With the very real chance that we will be teaching virtually at some point this coming school year, I've been thinking a lot about the integrity of students' work. I felt that this past spring when we quickly converted our physical classrooms into digital, I no longer had any control over the cheating that took place. Students who were struggling in the face-to-face setting were suddenly getting all the level 1 type questions correct. Not one single error. However, they were unable to even begin a higher level question. You know, the type that you can't just plug into an app and get the correct answer?
I feel that there are a few items that need to be addressed. Why do the students feel the need to cheat? Lack of confidence? Laziness? The need to get an A? The fear of looking stupid? All of the above? I believe that all students want to be good at math. They don't want to look incompetent in front of their peers or teacher. Somewhere along the way, we have to make them feel comfortable with being uncomfortable.
I think I could write an entire book on addressing the concerns that I have above, but for this post, I'm going to focus on how students can use a math app to help them learn, rather than blindly copying the solution.
I downloaded the app: Microsoft Math Solver - HW app
1. Learn from the worked-out solution.
Instead of giving an assignment where the student must complete problems on paper, assign them a problem where they have to explain the steps in a video. Yes, they can use a math app to give them the steps, but they will have to internalize and verbalize them as well.
In the first image, you can see the problem that I scanned from a textbook.
The middle image is the steps the program took in order to get the solution.
If you click on the arrows on the right side of the screen, the program will explain each step (3rd image).
Asking the students to create a video explaining the steps ensures that the students are at least looking at this information on the app, rather than only copying the steps.
Am I suggesting that you stop assigning written assignments? No, but include videos once in a while as formative assessment. Plus, watching a video from each student takes a lot more of your time than looking over a written assignment.
An added bonus, is that you can upload their videos to a class website for others to view.
2. Which method do you prefer?
If the app shows more than one way to solve a problem, have students compare the methods. Do they like one method better than another? Why? How are the methods similar? How are they different? Are there situations where you would use one method over another?
Here is that same problem from above, but now we can see that it was solved graphically instead of algebraically.
3. Learn from your past.
This particular app has a "history" button and the ability to bookmark certain questions. By using either feature (bookmark or history), a student can revisit problems they haven't mastered yet. They can scaffold as needed with some students needing to look at every step for help, and other needing to only check the solution.
I just read something interesting the other day about how many students really don't know how to study for math. Many times, the students will look over and complete question they already know. Most effective would be practicing the problems that they haven't mastered. I read this in Powerful Teaching by Pooja K Agarwal and Patrice M Bain. This information took me by surprise at first. But after refection it made sense that some students would want to boost their confidence with problems that made them feel successful.
This is an opportunity for us educators to help students figure out what they don't know. To get comfortable being uncomfortable. I want to encourage my students to tackle the problems that they don't yet know.
4. Partner/Group Work
One student has use of the app, the rest of the students in the group are working on a problem. The student with the app will scan the problem and help the other students if they need assistance. Repeat this with a different student having access to the app.
I visualized this taking place in-person, but I suppose it could work virtually as well. If the conference software you use allows for breakout rooms, this would be a group activity you could give a try.
5. Open Middle
Create or use open middle problems (CLICK HERE) or have the students work backwards and have the them check with the app.
For example: "Write a system of equations, where the solution would be in the third quadrant."
Another example: 2x + ?y = 43 and 5x + 3y = 41. The solution is (4, 7), what is the missing value?
Once they think they have the correct system, it can be scanned in the app to determine if (4,7) is the solution.
6. Learn Something New
Give the students problems they've never seen before and ask them to complete them using a math app all while trying to understand what is going on. I suppose this would be similar to flipping the classroom, but instead of a video they're using the app. Then in class ask the students to explain how to solve the problem, what methods they used and understood, and any connections that can be made to previously learned material.
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