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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.

    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!


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

Were you paying attention?

10 Oct

Do you ever feel like teaching is a dog and pony show? I know I do. Wouldn’t it be great to have a classroom full of students who come in prepared and ready to focus only on the lesson you’re presenting? All eyes are on you and they’re only thinking about the math not who Bobby was sitting next to on the bus, or if Lebron’s going to score 60 points tonight. But the reality is we’re competing with so many factors for our students’ attention. Some of these factors we can’t control, but it is important that we try our best to hold our students’ attention. This week for my grad class I read a lot about memory and how it’s related to attention. In her book “Human Learning,” Jeanne Ormrod states that attention is “critical for long-term retention of information.” We often say to our students when they miss something “Were you paying attention?” but we need to make sure we use strategies to ensure they are paying attention. I know that it’s hard to make every lesson the most exciting lesson, but I want to share with you a few tricks that have worked for me.

Remove Distractions

A lot of time when students walk into my room they are carrying what appears to be the entire contents of their locker. They get locker breaks, I don’t know why they need to carry around everything. I find their gigantic binders and reading books can be a big distraction. “Look at this huge packet of work you get in Social Studies.” “Isn’t this narwhal I drew on my binder hilarious?” When my students come in each period there are directions on the board for them to follow. They almost always start with “Clear off your desk except for… ( a list of what they need to start class).” I really stress these directions at the beginning of the year. I will even show pictures on the board of what their desk should look like. I find I rarely have to say “Put that away please,” or take an item because students just know it’s not supposed to be on their desk.


I love memes. Some of them are really clever. I do not love using power point to teach, but sometimes its just the easiest way to present typed information. So I like to jazz it up with memes. Here’s an example of a recent slide I used in class to give directions and the agenda:


I used to create the meme. It’s pretty easy to use. The kids really like the memes and have even emailed me some they think I should show. (Sidebar: The memes can also help with visual imagery (also in Ormrod’s book) of important information. I even had a student tell me on a following quiz that she remembered Grumpy Cat and read the directions twice to make sure she followed them correctly!)

Student Cold-Calling

Students hate to be called on in class if they’re not paying attention, and truthfully I don’t love calling them out. I’ve tried the popsicle sticks, but wanted more student involvement. I tried letting the students choose the next person to answer. When going over answers in class, I’ll choose the first person who volunteers, then that person chooses the next student. Then the second student chooses the third and so on. They are not allowed to vie for selection out loud and students have to pick a different person each time. This method has increased participation in the beginning (because if they’re first they can get it over with), but also attention has increased because they know a friend might call on them. Even after they answer they pay attention to see if someone will get caught not paying attention. Also it’s taken some responsibility off of me and I can circulate while they answer.

Awesome Possum 

This one definitely doesn’t work in every classroom. Some kids just can’t handle it. It’s all about setting up parameters for it. If I find my kids are tuning out, or getting out of control I will say “Awesome Possum.” This is their clue to play dead. This usually involves flopping over on their desk, and there shouldn’t be any talking. I try not to say it when they’re standing so I don’t have kids throwing themselves on the floor. They do not like to be the last one to play dead. So it usually gets quiet pretty quickly. Then I say “Awesome job Possums”, we let out a few giggles at the last ones to play dead and we get back to work. It’s a nice brain break, and it gets everyone back focused on me without calling any one student out. It’s really effective for coming back together after group work, but I like to randomly throw it into instruction to get their attention. But like I said, some classes can’t handle it so we don’t play.

There are a lot of other great strategies out there for getting and holding the attention of middle school students, but I gave you these four because they are easy to incorporate and don’t require any singing or dancing. I know there’s not a lot of time in our busy schedules to create amazingly engaging lessons every day, but if you’re bored teaching it, chances are they’re bored learning it. It’s okay to say to students “This may not be the most exciting lesson, but we’re going to get through it so we can apply it to basketball (or some other more exciting topic your students are into).” We have to work at creating memorable learning experiences for our students, and that starts with getting their attention. Do you have any great strategies you use for getting attention in your class? Share in the comments!