Reflections on the EFFL Workshop by Math Medic

I've just completed 106 hours of professional development this summer and decided that if I'm truly going to apply what I've learned, I need to reflect on the takeaways before I forget them. The summer began with the AP Biology Read in Kansas City, MO which accounted for 70 hours. Last week, I participated in an online APSI for AP Environmental Science for another 30 hours. Today was the last day of a 6 hour, online workshop by Math Medic on EFFL (Experience First, Formalize Later). Since this workshop is the freshest in my mind, I'll start with this one. 

I love Math Medic. First of all, they write a whole set of lessons that correlate to the AP Precalculus course. And secondly, they teach math the way I have always wanted to teach math...students learn by doing some activity that they can relate to (Experience First), but points them to the main ideas of the lesson. Anyway, by the end of the year last year I was also using Math Medic lessons for Pre-AP Algebra 2, especially for the way they consolidated the lessons (Formalize Later).

So, here are my takeaways: 

1. Project a blank "Experience" page that I direct students to write in certain work that their group has done. Last year, I just left them blank as I gave margin notes and pointed to student work up on the boards (my classes use whiteboards or windows to write their group work), but the work was hard to see.

2. Have students write the margin notes as I do, and they should write those notes in a different colored writing utensil just like I do, to help the notes stand out. 

3. Only focus on the challenging questions from the Experience page and chose different students to explain their thinking before connecting their explanation to the margin notes that are pointing to the main idea.

4. Know the main ideas before the lesson, so that I can better ask focusing questions that point students to the main idea versus just pointing then to how to get the right answer. Connect their thinking to the main idea(s).  Here's a Math Medic blog post about focusing versus funneling questions.

5. Taking this workshop also gave me the idea to share the essential knowledge statement(s) that go with the lesson and work with the students to determine what would be the most helpful information to write in the quick notes section. There are essential knowledge statements for me to use for both AP Precalculus and for Pre-AP Algebra 2.

I'm excited to see how my math classes will go in the coming school year while using these practices. 

Completing the Square with Blocks

Several years ago, when my Precalculus class made it to our Conic Sections unit, I realized that most of my students did not remember how to complete the square from when they learned it in Algebra 1 (and maybe 2). I was reading through the 5 (Math) Practices in Practice and Building Thinking Classrooms at the time and developed this activity to help walk students through developing their understanding of completing the square.

I divided the activity into four sections. The first samples start with just an expression with "x^2" and an even numbers of "x"s (b). They are asked to build a square, and are allowed to fill in any missing parts with single unit blocks (c). Eventually, we move into an odd number of "x"s, and then expressions with single units as well. 

By the fourth section of exercises, they are thinking through negative b values and the whole quadratic equation to complete the square for. For many students, being able to see the squares being built helps them to remember what to do when they see questions on tests that require completing the square to solve. 

Although I've traditionally done this activity in Precalculus at the start of conic sections, I'm going to add it to my Algebra 2 class next year as well when we are looking at quadratics. 

For this activity, I use some Algebra blocks I have as well as Cuisenaire rods paired with "x^2"s that I made out of card stock. I still didn't have quite enough, so I also cut some sets out of scrapbook paper I had on hand. I actually like the paper sets best when we need to only use half an "x" piece when b is odd. Then we can just tuck half of the rod under the square. 

Here are the documents that I made to go with this activity. This document includes the directions for each section. This document has each of the expressions or equations to work with in each section.  The examples are formatted so that either each group of students can have a quarter sheet of the examples for each section or a large sheet that I post somewhere in the classroom for them to refer to.

A Regression Lab for AP Precalculus

Starburst Grab

 I'm teaching AP Precalculus this year. Although I am loving the course developed by the College Board and the thinking it is requiring of my students, I'm a little overwhelmed with all of the prep. It doesn't help that I am also teaching AP Environmental Science for the first time. 

Speedy Squares

Anyway, I spend plenty of time looking through posts from the AP Precalculus teachers Facebook group. One of the posts talked about regression labs that a teacher was doing when they got to topic 2.6. None of these regression labs are my creations, but I put them all together into a form that I could use with my students that guided their thinking, hopefully into deeper understanding. The original activities can be found on Math Equals Love and Stats Medic.

Measured Race Station

I modified Starburst grab so that it would be a cubic regression, although it wasn't a fabulous fit. Then we had two linear and one quadratic regression. 

The labs were a big hit with students. One change I'm planning for next year is to have students answer the questions about each station at the same time that they are making their graph and finding the regression equation and residuals. 

Here's the document that I put together that includes both the handouts that I gave to each student as well as the directions that I placed at each station.