All this talk over #MTBoS and #iteachmath has sparked a personal motivation to start blogging again. I believe all the conversations happening on twitter in the last week indicate a difficult yet positive shift in the Math Teacher Twitter community; this is a time we will not forget. There also appears to be an increased amount of engagement within the community, so what better time to post again?

Julie Reulbach posted a weekly blogging challenge that I want to be part of as the school year begins to rev up. This week’s focus is on goals.


During my summer session of grad school, the professor drew the following diagram:


She explained most teachers believe a student’s mathematical understanding progresses the following way; teacher introduces concept A, students show proficiency in concept A, teacher moves to concept B, students show proficiency in concept B, teacher moves to concept C and so on for the remainder of the school year. If a student happens to struggling on concept C, teacher backs up and reinforces the link between the two.

Each concept is dependent upon the previous, a single broken link causes problems with all other connections. This view forces teachers to not push too far on a concept or provide challenging material due to the fear of breaking a link.

She then erased the chain of concepts and drew the following:



The image above changed me.

The professor explained this as a Web of Understanding (If this credits back to other folks, please let me know!); the missing link between concepts B and E is not a problem because through transitivity the concepts ARE linked.

Now, if a student is struggling with concept B, there are multiple links a teacher can reinforce, since multiple concepts are linked to one another. Or maybe, there is no need to backtrack and fix a link because the others may be just fine. A broken link no longer causes issues with all other concepts.

My Goal for this year is to create a classroom where students see math not as a linear topic from one concept to another, but a web of interlinked concepts connected to one another. I hope to promote equity within my classroom in providing all students with challenging content, not just the students who have solid links from one concept to another.


Adding Polynomials

In an ongoing process to better teach the boring bits I have worked out a new way to introduce adding polynomials.  I feel like I should justify what I have been doing over the last… 7 months… but lets just say I have been busy in the classroom. Anyways; here are goods.

Start off by asking students to evaluate the following:


Walk through it to make sure they totally understand, this should be easy peasy for them.

Then throw this up:


Tell ’em you will race them and give ’em a 30 second head start, keep in mind that the previous problem has set them up to plug 2 into EVERY. SINGLE. X they see, so it is going to take them forevvvvvvvvvveeeeeeeeeeeerrrrrrrrrrrr to evaluate this expression.

After the 30 seconds is up announce that you are starting the problem (do this on a scratch sheet of paper by your desk, so they can’t see what you’re doing). Combine like terms, get this thing down to a trinomial (or possibly binomial) and then plug in 2 for x.

Announce to the class that you have finished the problem (in all my classes this was before they had even finished writing it down) then let student sit, perplexed, as to how you solved the problem so dang fast.

This gives at least some reasoning as to why mathematicians would ever want to add like terms.

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.


This year was great. I had awesome students, great collaboration with colleagues and daily reflection. I took some time after school wrapped up to go back and read through all my posts. I noticed that first 70 or so were pretty rough. I was in a weird place; trying to establish credibility and write like all the other bloggers out there I look up to, yet at the same time make my posts unique.

At times blogging every day was stressful. There were a couple moments out there where I almost threw in the towel… I spent 5+ hours each Sunday putting together fresh and new lessons for algebra and geometry (I didn’t reuse a single set of slides I created last year… mostly because of a transition from PowerPoint to SmartNotebook). But long story short, Sundays, 1 to 2 additional hours of prep each day and blogging wore me down after 38 weeks. Thanks to all of you, I made it.

This blog held me accountable in providing top notch lessons for my students each week (I dreaded the days where I had to write about using a Pizzazz or Kuta worksheet). I was also able to reflect each day on what went well or not so well, which, in my eyes is extremely important.

Basically, I am trying to say I am happy with all the improvements I made throughout the year.

But…I still want to be better. a lot better.

Here is what the future holds Quadrant Dan and myself…

  • I am really happy with the number of lessons I have stock piled on this blog. Next year, I will not be continuing a daily blog. I do however plan to post frequently. I want to dig deeper though and increase the quality of my posts, rather than quantity.
  • The main reason for the discontinuation of daily posts is next year I gained another class. I will be teaching algebra, geometry and IB math studies. The IB class is going to add an an enormous amount of work to my plate. Plus, I still have a lot to do for algebra and geometry; three preps will be intense.

I am excited for August to roll around and start my third year. Feel free to tweet at me @danburf, comment on an old post (I love questions), or drop me an email at anytime. Let’s keep these great conversations rolling!

Day 180: This is it…?

Ok, I have to come clean… we technically have two days of school left . Two snow days earlier this year, added two days to the school year. According to the calendar we are done today, however, June 11th and 12th are just-in-case “Snow day make-up”, which were put to use this year. But today was my last day of instruction, Thursday and Friday are all finals.

Algebra started off by filling out Who I am… Now. I hung onto the copies they filled out on the third day of school and passed those back today. It was fun looking at how their personalities and interests changed throughout the year.

After, students pulled out their phones/tablets and filled out another Teacher Report Card. Their responses were awesome. It is funny how students want their peers to think they are giving half assed responses, when in reality, they are meaningful and well thought out.

I made the mistake of not monitoring a student taking the final early close enough… So I had to reprint all the finals and shuffle the answers (I think there is a test of mine floating around).

While printing the tests I found these in my mailbox:

IMG_0710 (1)I love student letters…

I have a lot on my mind, most of which I want to write about. I am planning on re-reading my [Almost] 180 posts then writing on final post to bring closure to this 180 blog and by then, will hopefully have a game plan for what I want to do with this whole blog thing next year.  I keep coming back and adding paragraphs to this post, it is kind of like the first few days of summer; I don’t know what I am going to do with myself now.

One thing for sure… There will be more posts from me in the future.

If this is it for you, thanks for coming by. The amount of feedback and positivity I have received from this blog shifted and accelerated the growth my teaching practices in the best possible ways.I hope you continue to swing by next year.

Day 179: A look back

Jeopardy Review today, if you need something last minute, this is a fun way to spend a period (heads up, there are a few errors, it is fun getting students fired up about them though. I am keeping ’em for next year)

Anyways, Back in August I posted about this 180 day blog thing. I want to take a little time to re-visit the goals I put in place.

My Goals:

  1. Get plugged into the math blogosphere
  2. Challenge myself to always be better
  3. Accountability
  4. Provide resources for others


1.  I have met quite a few people over the last year or so, Twitter + this blog + other blogs have served as a corner for meaningful discussions. I have neglected Twitter though, I pretty much exclusively use it as a way to get this blog out there. I wanna work on that next year.

2/3.  Looking back, 2 and 3 pretty much go hand in hand. In my eyes, a successful teacher holds themselves accountable to always bettering themselves. Long story short, I spent hours prepping each weekend, were interesting enough to write about each day. This was really hard and became exponentially harder as the year went on.

4.  The amazing amount of support the #MTBoS community has provided is unimaginable. It is excited to see the community grow and great to be a part of it.

One more day…

Day 178: Review

Today was hot, I’d bet a lot of school across the country felt the same way. I gave algebra and geometry a list of the concepts that will appear on the final exam, suggested problems to review and set them loose. Finals are Thursday and Friday of this week so we have a good amount of time to review.