Problem Solving for Conceptual Understanding
- 1. By Tina Barkley UNC-Charlotte MAED 5040
- 4. To solve the problem would be rewarding They are curious and like the challenge They are willing to work on a solution They will tend to be more creative with their methods They will remember the process to find a solution They will be able to communicate their own methods effectively
- 5. A very important part of a student centered lesson is effective communication. This communication will be in pairs, small groups and whole group. Opportunities such as this provide social interaction that influences the students' mathematical learning. It develops from the students' questions and findings during explorations of solutions.
- 6. Teachers need to establish rules and procedures at the beginning of the school year Teachers need to support students’ ideas and be non-judgmental Teachers and students should have mutual respect for one another Teachers should provide a trusting environment within the classroom Teachers and students should listen to everyone’s ideas and discussions should be productive
- 7. Teachers should begin to provide these higher level thinking opportunities in the early elementary grades. By doing so, the following will occur: Students will begin to communicate by interaction with others The conceptual development of mathematics will begin to appear The students will be more sophisticated in their reasoning skills This provides a strong base for successful mathematics experiences in future years
- 8. Teachers will become more of a facilitator than an instructor. Characteristics of this type teacher are: Participant (but not too much information) Listener (non-judgmental) Inquirer (asking probing questions to develop critical thinking) Assessor (while students are exploring and discussing) Builder (of the community of learning)
- 9. Teachers should allow students to struggle with their explorations of the problems. It will open the door for students to be more creative and find answers on their own by different investigations and discussions with the learning community. By observing the students during this time, the teacher learns more about planning for instructional choices in future lessons (which gives them help from a different perspective) and can assess the students’ persistence, confidence, cooperation, communication, and the quality of their mathematical abilities.
- 10. Just as all students can share their own method of solving the same problem, teachers can share solutions that have been found in the past and explain why they worked to give the students yet another way to solve a problem. As long all of the solutions are communicated effectively, this helps the student understand conceptually, which is the ultimate goal of teaching mathematics.
- 11. Schoenfeld, who was mentioned earlier, states that “when the mathematics is meaningful and students are interested in what’s going on, the students who need to brush up on their skills seems to do so without too much trouble.” In other words, this is not a concern for teachers who focus on teaching for conceptual understanding. Anything that would need review can be done so at the appropriate time that it surfaces.
- 12. Of course most teachers are concerned with how these new methods will affect scores on standardized testing. This is a legitimate concern. Even though teachers should not “teach to the test”, they must make sure they cover all material on the standard course of study. With problem based learning there is no sequence to the particular concepts and so the teacher may feel as if they do not have control in this area. Also, each problem may take a substantial amount of class time, which may panic a teacher on whether all concepts will be covered by the end of the year.
- 13. What has research revealed about testing? Research states that there are comparable scores from students taught using the problem based method on standardized testing. These tests do not assess problem solving characteristics for which the student will need in the future. Students taught using a problem based method outperform those students taught using the traditional method in this respect. As Latterell, a researcher, noted in 2003, “problem solving is regarded as a process and not a product, standardized tests must be well constructed to measure problem solving adequately.” At this time, standardized testing is not an accurate indicator of this ability.
- 14. In conclusion… Schoenfeld states that “mathematical thinking consists of a lot more than knowing facts, theorems, techniques, etc.” Teachers should be evaluating what students can actually do in mathematics and not what they know from memory. To do this, the traditional method of teaching must be replaced with a more student centered instructional plan. Teachers must make it a priority to understand their students’ needs and provide optimal lessons for the students to become excellent problem solvers. By doing so, they will prepare students to enter the real world with the knowledge and conceptual understanding to be successful.