Creating Groups for Group Work

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If you plan on the students working in pairs or groups, a matching activity with index cards is a great way to insert a quick review activity into the day without it taking up too much time.

For example, if I plan on the students working in groups of 4, then I’ll pick some topic I think they need to review (for this example, I’ll pick Properties), then on four of the index cards, there will be an equation that shows the Commutative Property of Addition, four will have the Distributive Property, and so on.

I distribute the cards to the students (most of the time, as they’re entering class) and when it’s time for group work, I’ll instruct them to find their group according to which property is on their card.

If I know that certain students do not need to be in the same group, or if I want to make sure the groups have an equal number of higher-level and lower-level students, I will actually plan those groups in advance, and write the name of the student on the index cards as well. This also keeps students from switching cards if they find themselves in a group they don’t particularly want to be in.

Sometimes, for larger groups, I will also write a number on their card that represents the number of people in their group. That way, if an extra person shows up, they can debate on who’s the odd man out.

This works for any review topic. For solving equations, or anything with solutions, students could find their group based on their problems having the same answer. An inequality on one card and it’s matching graph on another would be great for a student to find their partner. So would a card that has graph of a horizontal line and a card that says “slope = 0.” Even definitions or theorems could be halved so that one student has “The sum of complementary angles” and the other student has “equals 90 degrees.”

The discussions that students have while trying to figure out how to organize themselves are absolutely wonderful to listen to.

On top of that, since it’s only one problem on one card, most students don’t even think they’re doing review “work.”

** To keep this from being time consuming, play an upbeat song and inform students they need to be in their groups by the time the song ends. Students love it.

Math Notebooks

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Around my third year of teaching, I started giving notebook quizzes and have kept this procedure ever since. (Not an “open notes” quiz, it’s basically just a notebook check). Many teachers I talk to don’t this, but I like notebook quizzes for two reasons. First, students are more diligent about taking notes and staying organized. Second, this is one of the ways my students are held accountable in my class for their Do-Nows or Warm-Ups, since I rarely collect or grade them.

A few teachers actually collect student notebooks, but I find the prospect of having to go through 35 notebooks very daunting!

A notebook quiz in my class consists of basic questions such as “What was the answer to do now #2 on the 17th?” or “In the notes section on the 14th, example 2 was a rectangle. One of the dimensions was (2x + 1). What was the other dimension?”

When I decide it’s time for a notebook quiz, I simply choose a student’s notebook, making sure it looks reasonable in regards to being dated, with organized do-nows, notes, etc.

The person whose notebook I’ve used gets a 100 by default. When the quizzes are done, we do a paper swap and grade them as a class. I don’t have to be organized, I don’t have to create a quiz in advance, and I don’t have to grade them.

This also has helped in regards to student absences since students are responsible for getting any notes they may have missed while they were out.

I only do this about once every 3 weeks and never announce them in advance.

NOTE: First, of course, I have to lay down the groundwork for the students during the first few weeks of class. Most students have poor note-taking skills and have to be taught to date their notes, label the sections such as “Do Now” or “Notes,” number their problems, etc.

Letters to a Fellow Math Student

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I used to never have much success with writing in math. The majority of what I got back read something like this:

“To solve a two step equation … first you subtract 2, then you divide by 6 and the answer is 3. That’s how you solve a two-step equation.”

So I ended up with stacks of papers that read like this, and really, what do I do with these? It simply showed me that the student knows the arithmetic of how to solve this particular two step equation. As far as it being a method for assessing student learning, I usually knew beforehand which students knew how to solve 2 step equations and which students struggled – simply from having walked around the room during independent practice.

Then I did one writing assignment that produced wonderful results. I told the students there was a Pre-Algebra class or another Algebra class in the building that was learning about two-step equations (or whatever topic I wanted them to write about), and they were having a hard time of it. So their assignment was to write a letter to a “fellow student” and share what they have learned and know about solving two-steps. I then gave them a list of requirements: they must use the words constant, coefficient, isolating the variable, explain how to check a solution, etc.

And those results were wonderful, I think because the students knew the letters were actually going to be read by somebody who might find them useful. Students who usually wrote big to make it look like they wrote more than they did were now trying to write smaller and smaller to cram more words at the bottom of the page. They added illustrations and elaborated and produced beautiful products.

The only catch is that this is a one time deal. In other words, you can only disguise a writing assignment as a letter once. Do it again and the quality quickly goes downhill.

Make sure you do actually give these letters to a fellow math teacher. It makes a wonderful assignment for the receiving teacher as students can check for errors, etc.

Finally, another thing this taught me is that if you want to improve the quality of a non-letter writing prompt, or any summarizing assignment in general, provide a list of requirements.

Grading Tests, Quizzes and Classroom Management

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I have rarely had the need to bring a stack of tests or quizzes home to grade. In fact, the majority are graded before class is over.

It helps that I can grade papers very quickly. And no, they’re never multiple choice or on a scan tron, I’m a firm believer of open ended questions when it comes to assessing students.

This is how I do it: I sit in front of the room on my stool as the students take their test or quiz. (Most of the time, I’m doing the test myself to create a key to use and to check, yet again, that there are no typos in the problems). They bring them up to me when they finish, and I grade them then and there. Here’s why I thought to comment on this procedure.

First is that the students love the immediate feedback. When my students first realize this is how I do things, they always comment on some teacher from a previous year who took weeks to return things to them.

But most importantly, it helps with classroom management. Students are restless after taking a long assessment, and they think they can whisper to their neighbor, whether their neighbor is finished or not. But my students know they’ll have to wait the next day to find out their grade if they make even one peep before the whole class is done. They hate this, especially when they know their graded paper is in my hand. I no longer have issues with talking during a test.

And I’ve never had a problem with a student rushing through just to get a grade. Students who take the whole period know that they can come back at the next class change and I’ll have theirs scored already, too.

Of course, I teach Algebra 1 and Pre-Algebra. I doubt I’d be able to do this with Calculus or Algebra II. And I do not in the least envy the essays English teachers have to pour through.