Let’s think more about the idea of deep practice for homework and what it might look like. The children that I am coaching to learn Algebra I are encouraged to complete the homework the idea of deep practice.
We are trying to move learners from “If at first you don’t succeed, hide all evidence that you tried!” an attitude of “If at first you don’t succeed, try, try again.”
When homework is assigned, part of the homework is to complete the assignment in deep practice. All complete solutions are posted my webpage and the answers only are posted on the Algebra I team’s MOODLE course (password protected).
Students are to work a problem, check the answer, and try again if necessary. To keep them from getting stuck, if they are not successful after three attempts they should move on to another problem, question, or task. So that we can diagnose their error in class, the student should simply x out incorrect work and try again.
When students come to class, they should know that their answers are correct or know where they have questions. As our class is getting settled, students should be asking and answer each other’s questions. I wander around and document how many answers are correct and how many they had to do in deep practice. Here’s an example of a student’s work on a traditional Algebra I homework assignment. (I just asked for a random homework page that showed deep practice from the students my last class on Friday.)
The diagnosis for the student above is really simple since there is evidence of her work and thinking. In problem number 4, there was a simple division error; she reduced 12/15 incorrectly the first time. In questions 5 and 16 (and other problems on the page) we can identify a pattern in her work. Her fundamental misunderstanding is about Integers. Subtracting is the same as adding a negative. The negative is missing in step two for this child every time the variable term is subtracted from a constant. A simple-to-fix error IF it can be diagnosed. (The correction for number 5 is also not correct…sigh…there is still so much work to do.) We should make the time to coach our students to value proof-reading their work and analyzing their mistakes for learning.
As fate would have it, I ran into the mother of the child whose work is displayed above the same day that I collected this example. Mom stopped me to tell me a story about her child, M. According to M and her mother, M has not felt successful in previous math classes. M’s mom says math is now M’s “favorite class”. Her confidence has increased significantly and is still increasing. M also feels comfortable asking you questions and knowing you will willingly answer them. Mom also says the biggest change in M is her willingness to make a mistake. She quoted her child “Mom, Ms. Gough has taught me that it is okay to make a mistake. We learn from them. It’s how we learn.”
“…it is okay to make a mistake. We learn from them. It’s how we learn.”
Let me pause here and say that I do not grade homework; I do not give credit for homework; I do not count homework in any way. We do, however, document homework; we also document attendance in Office Hours. My students help me with this documentation. If and when a student is disappointed or frustrated with their progress, we can look at their rate of homework completion and how much deep practice is attempted compared to the number of times they come for addition coaching during Office Hours. Often the data is very revealing to a student. I struggle with my homework, and I have questions, but I never come to work on these questions. Hmm… what steps could be taken to begin to improve?
One more thing about the above work…We have had to work really hard to correct a misunderstanding with kids that you can see in the above work. She has documented that she had 6 correct answers and 6 deep practice. From my point of view, she has 11 correct, and 1 that still needs work. It has taken about 3 months to get kids to the understanding that their homework is “correct” if they arrived at answer with good work no matter how many times they had to try.
We are trying to move learners from “If at first you don’t succeed, hide all evidence that you tried!” to M’s attitude of “…it is okay to make a mistake. We learn from them. It’s how we learn.”
Fascinating example, given that student did not engage in another round of deep practice for #5. And isn’t the solution to #26 incorrect, too? (Answer is correct, but work is flawed.) In this case, why might the student not be reading the posted solution more carefully? Is this really “deep practice” happening? In this particular case, what was intervention used? What was the ice on the berg beneath the surface?
Love the parent story and student quote! May we all learn from our mistakes and our prototypes.