People often mock me when I talk of paperless math (and rest assured, I still believe in using paper within a math class) and using mental math. However, I see a real value in using student discourse, mental math and multimedia tools within a math lesson. I used the following with a group of fifth graders and the students have been moving further toward meaningful dialogue and conceptual thinking.
Math Discourse / Mental Math
Types of Apps:
Drawing App
Voice App
Comic App
Camera
Survey / Forms
Bonus: Splice
Step One:
Mental math problem:
317+764
Step Two:
Have students write out their answers afterward using a drawing app. Let them explain, verbally, their process using a voice app.
Step Three:
Explain the discourse process and then have them record the discourse with a partner.
Sample Questions:
Clarifying
What process did you use?
Why did you choose to use that process?
Why did you choose that step? (find a specific step)
Can you explain what you were thinking?
What part was challenging for you? How did you get past the challenge?
Analytical Questions
Why does your process work? Is there a scenario where that might not work?
What can you do to prove to me that your process was correct?
Is there another way to look at this?
How did you arrive at that conclusion?
Is there a more efficient way to do this process?
Diagnostic Questions (If You’re Stuck)
What did you do to get to that point?
What part are you struggling with?
Is there another strategy you can use from another math process?
Can you predict the answer and work backward?
What do you already know? Can you build on this?
What information are you missing?
Step Four:
Students can “bump” the audio with one another. Then, individually, students now listen to the discourse and rate themselves on how they did as a pair (using a survey app)
| Falls Far Below | Approaches | Meets | Exceeds | |
| Clarifying Questions: How well did you do at asking clarifying questions? | I asked one of the questions. I had a hard time figuring out what a clarifying question was. | I asked multiple questions using the guide that you gave me. I tried to use a follow-up question. | I used the questions in my own words and asked follow-up questions. | I had a full conversation where we each talked about our process with questions and answers in our own words. |
| Analytical Questions: How well did you at asking analytical questions? | I asked one of the questions. I had a hard time figuring out what an analytical question was. | I asked multiple questions using the guide that you gave me. I tried to use a follow-up question. | I used the questions in my own words and asked follow-up questions. | I had a full conversation where we each talked about our process with questions and answers in our own words. |
| Diagnostic (If You’re Stuck) Questions: How well did you do at helping one another when you were stuck? | I wasn’t able to determine when or how my partner was stuck. | I tried to ask diagnostic questions, but I couldnt find the mistake. Or I solved it for my partner. | I asked diagnostic questions that helped my partner figure out his or her mistakes. | My partner and I both used diagnostic questions to have a full conversation about how to solve the problem differently. |
| Answers: How well did you do at answering questions? | I used one-word answers. | I used complete sentences. | I used complete sentences and gave a reason why. | I used complete sentences and asked questions as well. |
| Math Vocabulary: To what extent did you use correct math vocabulary? | I didn’t use any math vocabulary. | I used one math vocabulary words. | I used several math vocabulary words. | I used math vocabulary words without even thinking about the fact that they were vocabulary words. |
Step Five:
Try it again with a new partner. This time, don’t use the rubric.
Step Six:
Reflection
Option 1: Using e-mail or a word processing app, describe, in a sentence how your process was similar or different from the process of your neighbors.
Option 2: Using e-mail or a word processing app, describe why it’s important to think through one's process
Step Seven:
Using a video app, take your notes, images and audio and put it altogether into a presentation about how to solve this type of problem. Send the final product to your teacher. Or you can create a slideshow using comic program and show the mental process with thought bubbles and character dialogue.
John T. Spencer is a teacher in Phoenix, AZ who blogs at Education Rethink. He recently finished Pencil Me In, an allegory for educational technology and he's working onSustainable Start, a book for new teachers. You can connect with him on Twitter @johntspencer