I've done a lot of reading this week and I feel like I have a good handle on math workshop and what it will look like in my classroom this year!
If you haven't yet read this book:
I was wrapped up in creating math choice boards and centers, classroom organization and all of that fun stuff, but really it is less about that and more about facilitating high-quality math experiences for your students.
John Tapper, in his book Solving for Why, talks about three stages of math understanding that can help guide us toward meaningful instruction for our students:
1. The use of models: models are a cognitive structure that a student uses to understand a mathematical idea. The models can be a concrete, representational, or abstract analogy. Base Ten Blocks are an example of a model for place value/base ten system. Another example of a model is a an open number line for addition and subtraction or fractions.
2. The use of strategies: A strategy is more complex. Strategies use models in a specific context to solve a problem and help students to generalize approaches to mathematics. Strategies are best learned by students as they find a need for them in their problem solving experiences. It usually is less effective to "teach" students strategies before they have had a chance to explore a concept. Using landmark numbers or tens when adding or subtracting is an example of a strategy.
3. The use of algorithms: Algorithms are the shortcuts or procedures we use to do something efficiently over and over. Algorithms become counter-productive when students don't understand the concept behind it (i.e., WHY it works). Thus, students need to go through the model and strategy stages BEFORE landing on an algorithm. Otherwise, problems will arise down the road.
In the book, Tapper goes into much more detail about each of these stages, but you get the general idea. Most important is that you can diagnose most of the issues that students are having with math by analyzing their use of algorithms, strategies and models. Chances are your strugglers haven't built up strong models and/or strategies to solidify their understanding of certain concepts, which has a snowball effect on their math learning.
So back to math workshop! Math workshop becomes the organizational structure that allows you to help students build bridges between these math stages!
John Tapper structures math workshop with a "Main Lesson-Menu Lesson Plan" format (which I will be utilizing this fall in my classroom). It looks like this:
- Big Idea/Focus (Concept Students are Learning)
- Launch (5-10 minutes) - Activate prior knowledge and connect to new concepts upcoming.
- Explore/Main Lesson (20-30 min) - an investigation or inquiry for students that involves lots of student interaction and talking. Teacher facilitates with good questioning techniques. Will usually end with one or two problem solving activities (related to the big idea/main lesson) that students can work on independently or with a partner.
- Menu (30+ minutes) - A weekly menu of activities to reinforce concepts being taught/learned. Usually involves at least 5 "required" menu activities and a few optional choices. The menu is broken into these main categories: (1) Finish Main Lesson Work, (2) Number & Operations (computation practice), (3) Problem to Solve (4) Math Game (related to big idea) and (5) Math Journal (prompts given that focus on big idea).
- While students are working on menu activities, I can work with students independently and in small groups.
I have re-created John Tapper's form for planning your lesson and menu work. I have provided a PDf format, and the editable Powerpoint file (in case you like to type in your plans).
I know this looks a bit different from what I was thinking a couple Mondays ago...but I am new to this and my ideas about math workshop are evolving!!
I love this approach because it offers so much flexibility and it has a strong focus on problem solving and higher level thinking. I also love how the menu lasts all week, making it lower maintenance for me. Within the menu activities, differentiated choices are offered to accommodate your different learners (he suggests using "one dot problems" (easier), "two dot problems" (medium), "three dot problems" (challenging) for both the numbers and operations and problem-solving menu choices.
I plan to have students use a "Math Workshop" folder to collect the work they do throughout the week, which can double as a portfolio. They could keep a selection of problems they solve throughout the school year as a record of their evolving math thinking. This, along with their math journal, would make a great discussion piece during parent teacher conferences. All other weekly math work and menu work could be sent home each week.
My next mission is to come up with the activities that will be used for the weekly menu: math problems, journal prompts, and games! I plan to create some things and purchase a few too. Marilyn Burns book "About Teaching Mathematics" has many suggested whole class and menu problem solving activities. I have a very, very old edition of that book which I am going to use, because her new edition is outrageously expensive.
Have a great week!
Love and peace,