Monthly Archives: March 2017

The Day I Didn’t Know a Math Standard I Taught

Two weeks ago it happened again. The dreaded moment I realized I didn’t understand the standard as well as I thought. It was demoralizing. I didn’t know the standard I was asked to teach my students. It doesn’t happen often but it does happen. I’ve contemplated making a blog post about this very topic but have always decided not to. I was leery of making myself vulnerable. Until now.

After 15 years of teaching math, I would say I know my content well. I’ve always loved math. I’ve unpacked standards, repacked and unpacked them again. For 10 years I wrote questions, based on standards, for our state test for every 7th and 8th grader in the state. The questions were quality and went through a battery of tests to make sure they were valid. They passed.

The most recent standard I thought I was teaching to my 8th graders:

Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.

The key word here was, “derive.” My students have always used the formula when finding area that involved trig ratios but never derived it. I looked at the standard and thought, “how does one derive this?” I honestly didn’t know how to derive it. I found a video online and, after quickly watching it, I quickly remembered how. The guilt then set in. How could I have not known how to derive the formula? My instruction and assessment both changed. Last week I gave my students the assessment.  The question simply stated, “Derive the formula A = 1/2 ab sin(C) for the area of a triangle.” All my students demonstrated proficiency.

If there is one thing Standards Based Learning (SBL) has done, it has made me a far better teacher. I started SBL last school year. All of my assessments were now reported to standards. I made detailed rubrics that would guide students to proficiency. Prior to SBL, I had used standards in my teaching. For many years I would occasionally look at the common core standards either at a math meeting or on my own while planning. I went on with my teaching. To give myself some credit, I was teaching nearly all of the standards. I just wasn’t teaching them as in-depth as I needed to. I thought I was but when I started making rubrics, it was eye-opening. I had to make 4-point rubrics that went into detail about how students could demonstrate proficiency on each level in each standard. This alone is what has made me a far better teacher. This was my accountability. When standards drove my instruction, I became a master of the content.  When standards didn’t drive instruction, I fooled myself. I taught my content first and then when I occasionally looked at a standard, I would tell myself, “Yup, I taught that.”

How could I ask my students to demonstrate proficiency on standards that I didn’t know well enough? I couldn’t.

Last year was an eye-opening year for me. I not only knew my standards, I lived my standards. Everything in my classroom was based around these standards so I had to get it right. I did. My students made more connections between concepts than ever before. I watched my students not only make connections across concepts, but also across grade levels. For example, instead of students learning Pythagorean Theorem (P.T.) in 6th grade to find missing sides of triangles they now learned that the P.T. and its converse are conditional statements as well as finding missing sides. In 8th grade they make the connection to conditional statements in geometric proofs. They then proved the Pythagorean Theorem from triangle similarity. When students learn about circles they will derive the formula of a circle all because of P.T. It all correlates. It all meshes. It makes sense. Students are aligning the concepts vertically across grade levels as well as linearly within the class.

In year two, I continually strengthen my understanding of the standards. SBL has made me keep myself accountable. I am always striving to get better. In my classroom, it’s okay to make mistakes. Failure is a part of learning. I want students to have a growth mindset and use these setbacks as ways to improve. Failure is a beginning, not an end. If I’m going to ask my students to reveal their setbacks, then I have to lead by example. Not knowing my standards in-depth was my setback but I used it to grow. I used it to improve. I will never stop learning.




The Day a Student Threw Away His Math Work

In my flipped classroom, students work on the practice in class. The practice can vary. Students will sometimes do an activity while other times students work on challenging problems that involve collaboration. The practice is always given to reinforce the concepts students learned from my videos. The practice is done in class while I walk around assessing students. Sometimes I ask questions while other times I sit back and watch them do the work.

Before my flipped classroom started 5 years ago, students would do homework. I would expect students to keep this homework in their neatly kept 3-ring math binder. I wanted students to have access to all of their homework in case they needed to pull it out to look at it. I would often do surprise checks to check how organized their binder was and, consequently, would give them a grade on it. I wanted to make sure students were learning math…by keeping all of their homework organized in their math binder. Sigh. To give myself some credit, I did the best thing I thought would work at the time. I’ve definitely come a long way in my ways to check for learning.

Fast forward to today. I no longer grade or collect any formative work. I constantly check this work daily while giving feedback, asking questions and leading students to revise their work. Students receive no score for anything other than summative work. While I no longer collect practice, the expectation is that students still are checking their work and answers with the answers I provide them. Students have answers always readily available to them. I strongly feel students need instant feedback at anytime while they are doing practice. This way students can revise in real-time not having to wait for me to come around.

Recently at the end of class I watched as an 8th grade student (we will call him Bob) finish his practice after he got a difficult problem correct. He exclaimed, “YES! Finally, I got it!” He had worked on this problem for about 15 minutes. I looked over at him with a smile. I then proceeded to watch as he got up, crumpled up his 2 pages of neatly written math practice that he had persevered in solving for an hour, and toss it in the air into the recycling bin. I was shocked. Appalled is probably a better word. How can someone who worked so hard on something throw it away!? I still thought students kept everything in a binder so they could pull it out when they study for an assessment if they needed to.

I sauntered over to Bob and asked him why in the world would he throw his work away? He responded, “Why would I want to keep it? Isn’t the purpose of the practice to help us understand the material better? I now know the material”  It was a good point. Actually, it was a very good point.

I thought about what Bob said at lunch. I walked into my colleague’s office. Garnet Hillman, an awesome instructional coach, is my go to person when I have questions. I told her what happened. The replay of him crumpling up the paper and tossing it into the recycling bin replayed in my head all afternoon. Then, it hit me. Bob was right.

Why would I care if he threw the paper away? For so long, my students always did things out of compliance. Bob throwing the paper away, right before my very eyes, proved to me one thing. Bob cared more about learning than compliance. He did the practice and persevered through the work to learn. He reflected on his work throughout class through my feedback and by checking his answers. The learning happened! Once the learning happened, there was no reason to keep the practice. It wasn’t about compliance, it was about learning. There was no grade attached to the work, therefore, the primary focus of completing the work was to LEARN it, not to earn a grade.

Two years ago I stopped grading and collecting work as it was eating up so much of my valuable time.  I honestly thought students would no longer do it since I wasn’t giving a grade for it.  Just the opposite happened. They kept producing quality work. Fast forward to a day last month when I watched Bob throw away his work. Little did I know at the time but Bob just solidified everything I was hoping would happen. Students were now doing the work because of the learning, not because of compliance for a grade. There was no need to keep the work. The practice was used to learn the concept. Thank you Bob!

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