Benefits of using Problems of the Week as a regular part of your math
PoWs have great motivational value for students:
- Many students comment that PoWs are fun!
- Submitting solutions online provides the potential for a different audience. Many students are inspired to apply greater effort for an outside reader. By the same token, they often are more receptive to feedback they receive from them.
- We publish some of the exemplary online POW solutions that we receive along with Gold and Silver lists. The potential for recognition on the Internet is a powerful motivator.
PoWs inform and facilitate the teaching process:
- They allow teachers to examine and discuss students’ work and refine their teaching practices based on what they learn from it. Student solutions to the PoWs provide a window into the thinking of students and can serve as a valuable tool for assessing their progress.
- PoWs allow teachers to differentiate instruction among students at various developmental levels. They lend themselves to a variety of strategies and levels of sophistication. Most often they don’t depend on any specific procedure or algorithm. Students can approach them from whatever level of understanding and skill they possess. Teachers may simplify or scaffold problems to make them more accessible to students at lower developmental levels, or extend them to challenge those who are ready. It is not uncommon for the same problem to elicit both guess-and-test as well as algebraic solutions.
- PoWs can be used flexibly to accommodate students with different learning styles. Students may work individually or in pairs or groups. PoWs take advantage of students’ learning strengths; visual learners may draw pictures or diagrams, kinesthetic learners might use manipulatives or act out a situation, analytic learners can create tables.
- PoWs give students experience with constructed response problems. Many states now include such problems in their assessments.
PoWs and the NCTM Process Standards:
PoWs are an effective vehicle for learning and reinforcing mathematical concepts and skills. They address the Process Standards as proposed by the NCTM and promoted by many states in their mathematics standards.
PoWs help students build mathematical understanding. The problem context helps students attach meaning to the mathematics and make sense of it.
PoWs emulate the process of problem solving in the real world. Students analyze the given information and apply knowledge and skills in different ways. There is not an obvious path to a solution.
PoWs expand each student’s repertoire of problem solving strategies. They help students develop approaches for making progress when they are stuck.
PoWs create opportunities for students to reflect on the problem solving process and develop metacognitive skills. Being a proficient problem solver involves being able to plan, monitor and evaluate one’s own thinking. A problem context provides a way for students to judge the reasonableness of their answers.
Reasoning and Proof
Justifying one’s thinking and procedures, both orally and in writing, is fundamental to mathematics. PoWs provide the opportunity for students to develop this habit of mind and learn that mathematics makes sense.
Writing is an important component of PoWs. The process of putting thoughts into writing serves to clarify and organize the student’s mathematical thinking.
The writing that students do in PoWs makes their thinking visible, allowing the teacher to help them move forward.
PoWs help develop literacy skills. They provide an authentic opportunity for students to strengthen reading comprehension and technical writing skills. The ability to write clearly and with appropriate detail is invaluable throughout school and beyond.
The richness of the math in PoWs helps students make connections with other mathematical ideas and with contexts outside of mathematics.
PoWs encourage students to identify analogous problems and situations which helps them generalize their learning and apply it more efficiently to new situations.
PoWs invite a variety of forms of representation. Students often use manipulatives, tables, graphs and diagrams in the process of solving the problem as well as in communicating their results. These representations allow teachers to move students from arithmetic calculations toward algebraic generalizations as a natural next step in their mathematical growth.