So here we are, a couple weeks into the new school year and by now math lessons are well under way. In RSU 5, teachers teaching grades kindergarten through sixth grade are now all officially in the same boat; we are teaching a brand new curriculum, and using a brand new online data reporting system. For this first entry of the new year, I will address beginning-of-the-year teaching strategies as they relate to the instructional shifts inherent in the new Everyday Math 4 units.
I could go on and on about the things I personally like about the instructional shifts in the new Everyday Math program, but I want to focus here on the challenges that come with these shifts. One big reason to celebrate what is happening with the new EM4 units (and the similar shifts that are happening in other popular math programs) is this focus on understanding, collaborating with peers, and communicating students' mathematical thinking can and should lead to an important outcome often missing from the K-6 math experience: Joy. This is not to say that before this edition of the program there was no joy in learning math, but with the greater focus on understanding and communicating mathematical concepts, students gain greater access to the art of solving problems.
Whether it is through landscaping in the back yard, measuring ingredients of a recipe, or solving a labor dispute, real problem solving is part of our human nature, and we often solve problems with help from our peers. Playing games that involve strategy is something that we do to entertain ourselves when there aren't fun problems to solve in our immediate vicinity. Whether it is football, Monopoly, Risk, Pac-Man (Sorry, I grew up in the '70s and '80s), KenKen, Sudoku, or the latest edition of World of Warcraft, we create imaginary problem solving scenarios to occupy and activate our brains because it is fun to solve problems. If we are lucky, we will grow up and get paid to solve the kinds of problems we like to solve. Rarely will we be asked to solve those problems all by ourselves, but we need to be able to perform the foundational operations, with confidence, by ourselves. The new EM4 lessons, via the Common Core Standards for Mathematical Content and Practice, aim to provide opportunities for students to gain confidence in their foundational understanding of operations and algorithms, so they have the tools they need to solve interesting and engaging problems. Sometimes they will solve problems independently, but more often your students will be working in groups and pairs to solve problems.
So what is the best way to prepare students to work collaboratively and to communicate their mathematical thinking (both to each other, and on paper)? They may not have done this as much in the past, and now they are suddenly expected to do it A LOT this year.
Your students may not be used to spending so much time working collaboratively to solve problems, and they may not be comfortable or confident communicating their mathematical thinking. Especially at first, some students might miss being told how to solve problems and they may wonder why that is not happening so much anymore. Some may even have conditioned themselves into (sadistically?) enjoying the old fashioned skill-and-drill number work, but transitioning away from the more traditional "I do, we do, you do, then you do it over and over again" style of teaching procedural math leaves some students expecting to be told how to solve a problem before being given the task to solve a problem. They are used to being given the strategies to solve problems, rather than being given time and collaborators to help discover strategies and find their own solutions.
For this transition to happen, students need opportunities to practice solving problems in teams and with partners. It is important to not just dive into collaborative work with long periods of unstructured time for groups to brainstorm... Structure their time in segments at first with specific tasks. Give them a few minutes to determine exactly what it is they need to do, and a few more minutes to determine all the tools and information they have to solve the problem. Check in with them frequently to make sure they don't check out and that they are actively seeking to answer questions to overcome roadblocks that might be holding them back. Open Response lessons will allow for this practice, and even give a second day to review their work and make revisions.
Sometimes a specific protocol can help. In an earlier blog entry, having specific assigned roles when working in groups was discussed. One person can be given the role of ambassador, with special permission to check in with other groups to see what their strategies are. Another can be in charge of taking notes, recording all ideas and outlining them or diagramming them. Another group member can be in charge of making and/ or checking all calculations. Every student should be actively participating.
Students will be expected to independently explain their mathematical thinking very often this year! This will be in assignments and on assessments, but it will also occur regularly when they work with a partner or a group. Students will have to share their thinking with peers, and evaluate each other's mathematical thinking. They start this in kindergarten, when their teachers help them decompose their solutions and quantitative grouping. Teachers might ask, "How did you know the blue pencil was longer than the pink pencil?" or, "You told me you made a triangle and a rectangle. Can you tell me how you know that one is the triangle?" In the first grade, teachers work throughout the year to help children write their thinking on paper and draw pictures to support and represent their thinking. By the time this year's first graders reach the second grade, they will have had two years of experience communicating their mathematical thinking.
This year's fourth, fifth and sixth graders have not had as much experience with this kind of work, and it may be difficult for some of them. Often high performing students have trouble "explaining" why or how they solved a problem the way they did. "I just knew it," you will hear, or, "I did it in my head." Just like with 5 and 6 year olds, asking a lot of "how do you know" questions will help them deconstruct their strategies. "How do you know the area of that figure is 64 square centimeters? What is a 'square centimeter,' and how does it differ from a regular centimeter? How do you know which is the width and which is the length? Does that matter? Why? What does your drawing represent? Can you can prove your method is correct with another example?"
It is a transition year for us, with new, updated units, and new total alignment to Common Core standards, so give yourself and your students time to practice and get comfortable with the changes.
Make sure expectations are clear. Students should be using indoor voices when solving problems and collaborating, and group/ partner work should be monitored with frequent check-ins, either on a group-by-group basis (circulating from table to table), or by checking in with all groups at once. This time of year, both teachers and students will need to practice, practice, practice.