Resource: Math Workshop Naturally Differentiated Context
What is Math Workshop?
Let`s begin with a simplified step-by-step overview of the model...
1. The teacher presents the context, which can be a contextualized experience or a book/story to the class seated in a circle. The experience or story must be rooted in context and age appropriate so that students focus on the problem to solve and not unimportant variables.
2. After giving the context the teacher gives students the problem to solve. Students often work in pairs and small groups to collaborate and are encouraged to use tools and record their thinking. The teacher circulates, taking observational notes, asking students to explain their process, and prompting students to move in the direction of using more complex math skills.
3. After work time, students return to the circle and the teacher asks students to share their strategies for solving the problem. The teacher is thoughtful in picking students to share strategies that the class will benefit from hearing. Then the teacher models the strategies shared.
4. The process is repeated the next day, with a review of what happened the day before and the problem within the context changed so that students have the opportunity to experiment using the strategies that they heard about the day before.
5. Over the course of the math unit, students apply strategies that they have heard in Math Workshop to new problems within the same general context.
This is a very basic overview of how teachers can use contextualized, naturally differentiated math contexts within the math workshop model. The model is appropriate for students of all ages and is highly effective in motivating students. Click the pdf below to and learn more about Math Workshop.
Example Series of Math Contexts for Kindergarten/Year 1
Each winter all of our Kindergarten students go on weekly field trips to the ice skating rink. I used this weekly occurrence as a math context to develop number sense, as all of the children shared and were motivated by the experience of going to the rink. Take a look at the graphic below to see how students progress through the big ideas, concepts, and strategies within number sense. When designing the math context and predicting how students may respond, I used this graphic. This graphic shows where each student is in their understanding of number and where their next steps need to be. It is also helpful to print out this graphic and use it while observing the students! Kindergarten students are typically in the bottom third of the graphic.
Here are the contexts I created...
Context One: How many ice skates does our class bring on the bus?
When presenting this question to the class I purposefully omit how many children are in the class. I also purposefully omit that every child brings two ice skates. Part of learning how to solve a math problem is understanding which information is relevant to solving a problem.
This is a complex problem to solve with high numbers. Before beginning work time I make sure to point out the number line, hundred chart, math racks, and manipulatives available to the children. I also remind students to record, draw, and take whatever notes they choose to think through the problem.
After discussing the problem as a whole class and considering the different ways that children might solve the problem, I normally pair up students to work together. I encourage collaboration and discussion during Math Workshop as the children can observe and learn from each other. During this time I circulate, ask questions, and take notes about which strategies the children are using. Often, the less advanced mathematicians draw all of the ice skates and one to one count using tagging. The higher mathematicians often draw lines or the number two repeatedly and skip count to solve.
After work time I invite everyone back to the carpet to share. I purposefully pick children to share certain strategies and then model the strategy a second time.
2. Context Two: How many ice skates do both Kindergarten classes bring on the bus?
3. Context Three: When we go to the rink only five children are allowed to sit on each bench. How many benches will we need?
During each of these contexts the lower level mathematicians often use representational drawings and pictures to think through the problem. As children become more sophisticated mathematicians they are able to use symbols, lines, dots, or numerals to think through and solve the problem. Lower level mathematicians often tag and one to one count to solve the problem while higher level mathematicians solve using skip counting or even doubling. For example, there are 15 students in the class. A high level mathematician could skip count 15 times or double the number 15. Higher level mathematicians are also more able to explain their process and prove their answer. Learning how to explain a math strategy takes time and a certain degree of confidence. By providing a classroom culture that is supportive and celebrates challenge we can help every student take more academic risks and more readily share their thinking process. During these contexts the higher level mathematicians are pushed to try new strategies and explain them while the lower level mathematicians learn from their classmates during pair work and class discussions while being encouraged by their teacher.
Each of these three contexts develop the same set of big ideas, concepts, and strategies and students can apply what they learned in one context to the next. I hope that this post is helpful in planning your own naturally differentiated math contexts. Please share contexts that have worked for you in the comments!