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SitCog and the Pythagorean Theorem

7 Nov

This week in one of my grad classes we’re studying the theory of situated cognition (Sitcog). This is a really interesting theory that suggests one can only learn when in the proper setting. That doesn’t mean a quiet learning environment with minimal distractions; it means students should be doing and learning through practice. Sitcog claims that knowledge is not an idea or entity, but an action that can only manifest given specific context. Knowledge is  demonstrated with the learner can successful navigate a situation. This goes much further than practicing math facts and demonstrating that one can correctly perform the steps to solving an equation. Sitcog relies on students working through problems, projects, and cases to deepen their understanding in a richer way than any worksheet could do. Students will see value in learning when they can apply it to real-world situations. Yes, these problems are often challenging for students, and in middle school it is especially difficult to get students to learn by doing. Teaching through problem, project, or case based learning is not something that many of my students are used to, but by presenting students with situations that require them to apply knowledge beyond a word problem on paper they are truly learning the material.

Sitcog also stresses the role of a learner as an apprentice and suggests that one will learn best through legitimate peripheral participation. Student teaching is one example of this. As a student teacher I worked along side a professional who guided me through what I should be doing in the classroom, offering tips and suggestions. In applying this to the classroom, the teacher becomes more of a coach or mentor to students. It is not the role of the teacher to give answers or provide a step by step solution. This is difficult because as educators we naturally want to see our students succeed, and taking a guiding or questioning role is not always easy. But we also know that seeing students engaged in authentic learning experiences creates an opportunity for students to reach that “ah-ha” moment on their own. This makes a huge difference as opposed to us just telling them what to do.

I wanted to try out this theory in my own classroom so I created a problem-based learning activity for my students. We’ve been doing a lot of work with the Pythagorean Theorem, and I’ve been stressing application problems. I keep telling my students that real life will not hand them a sheet of pictures of triangles with missing sides, so they have to get used to solving the tough real-world problems. I really wanted to create an activity that could actually happen, where students could actually apply their skills. Here’s a brief overview of the activity.

  • Students work in pairs to complete a packet with questions and instructions.
  • The object is for students to build a wheelchair ramp so their friend who was recently injured in a car accident can come visit.
  • Students are given ADA specifications and a scale model of the ramp they will need to build.
  • Students had to measure the height of their ramp and then the length using a centimeter ruler. Using the scale 1cm = 1 foot, they had to calculate the length of wood needed to build the ramp. (Here’s where they use the Pythagorean Theorem)
  • After calculating how much wood they needed, they visited Lady Balsa (me in ridiculous safety glasses that I could have borrowed from Lady Gaga hence the name) at Lowes to get their wood.
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    Lady Balsa and the Cutting Table at Lowes.

    • Note: This is where I really stressed students as problem-solvers. I told them their teacher was not available as they were to imagine they were at home working through this problem. Lada Balsa could really only help them with cutting wood at Lowes (I also said she charged double for at-home consultations). By creating a character for myself, I was able to step out of the teacher role and observe students in learning. Of course I wasn’t able to complete take myself out of the picture, but it was great to see students run with my alter-ego and try to work through the problem on their own.
  • They were able to select the wood (light or dark), and then it was cut to their specifications.
  • After groups finished we discussed the different ramps and where errors happened, and the different ways to solve the problem.

This went way better than I had anticipated. I expected students to struggle with knowing how to set up their measurements. There was a lot of great math in this activity. Students had to use skills to measure, solve ratios, compare slopes, scale models/drawings, and of course the Pythagorean Theorem. I did try to make it a fairly easy problem as this was the first time I was implementing this sort of activity. The students enjoyed it so much that commented how they wished we could really go to Lowes and that I should dress up like other people more often. I’m definitely wanting to try more of these sitcog activities in the future, and as students become more acustomed to doing these activities I will increase the level of difficulty. I encourage you to try out some problem-based learning activities in your own classroom. Check out Yummy Math to get you started!

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Some of the finished ramps. You can see the third ramp miscalculated by asking for too short of a length, and the ramp in the back was far too long.

For a complete look at the activity packet, check out this link: PDF of Activity

Exponents and Dollar Store Puzzles

30 Sep
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Student desk during activity with question card, work sheet, and puzzle pieces.

Do you ever get tired of giving students endless practice problems from textbooks or worksheets? I do! A friend of mine that teaches remedial math shared this activity with me, and I want to share it with you all! My 8th graders love it, and I love it because they’re practicing their facts, working collaboratively, and I’m able to do a quick check to see if they’re getting correct answers.

  • I feel like this activity is really easy to explain in person, but my typed explanation might sound like this is a complicated activity. It’s not! Hopefully the pictures will help. 

Here’s the gist: Students are given a blank sheet that’s separated into 4 boxes. On a table in the front of the room I have divided puzzles and cards. Each group gets a card with some problems on it. They all solve the problems on their sheet in the box with the picture that matches the card. When they’ve decided as a group that they have the right answers, they send one person up to the table with their answers. I check their sheet. If it’s right, they get some puzzle pieces and another card. They start the next card in the corresponding box. They must send a different group member up for answer checks each time. On completing the fourth card they get the rest of the puzzle pieces. Usually the first group to complete the puzzle wins a prize.

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Front table setup during the activity. The first card they get without pieces, then as they get cards right they get new cards and pieces. The last pile is the pieces they get after completeing the fourth card. 

When preparing the activity I make copies of the worksheet for each student. Then I print the problem cards on cardstock. I use a different color for each group. This helps me to keep things organized when handing out the pieces. I got 24-piece puzzles from the Dollar Store. This works perfectly because I can give them 6 pieces for each correct card (MATH!!). I got different puzzles so the pieces don’t get mixed up. The kids love the Jake and the Neverland Pirates puzzle. I don’t show them what their puzzle looks like ahead of time. That would be too easy!

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Exponent Rules Cards

I usually use this activity for review. I’ve even used it in my algebra class, where each card was one problem (Like writing linear equations from two points). I typically give students 20-30 minutes depending on the problems. As groups finish they’re allowed to start on their homework.

Bonus: Here’s a link for a free download of the cards!!

Free PDF of Cards and Work Sheet

The cards here are exponent rules, but feel free to use the blank sheet to make your own questions. I’d love to hear from you if you use this in your classroom. It really easy a cheap and easy activity with minimal cutting.