Scaffolding

Scaffolding is all about connecting content with students' experiences, whether they are real life applications or things they have learned in previous classes. The math curriculum is set up to provide scaffolding for almost every content strand. From Math I to Math II to Math III and even through the higher level maths, concepts build on one another. 

Krystal and I (because, yes we are the best team ever!) are giving ourselves and our students the opportunity to scaffold throughout their math courses with the math notebooks we are doing. Many of you know already, but students will essentially use the same notebooks through Math II and Math III (and hopefully their college classes as well!) The notebooks are section by broad concept topics (Expressions, Functions, Quadratics, Exponentials, Geometry, Trigonometry, Statistics & Probability) so that we can continue to add to concepts we've already talked about. 

My students are liking the notebooks for organization. They don't necessarily see the value just yet (we haven't truly gone back to a topic that we have already talked about to add a page). I think they'll like it a lot next year when they need to review for upcoming concepts. I'll like it a lot better when I can say "I know you've looked at this before. It's on page G4". 

Classroom Talk

Like I said in my last post, Krystal and I are really trying to get away from the "sit and get" style of learning in our classroom. We have worked hard throughout the semester to find activities for our Math II classes. My Essentials of College Math course has activities built in to the curriculum that was given to me. I'm pretty happy with the types of learning taking place.

As everyone knows, my classroom is set up in groups. This is definitely the easiest way to make classroom talk happen. My groups for my freshmen are set up with purpose. I allowed my seniors and sophomores to choose their seats from the first day (and they never got on my nerves with excessive talking, so they kept that privilege!) The seniors and sophomores have moved seats some (mostly based on their "friends" and drama, but a few have moved in order to have a better learning experience!). The freshmen tables have at least 1 A student and I tried not to put too many struggling students together. They are also based on who talks way too much, though I think some of the freshmen would talk to a brick wall if no one else was around.

I have been impressed with the mathematical talk happening in the many different activities. One recent example is the volume discovery we did with the geometric solids and sand from prom. First, the students grouped the solids into prisms, pyramids, and other. They had to discuss the difference between the prisms and pyramids (prisms are stacked shapes and have parallel bases, pyramids come to a point). Then, they had to match prisms and pyramids based on their bases (triangular prisms and triangular pyramids match, etc). I heard many good vocabulary words and explanations happening within the groups. Finally, they took the prom sand, dumped it in the pyramid, then found out how many times a pyramid fills up the prism with the same base (which was 3). Students also had to think about the volume, and write what they thought the formulas would be. We did some other things with the shapes, but this was the most self-guided and had the best outcome as far as classroom talk.

Questioning

When anyone thinks of a typical math class, they immediately think of a teacher at the board talking and writing while students are taking notes. Then, students get 40 problems for homework and that's it. However, Krystal and I are trying to do things very very differently.

At times, questioning in math is very direct. There are often right or wrong answers with no wiggle room. However with enough preparation, there are plenty of opportunities for students to be creative in their responses. In comes the Geometric Proof Portfolio. Krystal and I worked on this Portfolio for over 3 hours one afternoon. The time grading was much much larger. However, with our portfolio, we gave students the opportunity to express their knowledge in a way that there wasn't just a right or wrong answer. In the portfolio, they were able to draw, describe, explain, and answer questions in a much better way than a multiple choice test. 

During the Questioning session at our in-house PD and the PD Krystal and I attended, we talked about the Webb's Depth of Knowledge. The program the county uses to make tests have DOK levels printed for multiple choice tests. Most of the levels are 1 and 2... Use, Recall, State, Tell, Infer, Construct, Summarize. However, most of our questions in the portfolio questions fall under the 4th level... Design, Synthesize, Create, Critique. 

While most students did not receive high grades on this portfolio, I was very impressed with the ones that did. Most students lost points for not following directions. Laziness, the fact they "had to" do it over Spring Break (even though they were given an entire class period to work on it), and not paying attention to detail were the biggest causes of low grades. 

High-level questioning can be tough, but with enough planning (and Starbucks), great work can be achieved!