Communication is an important part of mathematics. As a math team in our school, along with others involved with mathematical education, we have discussed what Strong Work in Math looks like. We discussed many different components including Mathematical Inquiry, Demonstration of Knowledge, and Work Habits. One component of this discussion was Mathematical Communication. Students are strong mathematical communicators if they can
a) Show their work using writing, charts, diagrams, etc
b) Use appropriate mathematical terminology and notation
c) Organize complex ideas
d) Use metacognition to help explain the process they undergo during problem solving.
Weekly, I present my students with a problem I would like them to solve to demonstrate their inquiry and mathematical communication skills. I like to have the students journal about their problem. As Tuttle (2005) states “Writing provides unique evidence teachers can use to assess student mathematics skills. The answer to a problem alone does not tell teachers how students are learning.”
Unfortunately, not all students are great mathematical writers…yet. Frequently, students will say to me “I know what I’m doing, but I don’t know how to write it”. My response is “Show Me!”
Often, my greatest understanding of student thinking comes from the conversations I have with them. In these conversations, I can find out what strategies they used in problem solving, what stumbling blocks they encountered and how they overcame them, how their conversations with others in their math community helped them to develop their solutions, and how or why they know their solutions are correct.
This year, in order to be able to more frequently learn how students are solving problems, I am using an iPad app called ‘Show Me’. With this app, students with 1:1 iPads are able to demonstrate and explain their understanding. The app is like a digital whiteboard where students can show the steps to their problems. It allows them to import photos and draw on them, all while recording their voice explaining their thinking. Their recordings are then stored online and only those with access to the link can view them. Sometimes I will explicitly ask students to create a ‘Show Me’ just so I can hear them discuss specific aspects of their problem. I will give them guiding questions on some of the things I would like them to talk about. Other times, students choose to create a ShowMe to help explain the strategies they used in problem solving, as in the one included below. Now that they have tried the app and see its benefits, I have students requesting to use the app to better demonstrate their understanding.
View a ShowMe here.
Here's another example.
In order to gain more insight into the effectiveness of this tool, I surveyed all 50 of my students to determine if they prefer to express themselves mathematically using ShowMe, Written Responses, Face-to-Face conversations, iMovie, or other methods. The survey also included written questions about the effectiveness of the tool. Some of the results are as follows:
Advantages of Show Me
“Show Me can sort of help get your ideas out because you are talking about them and not just writing about them. It also helps that you can put photos into the project.”
“You can talk while showing what you did or are doing.”
Disadvantages of Show Me
“I find it difficult do be accurate drawing lines and other drawing things.”
“It picks up every little noise so it takes a long time to get it perfectly silent except for your voice.”
Which would you choose to do in order to best communicate your thinking in Math?
- Show Me = 42% of students
- iMovie = 8% of students
- Written Response = 26% of students
- Face-to-Face conversations with the teacher = 24% of students
- Other (specify)= 0%
Though I do think that mathematical writing is important, I also think it is a skill that needs to be developed. I am currently working with my students to guide them through becoming better mathematical communicators. This includes thinking about their thinking (metacognition) as well as learning how to use math as language itself (through showing their work, using appropriate notation and organizing complex ideas). For those students who have trouble communicating in writing or prefer speaking, I appreciate Show Me. I also enjoy listening to the students as it does provide me with a different kind of evidence of their learning.