Category Archives: Reflection

A Dangerous Place: Old vs. New

I’m ready for students on Monday.

This year I’m teaching:

  • Three sections of algebra
  • One geometry
  • One IB math studies

Planning for the first week was awkward because I had fairly solid lesson plans from last year, which has never happened to me. During year two I had some ideas from the previous year, but because of a transition from Powerpoint to SMARTnotebook, I didn’t have anything prepared.

I feel like my slides from last year are dirty; I don’t wanna touch ’em, it feels weird not having to start from a blank SMARTnotebook slide.

I’ll be honest… When I came back to school early last week, turned on my computer, navigated to Algebra 1 -> Chapter 1 -> Week 1 -> Day 1 the thought of not even looking through the slides till students were in the room crossed my mind. “This year could be easy.” I told myself, “Last year was great, what do I really need to change?”.

That didn’t feel right though.

Last year, I invested hours into my lessons and slides each week, I was working through the content and planning a couple days ahead of the students. Even though I haven’t met my students this year, I already feel a disconnect when thinking about reusing every lesson and set of slides from last year. There isn’t any excitement on my end.

Yesterday, my school had its yearly kickoff staff meeting. One of the administrators spoke to me. They threw up a slide saying change 10% of what you do each year; I can do that. I’ve already gone through and mixed things up for the first week. I didn’t start from scratch, but did make some changes that felt right, my first week feels like it has a nice polished shine to it now.

Some of the motivation behind working so hard last year was to make my life easier during years three/four/five. It is ironic now because I want to keep growing and those slides feel they are impeding on my growth as a teacher.

I believe this year will be big in defining where I go next: Will I be a teacher that uses 20 year old lessons and resources? Or one that spends 6 hours at school on Saturday/Sunday planning? I don’t want to be either of those, but something in between the two.

Stay tuned.

Day 49: Is a picture enough?

This year I have made a lot of great mistakes to learn from and this blog has been a great place to reflect. Here is the latest greatest mistake:

In Geometry we were talking about classifying triangles by side length and angles. I asked students to classify an many different triangles as possible. About 2/3 of them did it using pictures paired with words, while the other 1/3 used only words.

This alone is really interesting to me. So much of math seems to revolve around definitions that are created using words. But at the same time I can define parallel lines by drawing them, or classify an angle as 90 degrees with a simple symbol.

I went along with students and created the following collection of triangles.



As I asked for each triangle, students were pairing perfect definitions to them, which made creating a visual representation easy.

After we came up with 7, I didn’t say much else and started them on a worksheet.

About 5 minutes into the worksheet students ran into this:


We stopped for a little and talked about it. Triangle BDC is equilateral and isosceles. Our visual representation didn’t include the fact that all equilateral triangles are also isosceles. An easy fix was just putting *at least two congruent sides under our visual representation.

Is a picture enough for a definition? Is a question that I am pulled both ways on. On one end my students were accurately describing each triangle with congruent marks and could translate those images to words. During class I felt that students had a strong enough understanding to move on. Also, I bet that most people wouldn’t write out the definition of isosceles triangle as A three sided polygon with at least two congruent sides. At most the definition would be A triangle with at least two congruent sides.

On the other end, most pictures don’t show the special cases, so the fact that my students didn’t see the special case adds a lot of value to written definitions.

I still have a bitter taste in my mouth from written definitions in calculus, so I am reluctant to pick a side here. Maybe there is a place in mathematics for both….

Let me know what you think.

Day 23: Case of the Mondays

Today was pretty rough in first period Algebra. I made it about halfway through the lesson and lost all motivation to move forward. The content was dry, students were half asleep and I realized there was almost no value in what I had prepped.

Before going into that, my next period I had to start with something to get students going and to get me going. So I had students go through this activity. It was really interesting to see students become so quickly conditioned, which makes me really think about how easy it is for ME to fall back to direct instruction at times.

Students are so used to having 20 minutes of lecture then 30 minutes of book work followed up with homework that I feel like I am abusing the system when I structure class in that way. This style is so natural for students and nice because all the expectations are already laid out on my end. But, I went into education with a different style of teaching in mind. I do not feel any passion in the subject of students when I teach that way.


I started today with the following slide:

More of them rates

More of them rates

Students ask for the price; so I gave it to ’em.


Do we want $/oz or oz/$? Calculate whichever you think is the most useful.


We had a nice discussion about how grocery stores do this for every. single. product.

Then I had a voice in the back of my mind…

“If stores do this for every product, why bother calculating these rates?”

I ignored it for a while and transitioned into more rates. After students did enough to get bored I mixed things up:


“Where did the dollar sign go?” was the question I asked students. None of them could answer.

Perfect, this leads really well into dimensional analysis, which is exactly what I had prepped for.

We converted between feet and inch for a while then I threw up mph to ft/s and this happened:

A rounding error happened somewhere along the way.

A rounding error happened somewhere along the way.

Students were able to see what was going on behind the scenes, which I thought would be good. We checked our work using Google.


This is the point where I broke down. What is the point of using long hand conversions when Google can do it in 0.28 seconds? Throughout the day I kept telling myself that it is important for students to see WHY something happens and where units come from, but deep down inside I just don’t believe that.

Today, there was no real foundation for why we use unit conversions, it was just there to say I had taught it. I could give students a bogus answer for why we use them and move on, but in reality Google is just flat out better. I am not really sure where to go from here, probably just keep moving forward and check this off as a great day for personal reflection.