Modeling with Mathematics (Math Practice 4) is not just for math! Using models (with or without mathematics) to help students visualize and interact with concepts can (and should!) be done in every content area. Using models helps students analyze relationships in order to draw conclusions. I have seen my 2nd grader practice this standard in her nightly math homework as she uses “counters” when adding tens and ones, for example.
What does this look like in a high school classroom? One example comes from Sunny Lee’s math class last year. Click here to revisit her lesson. Another comes from Becky Nelson’s atom-building lesson in Biology. In my English class using a model may mean that students create a graph as evidence that will help strengthen their argument in a research paper. Or I might have students use mentor texts to explore characteristics of a particular writing genre and then ask them to create their own model writing of that same genre. In history, P.E., or any class, students could create an infographic to explain a process or concept (see end of post for ideas).
A Model Lesson (Modeling with Mathematics in Science!)
Kathryn Smith invited me in to watch Math Practice 4 in action in her Honors Chemistry class. Before I discuss the lesson, however, did you know that Kathryn is a model?!??! Yup! She is a model teacher, reflecting on student performance and then adjusting and improving as needed. In fact, her reflective teaching practice is what led to this amazing modeling with mathematics lesson! Kathryn didn’t simply say, “85% of kids failed this quiz on empirical formulas. Oh, well! The kids did fine last year. They should have studied harder.” She didn’t complain, place blame, or claim she had to move on. Nope. She instead used the results of the formative quiz (which do not go in the gradebook) to inform her next steps and sought out methods to increase student achievement in stoichiometry (don’t worry, I had to look it up as well. Go ahead and click on it….I’ll wait! Still confused? Try this!) Alright, now that you learned something new… let’s examine Kathryn’s next steps. She turned to a science journal called the Journal of Chemical Education to research a bit about inquiry-based lessons in an effort to improve her practice and help her students find success. (Yes, she is a nerdy science geek who subscribes to science journals so she can continue to develop professionally! I LOVE THIS ABOUT HER!)
As she read she had an ah-ha! moment…students can often do the math, but struggle with the conceptual idea of what is actually occurring. As a result, she set a new objective: Students will use models to represent chemical particles to find formulas of chemicals. (Yes…Math Practice 4 to the rescue!)
Kathryn decided to use Legos she already had on hand and set up a lab for the very next day. Prior to the lesson she reviewed notes (using the Notability App on her iPad) and called on students using a random name generator app. (Technology!)
She explained the objective and then students met with their lab groups. During the lab students rotated stations and discussed the models (Collaboration!) so that they had two different sets of data.
The magic happened once the class came back together as a whole group. The Legos were metaphors for moles and Kathryn described molar mass as “Lego mass” to help the students make the connection. Kathryn purposely left some Legos missing so that students would ask the types of questions she knew would lead them to discovery. When she walked students through different reactions with the Legos and prompted them to ask questions, she saw recognition on their faces and heard, “Oh! Now I get it!” over and over again. Students then came to the conclusion that chemical reactions are actually just a rearrangement of matter. Success!
The next day Kathryn used Socrative as a formative assessment and to give them more practice (results did not go in the gradebook!). Students tackled the math in groups (Collaboration!) and as Kathryn circulated she heard kids say, “This is just like the Legos!” The data from Socrative confirmed that more students understood stoichiometry and that students were ready for a summative assessment (results that WILL go in the gradebook!) and guess what? The dismal 15% passing rate on her initial assessment was now a bright, sparkling, sunny 85%. WOW! Modeling with mathematics played a vital role in moving these students toward success. Student success can also be attributed to her approach to teaching. Kathryn observed that her group this year is much more kinesthetic and what worked with last year’s students does not work as well with her current classes. She adjusted accordingly instead of simply using the same materials and lessons as she has in the past. Her ability to reflect, to differentiate, and to modify makes her a model teacher! Thank you for sharing your teaching life with us, Kathryn!
What does Math Practice 4 look like in your classroom? How can you build in more opportunities for students to create models to understand complex concepts? Let me know if you would like to brainstorm ideas for your class! This would also be a fascinating lesson study topic.