An open-ended math problem must have multiple solution strategies and multiple answers and ways to get to that answer. These open-ended math problems can be used for assessment, mostly at the formative stage when first introduced in a classroom. When used for assessment, the problems give students an opportunity to show if they understand or don’t understand the math concept presented in creative and different ways. Also, they require students to use reasoning, problem solving strategies, and communication skills. Teachers are cautioned not to use only procedure and algorithms because it gives students only part of the math picture – and that is when true understanding is lost.
High-quality, open-ended problems should:
- involve significant mathematics
- have the potential to bring about a range of responses from incorrect to simple to general
- have a balance between providing too little information (an ambiguous problem) and providing too much information (making the problem restrictive and closed)
At first it can be challenging for students to work this type of problem because they may not have experience with “explaining” their reasoning. This is part of the process and must be developed and modeled for students to gain mastery and confidence. But, once students develop a habit of practice, they can gain confidence in their math knowledge and communication skills. It can also provide them with more ownership in their learning.
I can definitely see where this can be used in the math class, but it will take some time to develop the habit. The connection between mathematics and literacy with this process would be wonderful to utilize. I could encourage a student who always wants to read and write stories to engage in a math problem by having them write their explanations and reasonings. Likewise, a strong math student who is not comfortable with communication (writing and speaking) can receive great practice within an environment/topic that they feel proficient. This would also be a great opportunity to have small groups or pairs work together, strong and less proficient students working together, then share out with the class. I can see the benefits for use with special ed students, on-level students, and AIG students. Each level of proficiency improving from their level as they got more and more comfortable with problem solving. This could be a fantastic way to begin class with a “problem of the day” or even to end class with and have students think overnight and bring in their solutions the next day.
Katie, I did try to the go the http://www.heinemann.com/math searchable website. I set up a new account but couldn’t access any of their literature or examples about open-ended math problems/assessments. Did you find the same? Or were you able to see some of the problems?
Second, I did research the open-ended math problems/assessments a bit and found this blog post about the subject: http://davidwees.com/content/open-ended-problems-elementary-school-mathematics/. He has some great sites to visit with examples as well as a few good books to use as reference and practice. Did you find anything?
The article mentioned having to endure the “challenging” and “time-consuming” aspects of this as it is difficult to accomplish quickly. As pre-service teachers and soon to be teachers in our first year, how will be implement this and become proficient without adequate resources? Are these thing that we will need to seek out and perhaps fund on our own, or do you think our colleagues will help out? I know that at the school where I often substitute, teachers gladly share resources and information. I hope this is the case everywhere!