What I Did Differently This Year

A roundup of things I did differently, or that I continued to evolve with, this year in my Math classes:

Visibly Random Groups

Groups of 3 students sitting together. New partners & new desks every day. I used playing cards given out at random as students entered class to assign students to tables – with hanging numbers indicating which tables made which group. More details about VRGs here.

Kahoot!

2 to 3 days per week I used Kahoot as our bellwork. Kahoot is an interactive quiz that the kids answer using cell phones/tablets/laptops. I have created a bank of basic skill-based multiple choice questions for each of my courses and we often start class by playing 10 randomly chosen questions. Correct answers get points & the faster you answer, the more points it’s worth. The kids really love this & it’s a great way to practice basic skills.
What’s especially cool about Kahoot is that they have pre-made question banks for lots of different topics and courses, so you can play this with almost no prep work required. Julie Reulbach does a nice job of outlining her experience with Kahoot this year in a blog post here.

Problem-based Learning

As much as possible, I try to start with a problem to solve, instead of starting with a lesson. Sometimes this is a hands-on activity in the style of Al Overwijk & Bruce McLaurin. Sometimes it’s 3-act math in the style of Dan Meyer. Other times it’s a word problem from a textbook stripped down to make it more open (like here & here) and solved on vertical non-permanent surfaces (see next). Students always started by estimating the answer (too low, too high, best guess), collect data/measurements if needed, and then solve. And at whatever point students get stuck, or need to learn something new, that is where I go to the board for a mini-lesson before having groups return to finish solving the original problem given their new knowledge/skills.

Vertical Non-permanent Surfaces

In our visibly random groups of 3, we solve the problems on whiteboards & blackboards. This gets students up out of their chairs, working together, thinking. They try out different ideas because they know it’s easy to erase whatever doesn’t work. It allows me to see everyone’s work all at once and give prompt feedback on their progress. Students can also look around at other boards to get ideas if they’re stuck. More details on VNPSs here.

Khan Academy

Now hold on with your booing & your hissing … Math teachers love to have a hate-on for Khan Academy. It’s not a replacement for a math teacher, and it has it’s disadvantages, but they have some good exercise sets that can be used as homework instead of problem sets from the textbook. At the beginning of the year the homework on KA was optional as I explained here, but in the 2nd semester the homework for my grade 10 academic class was mandatory and tracked daily.
The students sign up with you as their “coach”. You can set a certain exercise as homework with a due date. The site then summarizes who has and who has not finished their homework. You can also see how many problems they have attempted to solve and whether or not they got the correct answer. The advantage for the students is that if they get stuck, there is a “hint” button (which isn’t so much a hint, as the next step explained) and a link to the infamous KA-created video related to that specific problem.

Spiralling

Instead of teaching unit by unit, I have continued spiralling the curriculum. This means teaching every expectation in the curriculum over the first few weeks, albeit in an introductory fashion. Then we cycle through all the material for a 2nd time, delving deeper. And then again a 3rd or maybe 4th time through depending on time. Mary Bourassa has a good explanation here of spiralling.

There are a few smaller things I introduced also such as the wireless keyboard, a “tech tub” with 5 chromebooks for students to borrow when needed, posters of course expectations & mathematical processes on the walls, etc.

For next year:

  • Make my evaluation tools match the group-work, problem-based learning we do in class.
  • Work on recording the observations & conversations that can inform a student’s final grade in addition to the products they create (tests, tasks, projects, etc).
  • Improve my Link Crew class that I taught for the first time last year.

– Laura Wheeler (Teacher @ Ridgemont High School, OCDSB; Ottawa, ON)

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WYR: A pound of dimes or quarters?

One of the bellwork activities I like to use are Would You Rather (WYR) questions.

John Stevens (inspire by ~Hedge~) put together a WYR comparing values of coins based on weight with US coins. I liked the idea & decided to put together my own for the first day of semester 2, but using Canadian currency. Here it is:

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Which choice would you rather? Don’t forget to justify your answer!

