As I reflected on how we are struggling with the problem-solving process, I think I realize why we may be having difficulty.
When we teach reading, we introduce skills and students apply those skills as they read - reading to learn something new, reading for pleasure, reading to answer questions, reading to understand. When students can apply their acquired reading skills to select books of their own, when they know how to find information about a topic they're interested in, when they can discuss a book or a story with others, or when they can persevere to make sense of a difficult passage or article, we are confident that they have the skills to be a literate learner.
Yet we do not provide opportunities for students to apply math skills to real-world problems which are all around them. We teach skills in isolation, and after students have practiced that skill and seem to understand the process, we move on to the next mathematical concept. We may assign word problems that may or may not be realistic or meaningful to students. We may play math games or read books about math or sing songs, but we don't give students the opportunity to apply the math skills in a meaningful way so students can make sense of why this is important to know and be able to do.
Rather than make up problems involving percentages or decimal points, why not have students look at newspaper ads to determine which store has the best value on a laptop or a Wii? Can we have students plan a meal and then determine what they will need to purchase at the market and how much that might cost? How about walking around the school and taking photos of different patterns they find and putting together a slide show? Or bring in menus from a restaurant and have students figure out what they could buy with a certain amount of money.
Our fifth grade has an organic Hope Garden which is hands-on and project-based. Students learn science and social studies concepts; they research so they can post a comment to a question on their Hope Garden blog; they decide what they want to plant and why; and they do math. Lots of math. Students measure the plots and determine the perimeter and area of each plot as well as the whole garden. They do experiments and measure the growth of different plants. They predict how many ears of corn they will harvest and share their strategy. They weigh their harvest, decide on how to package what they've grown, and keep track of their expenditures and profits. All these different activities help students realize that literacy -- reading, writing, AND math -- can be part of their everyday lives. This relevance is what makes the Hope Garden so popular with our fifth graders.
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#SAVMP
When you think about it, what you are saying is true. So many times we move from concept to concept. While we do go back to review previously taught material, many times the math is not necessarily related to the outside world. People say that the only way to get better at reading and writing is to actually read and write. This is also true for problem solving. In order for students to really understand how to solve problems, they need time to actually solve problems!!
ReplyDeleteI agree, JS! I especially like your last statement; we need to make time for students to solve problems.
DeleteI also think we have to give as much time to "talk story" during math as we do with reading. We can read a story and students can talk about what they think will happen or how they felt about the story. But do we ever stop to think about having an engaging conversation in math? Not really. Some of us grew up in a classroom where you solve math facts using an algorithm to get one right answer. But with paradigm shifts and the implementation of the Common Core, math has taken on a new meaning. Students need time to explore and discover as well as engage in mathematical discourse (communication) to gain a deeper understanding of concepts. Although there may be an answer (a single number or multiple ), there are different ways of getting there (strategies). The idea of using the CRA model can help students develop these understandings if we provide them with the time. Often times we allow students to use pictures, numbers and words but we sometimes forget including the exploration with the use of manipulatives. Students can "talk story" during this time. Then the question arises: When do we have time for them to explore? Think then about this: If we allow students to write using a process over a period of time, why then do we not give them this same kind of time to solve during math using a process? This, being problem solving. Seems to me like these would be great argumentative pieces as they justify why their answer makes sense.
ReplyDeleteYou are as passionate about math as I am, Lynele Basug :-) We will continue to share the beauty of math and problem-solving with our teachers and students.
DeleteIf I listed the essential skills and processes I use for math literacy, in problem solving, it would include the following: using prior knowledge, making connections, setting predictions, forming inferences, visualizing (see words in pictures), identifying setting, characters, and problem, selecting important details, making summarizations, asking myself questions, and validating predictions, inferences, and answers. It is interesting that these are the same skills and processes I use when I read.
DeleteI believe we haven't been taught -- hence, we don't teach math as a literacy. For too long, we've taught math as algorithms, a process to get the right answer. Math is much more than that; it's understanding what the problem is asking for, and that's why your list of skills and processes makes sense. We need to do this with students in our classrooms or math problem-solving will continue to be a challenge for teachers and students. Thank you for sharing!
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