6. Attend to precision.
How are fourth and fifth grade teachers helping their students attend to precision?
How can students be helped to:
- communicate precisely to others
- use clear definitions in discussion with others and in their own reasoning
- state the meaning of the symbols they choose
- careful about specifying units of measure
- calculate accurately and efficiently
- give carefully formulated explanations to each other
What are you doing to help students develop this practice? What makes it hard? What challenges are you encountering?
Re: “calculating accurately and efficiently” – students can improve through daily practice (e.g., multiplication facts) both at school and at home. What are other schools doing to encourage fact fluency? Timed facts tests can be controversial with some parents and staff, yet it’s critically important that students are fluent in their multiplication facts before they can accurately solve multi-digit multiplication and division problems.
In order to be precise in math, one has to practice daily. Fact fluency levels the playing field for students: if they all are automatic with their facts, they can all move forward.
Currently we require students to show all of their work so they can easily refer back to it when explaining to peers how they solved a problem. We use and encourage students to use the proper terms in our math talk. For example, when talking about a “4″ in the tens column, we say “40″. We require students to check their work to make sure it is accurate. A challenge that we face is that students often want to just be done and do their work in their head.
One challenge that we encounter in our classrooms is students want to go too fast. For example, they miss important information in word problems if they are rushing. To attend to precision in our classrooms, students are expected to read the problem 2-3 times, underline important information, and write out the question being asked. Therefore, students follow a process to complete word problems that encourage precision. Students often pair-share with each other to help one another with clear communication.
We are helping students attend to precision by encouraging them to use the correct math vocabulary in discussions with others and in their own reasoning. We are having them build “working definitions” for vocabulary words based on their experiences, and are having them continually revisit these definitions to refine their meanings. These vocabulary words are not only in their math journals, but also on a student-created vocabulary word wall. We regularly incorporate games into our math lessons to reinforce these vocabulary words.
We have daily time scheduled for whole group and small group discussions to help students learn to communicate precisely. We provide open-ended questions and problems to generate discussions and share strategies.
One of the greatest challenges that we are experiencing is that not every child has been exposed to communicating/explaining their thinking. This makes it difficult to have both large and small group discussions because students are unable to clarify how they solved the problem. Another challenge we are experiencing is that students only care about the answer & not the process that it takes to get there. They do not want to go back and check their work or check if their answer makes sense.
There are some pretty basic elements to precision, and then there are more sophisticated, “deeper” elements. On a basic level, we have to require students to be “neat” (or precise) in how they form numerals and line them up to perform calculations. I’ve seen so many of my students make careless errors because they can’t read their own numerals, or they lose track of their work. We can support this by providing them with graphic outlines, graph paper, and feedback. Also on a fairly basic level is vocabulary. No more “gazzinta!” We’ve talked about math journals, dictionaries, or word walls as ways that students can learn and record the precise “math language” that helps them to talk about or write about their words in precise ways.
A great way to help students to see the value of precision is to introduce them to a “real” mathematician, scientist, or even computer programmer. Meeting an adult who needs to be precise in order to see success is powerful for this age group, since they are at that unfortunate point in their development where they want to be a grown up!
Precision can also be supported by the questions we ask, and the rigor we demand. What unit are you speaking about? 49 what? Did you label your work? Can I read your writing?
One of our group members talked about having kids make “instructional videos” demonstrating to their parents or others how they are using a particular strategy. As in reading, publishing your work is a great motivator to be precise!
I have been holding students more accountable on daily work, homework, and tests to precise work by giving them specific feedback on it. I have students correct their work if they have left labels off or put incorrect labels.
I also am trying to teach children to go back and check their work by giving them a post-it note on incorrect problems on tests. They are not allowed to erase the original work, but can have a second chance to solve the problem on the post-it. I have not told them what the error is, but that the problem is incorrect. They need to search their work and redo the problem, fixing the error. I am hoping that they will learn to go back over their work before they are “done” by giving them a chance to fix their tests.
We are helping students attend to precision by having them use correct math vocabulary in discussions with others and in their own reasoning. We have them build “working definitions” as they explore concepts and continually revisit these vocabulary words to refine their meanings. Students keep these “working definitions” in their math journals and then create a vocabulary word wall for the classroom. We incorporate games into our lessons to help solidify these vocabulary words. We also include time in our daily routines for small and large group discussions for students to communicate the process they used to solve a problem. We provide open-ended questions to facilitate and direct discussion.
The challenges that we are encountering are that students do not know how to participate in discussions and communicate their thinking. Students are rushing through their work and are more interested in getting the “answer” than the process of finding the answer. They are not taking the time to go back and check their work and see if their answer makes sense.