– Laura Wheeler (Teacher @ Ridgemont High School, OCDSB; Ottawa, ON)

Equation Headbands

Last year, I read a post about Quadratic Headbanz by Mary Bourassa and thought it sounded like a great game!

I’ve been teaching mostly all MFM2P classes (applied grade 10 Mathematics) for the last two semesters. In the 2P course we only get into quadratic equations superficially. So I’ve been making mostly linear headbands for my groups. I’ve used the game in both my grade 9 and grade 10 applied classes so far. Here’s how it works:

I bought wide ribbon from the Dollar Store & cut lengths long enough to tie around their heads in a bow at the back; about 1 meter long I think? Then I wrote out a variety of linear equations on strips of paper that I taped to the ribbons:IMG_7869

Playing the game:

  • Each student is given an equation headband.
  • They are instructed to put the headband they were given on someone else who is not seated at their group ensuring that the person can’t see the equation you are putting on them.
  • Students walk around the room asking yes/no questions of their classmates. Questions such as “Is my slope positive?”. Classmates may answer yes, no or I don’t know. They are not allowed to ask the same classmate two questions in a row.
  • When they think they know their equation, they come to me and tell me their answer. If wrong, I send them back out to their classmates to keep trying. If they are correct, I remove their headband for them and send them back out to answer the questions of those students still working to determine their equations.

In the past few weeks I added a new step to this game: graphing. Not only did you need to determine your equation, but you had to create a correct graph on a handheld whiteboard with the Cartesian plane.
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My students found it tough but they did it! A good number of my kids knew their equation but were struggling to graph it. It was awesome to watch the stronger students that finished first go back and help teach their peers how to use the slope and y-intercept to make their graph (I had to remind them often not to graph it for them, help them by explaining & asking questions … “don’t touch their marker!”).IMG_7823

I use this game as a bellwork (although it takes longer than the usual bellwork task) on days when we might be doing more individual practice and thus fairly sedentary for the rest of class. This is a great way to have everybody up and moving around the room, talking to different classmates before settling in to the main seat work on a given day.

– Laura Wheeler (Teacher @ Ridgemont High School, OCDSB; Ottawa, ON)

Bell work: Fast fingers

(A continuation of my Bellwork series)

Fast Fingers is an activity I learned about from Link Crew. It makes a great Math warm up, ice breaker or could even be used in between class activities to help break up the day. Here’s how it works:

Pair off your students. I often ask them to find a partner wearing the same colour shirt, or same colour socks, or that has the same last digit in their phone number, etc. This way they pair up with someone other than their best friend that they always choose.

Instruct them to stand face to face & place both hands behind their back. Explain that on the count of three, they will bring their right hand out in front of them with a certain number of fingers showing as seen here (and I always physically demonstrate as I’m explaining):

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The goal is be the first out of your partnership to state the sum of the fingers shown. So for the photo above, the sum would be 5. The first partner to say 5 (often they SHOUT 5!) wins a point. I ask them to keep playing until one of them reaches 10 points.

Once the majority of teams have made it to 10 points, I end that round. Now I have them put their hands back behind their back. This time, I instruct, they will reveal two hands at a time – same task; first person to state the sum of the fingers.

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This past week I tried a variation by asking them to multiply instead. It worked great with one hand at a time; the students were already familiar with the format of the game as we had played it with addition previously. When we advanced to two hands each we ran into the problem where one of the groups thought they needed to multiply 4 different digits (one for each hand). I explained that, no, I would like them to count each person’s two hands as one digit. For example, in the above photo the student on the left has revealed 5 fingers and the student on the right has revealed 8 fingers. The product would be 40 (not 2 x 3 x 4 x 3 = 72). Although perhaps that would be another version of the game to try in the future!

