning because ultimately they are the ones coming up with the ideas and that’s an empowering feeling! I also think that more often than not, math educators forget that there is a difference between problems for learning and problems for confirmation and that they let the lines blur between what those really mean. I think that we need to watch that there are questions that help students to practice skills, but ultimately we need to see that they can think their way through a problem and apply the skills correctly. I think that by using these ideas to guide us towards conceptional understanding questions for confirmation and assessment questions for confirmation then we are giving our students the skills that they need and assessing them for the right reasons. Just recently I was helping a cousin study for his foundations 11 final exam and he was given booklet upon booklet of multiple choice review questions. While talking him through a lot of the content in those questions, it was clear that he was just able to take the multiple choice answers, plug them into a great conceptionally worded question, and get the correct answer without understanding any of the concepts that he was actually testing. So when, as teachers, we think about the problems we are assigning and where they fall on this taxonomy, we are giving ourselves a more accurate reading of the students skill set as well planning well rounded lessons that lead to the students further developing their critical thinking skills.

Week 6 Response: Sam Shah

Blog post: Senior letter 2013


This post, to me, was magical. I would have given anything for a high school teacher to have done that for me and I cannot wait to write letters to my own seniors one day. While he may complain that his writing was rushed, I think it was perfect. It spoke to my high school self, venturing off into university to seek out knowledge in the only subject I ever enjoyed. I wish somebody had given me his advice though, to live in the moment and to just enjoy learning things and knowing things. I always saw my degree as a path I had to go down to get where I wanted to be and having that mindset probably caused me to miss out on a lot of opportunities. I became immersed in the “work hard, play later” lifestyle and probably didn’t get enough joy out of the content and the learning. Things changed when I got into PDP. I found myself talking about the things I loved and was learning about teaching with other PDP students. I found myself buying books on assessment and differentiation because I just wanted to know everything that I could about them. Now I can totally relate to everything that Sam Shah is telling his seniors. I absolutely love this idea and I love his words of advice and I will definitely keep them in the back of my mind as I continue on my own personal learning journey. Sometimes you just need to take a step back and smell the roses!