1. Make sense of problems and persevere in solving them.
How are fourth and fifth grade teachers helping their students make sense of problems? During a recent online course focused on problem solving in elementary classrooms, these thoughts were shared in our discussions. I’ve received permission to quote them and provide them here as starting points we all might use to have a conversation.
Matt says,
My former 5th grade teammate let me hi-jack her Math class so I could try out a Math Forum PoW. The experience was very informative to me as a teacher and very engaging for the students.
The process of “noticing and wondering” seemed to perplex the kids. They weren’t quite sure how to respond. I gave them some examples to get things going but I can see that there is a need to do this on a regular process in order to establish problem solving routines and expectations. Before sending them on their way, we also talked about some different strategies for attacking a problem so they weren’t just left to “figure it out” without some ways in which to think about the problem.
Once students started working on the problem, it was very interesting to see who was comfortable with ambiguity and who really needed a concrete right/wrong answer. They would show me an answer and ask, “Am I right?” My responses were “Tell me your thinking. How did you arrive at your answer? Is there another way to solve the problem to see if you get the same answer?” Some really flourished and others floundered.
After a bit of time, some of the students were arriving at the right answer while others were still trying different strategies. At this point I stopped the students and explained that I didn’t want an answer to the problem but am more interested in how they solved/ tried to solve the problem. This is where I was pleasantly surprised. The students share a variety of ways they decided to approach the problem and all of them were viable/ plausible considering the problem.
After talking about the strategies I told the students that some of them had the right answers and that others still has some thinking to do. Instead of giving them the answer, I told them they had to show me their work and explain their thinking before I told them the answer was correct or not. This really got the students frustrated but excited at the same time. Many of them rushed up to me at the end of the lesson to explain their thought process. It added an edge of anticipation and actually got them excited about Math.
We felt that Matt did a nice job of not telling students whether they were right or wrong in their solution until they had really explained their strategies of solving the problem to him. This helped students persevere in learning to talk about their work and explain their math thinking. Many teachers are currently giving their students time to think independently (3-5 minutes depending on the grade level) so that they can try to make sense of the problem before having the chance to collaborate with peers.
We noticed that since the teacher did not want an “answer” right away, this might take the pressure off if a student is confused or nervous about getting the right answer. We like the idea of starting a class dialogue about how you might begin to solve it. This can trigger understanding and new ideas that can be valuable to others.
Part of our math day includes using a spiralling program that has some short problems to solve. During this time, students are required to do the problems on their own. They can use the resources within the book (glossary and notes from previous problems). We always go over the problems together and they are encouraged to write the correct answer and/or copy strategies that we used, so they can refer back to it the next time. This is a low-risk situation, as there is no “consequence” of having an incorrect answer; I don’t even correct the book, the students correct their own work. Over the year, they become more confident in trying a problem. Students also look forward to sharing their answers on the Smartboard when we correct. This also helps develop a culture of it’s okay to make mistakes. The goal is to try to figure out the problem, not necessarily get it right.
These descriptions creating a “low-risk situation”are great. I think particularly with students who might be disengaged or just not confident that they can solve problems, the more pressure we can remove, the better it is.
Good teachers allow students to have positive and inquisitive attitudes as they pursue their different endeavors. These attitudes contribute to their accomplishments. A good math classroom helps students develop these same inquisitive attitudes as they work through each activity. Learning by doing should be the foundation of good math classroom.
It’s important that students are able to read informational text accurately – otherwise, they will not be able to choose an appropriate strategy for solving a multi-step problem. We can help students make sense of a problem by reading through a problem together, discuss relevant vocabulary words, highlight the key parts of a problem (and discuss which parts are irrelevant to the problem), etc.
Another way to help students make sense of problems is through having students showcase their work. Several students could show their varying approaches to a particular problem, with partners or in small groups. This could foster rich discussion among students – we often find that students learn best from one another.
As I’ve used the Math Forum’s “I Notice, I Wonder” activity with students, I’ve found that what might appear to be an irrelevant part of the problem might just be the part that hooks a student in to try to make sense of it.
Hi Matt,
This is a function of “schooling” these students in grades K-4. You have inherited previous practices that emphasized “one answer only.” The work of teachers in the CCSS that are first helping students to develop the “habits of mind” embodied in the CCSS Math Practices first have to do specific lessons on risk taking, giving and receiving feedback, and discussion. Kids are so “schooled” to expect the interaction pattern that goes 1. Teacher asks questions, 2. Kids raise hands, 3. Teacher calls on ONE kid (usually the one who knows the answer), 4. Kid answers, 5. Teacher responds to that student, repeat. Kids need to be taught NOT to raise their hands and to speak directly to one another without having an adult always serving as an intermediary. You can do this is any content area, and once they enjoy the benefits of a more natural conversational style, they will easily begin to talk to one another instead of trying to please you or get the “right” answer.