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.