A few reflections:

  • It gets loud. I’m OK with that, but sometimes I wonder what other people think of my classroom :s I always close my classroom door while we do this activity so as to reduce the bother to my colleagues next door (I usually teach w/ my door open … do you?)
  • Some groups finish much faster than others. I try to keep an eye on when the majority of groups have reached 10 points & call the end of the round even if some groups aren’t there yet. Alternatively, I suppose you could see who can get the most points in a set amount of time to ensure everyone is finishing at the same time.
  • A lot of research states that Math should not be a timed activity, and I always give my students as much extra time as they need on evaluations. So I sometimes feel like maybe this isn’t the best activity as it asks them to be the quickest multiplier or adder. Quick does not always mean skilled or effective in Math. It can, but it doesn’t always. But I hope that even if it’s a high pressure activity for some students because it’s timed, the fact that only one other student sees their performance (not the whole class) will help mitigate any stress it causes.

How could you use Fast Fingers in your classroom?

– Laura Wheeler (Teacher @ Ridgemont High School, OCDSB; Ottawa, ON)

Bellwork: “Would you rather” Math

A continuation in my Bellwork series. You can find a description of what “bellwork” is here.

This one I do comes from John StevensWould You Rather blog.

For example, the other day we used this problem from his blog:

This problem required my students to do some currency conversions. These conversions helped my students review ratios & proportions from MFM1P & serves as a warm-up for the proportions they’ll be working with for similar triangles in this MFM2P class.

Some students simply used Google to convert the currency. Some students converted pesos into euros. Others converted euros into pesos. Still others yet converted both into Canadian dollars. I love when my students can see that there is usually more than one way to solve a problem!

The one thing I will admit is that these “would you rather” problems can take us longer than the usual 10-15 minutes I allow for bellwork. So I try to pick very simple ones (sometimes making my own) or I use them as a jumping off point to the day’s main activity – sometimes the “would you rather” IS the day’s activity if it’s complex enough of a problem.

Stay tuned for more Bellwork ideas to come . . .

– Laura Wheeler (Teacher @ Ridgemont High School, OCDSB; Ottawa, ON)

Bellwork: Number Talks in High School

A quick primer on the “bellwork” concept in case you are not yet familiar. Every period I start class with a quick 15 problem/question/activity on the board as the students walk in. They get to work on it right away, without prompting from me. I have a few different types of bellwork that I use. They are meant to take a maximum of 15 minutes (leaving 60 minutes for the activity of the day). In general the students spend 10 minutes doing the activity/problem, and then we spend 5 minutes discussing it as a class and sharing our ideas and strategies.

One of the bellwork types that I have recently incorporated into the mix is called “Number Talk“. The number talk is a way to encourage students’ number sense, flexible thinking about multiple solutions, and the ability to justify or explain their thinking. I learned about this activity via an online sumer course entitled “How to Learn Math” with Stanford prof Jo Boaler. She posted some great videos that really helped me see how to implement the activity in the classroom.

Here’s how I implement the number talk in my classroom:

As they walk in to class, the following is displayed on the board:

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I give them only a couple of minutes to solve (it’s not too complicated). For Number Talks, the majority of our 15 minutes of bellwork time is spent discussing the various strategies.

I start by asking a student for their answer. After which, I ask them to explain their thinking. As they explain their thinking, I write what they’re telling me on the whiteboard for everyone to see. Students often struggle with explaining their thinking clearly, so I will stop & ask them questions whenever they skip a step or don’t explain something fully. I will also put a name to strategies that they are using without even knowing it (distribution, commutation, etc.). The board winds up looking like this at the end:

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In our discussion I place the importance on HOW they arrived at the answer, not what the answer is (it’s pretty easy so most of them get it right). There are lots of video examples online of how to implement a number talk in your classroom. Here’s one such video from a 5th grade classroom: http://youtu.be/Y_SQ4dMxPoY.

My hope is that my students will become more flexible, creative thinkers, that they will learn to clearly explain their thinking & reasoning, and that they will know that there is always more than one solution that will lead us to the answer.

[updated 2017.01.05] Kristin Gray came up with this great idea of Number Talk Karaoke where teachers listen to audio of student explanations for a number talk & teachers can practice scribing student answers. Then teachers can compare & discuss the techniques used to scribe. Genius! Check it out here.

– Laura Wheeler (Teacher @ Ridgemont High School, OCDSB; Ottawa, ON)