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It is time for our annual MATH FAIR for kindergarten to grade 5 students. We are super excited about this!
What is a Math Fair? A Math Fair allows students to examine several different problems during the exploration phase, which lasts 2 days. Students then chooses a problem about which they become the expert. They will get to know this problem inside and out, as they will be presenting it to an audience at the FAIR SHARE Day. While, they have to know the possible solutions, they do not present the solution at the math fair. They are wanting others to try to solve their problem. We borrowed this idea from the work of the Galileo Educational Network. Math Fairs are a chance for students to engage with rich problems that make them use mathematical thinking and skills to figure out the problem and come to a solution (or two!). Problems can be solved by any level. In the past, we have had kindergarteners and grade 4s tackle the same question. The only difference is in the level of sophistication in the mathematical thinking and skill level. Math Fairs are a SNAP! S=Student Centered. Students are doing the work. They choose the problem they want to solve. They have to conjecture, test, reflect and make conclusions about the problems they are solving. Teachers are there to guide, ask questions and encourage students' thinking about the mathematics and how to present the problem to an audience. N= Non-competitive. This is not a competition. Students are not judged, and there are no winners or losers. Everyone wins because everyone is using their mathematical skills! A=All Inclusive. There is a problem for everyone, no matter their skill or age. Students usually choose problems that are just challenging enough for them. P= Problem-Based. All the problems are rich and multi-layered. They take time and lots of thinking to unravel and solve. Many have multiple solutions and all can be solved in multiple ways. The last couple of days of our Math Fair are dedicated to creating posters and practising how to share the problem with the people who will visit the Fair Share Day. The idea is for students to share the problem, not the solution. During the sharing day, students challenge their audience to solve the problem. They have to know their problem well enough to give hints and guide others to a solution. Visit our blog soon for some of the awesome posters that our students will develop in the next couple of weeks. 2018 Math Fair Problems This document has all the problems students were challenged with solving this year. Have a go! See if you can find solutions to some of them! I have been working with some of our younger learners lately. One of the questions I ask them is, "What do mathematicians do?" This question seems to puzzle them a bit. They believe the answer is far too obvious: "They do math". When I follow up with, "What kind of math?", the usual response comes in the form of a math fact.
While I expect that this would be their answer, it is a very narrow view of the work of mathematicians. Mathematics is a dynamic and varied study of a multi-faceted discipline. Within this discipline is number sense, shape and space, measurement, geometry, data management, patterning, algebra, and probability. All of these strands are interwoven, but we tend to study them as discrete entities. Herein lies one of the reasons students struggle to make sense of mathematics, but I will talk more about that in another post. Our question is: What do mathematicians do? Mathematicians:
When your child comes home, ask them how they were a mathematician today. Hopefully they will be able to see mathematics beyond the math facts and talk about how they persevered with a problem, or the connections they made, or learned a new strategy.
In mathematics, spatial reasoning involves the ability to see objects in 2 and 3 dimensions and to be able to rotate objects in your mind, with or without physically moving an object in space, or to fill in a space with different objects, or draw an image. Studies show that children with good spatial reasoning at an early age are more likely to find math enjoyable and will master concepts with greater ease. We use spatial reasoning when we are reading a map. Some of us have to physically turn the map to orient ourselves, while others can easily figure out in which direction they must travel to get from point A to point B. Spatial reasoning also comes into play when we look in a mirror. We have to be able to flip the image if we want to brush our teeth or hair correctly. Drivers use spatial reasoning all the time..."Will my car fit into that parking space?"; "Is there enough distance between cars for me to merge safely?" and so on. In order to develop spatial reasoning and strengthen our ability to visualize mathematically, we have to practice. This is a skill that is developed over time and repeated practice solidifies the connections in our brains. Once this is a solidly acquired skill, our brains do not need as much energy to access it. This ability becomes part of who we are, but really it is simply that our brains have such a strong connection to the idea that we really do not need to think about it too hard. The great news is that our brains can develop the capacity to think in space at any time. It just takes lots of practice with certain activities. Here are some activities that promote spatial reasoning: 1. Quick Draw. This is an idea from Grayson Wheatley, professor at the University of North Carolina. The idea is to look at a geometric image for 3 seconds and then "draw what you saw". You repeat this 2 times,until you finally copy the original image. Once the image has been drawn 3 times, you discuss what you see in the image. This is a great way to promote specific mathematics vocabulary to discuss lines, shapes, intersections, angles, etc. (Follow the Quick Draw link to Wheatly's explanation of how it all works.) 2. Quick Build. This is the same as a quick draw, but instead of drawing, use pattern blocks to copy the model. Once the model has been successfully reproduced, build the same "shape" using different blocks. 3. Build with Tangrams. Tangrams are 7 geometric pieces that form a square when put together in a certain way. They have been used for centuries to tell stories, as the tans can be moved around to make different figures. Grandfather Tang's Story by Ann Tompert is a great introduction to using tangrams to tell a story. 4. Draw tessellations. Tessellations are repeated shapes that have been flipped and rotated to fill in a space. M.C. Esher, famous artist, used tessellations to create his artwork. This is an example of one of Esher's tessellation paintings. To learn more about his artwork, visit: https://en.wikipedia.org/wiki/M._C._Escher For some of us, we equate problem solving to the word problems we did in our math textbooks. Word problem are not truly problem solving. These types of problems are designed to help students practice a particular skill or concept. True math problems are more complex and may involve the use of several different concepts in order to solve. The solution is not immediately obvious and they take time to solve. It is important that we have varied and multiple experiences with both these types of problems. One to practice a new skill or concept and the other to apply our mathematical knowledge beyond the simplistic.
This type of 'problem' has its place in mathematics and it is important for children to engage in this type of work. However, it does not engage all aspects of problem solving that are necessary to be mathematical.
A rich, complex problem will ask us to think deeply about a situation and how we might make sense of it mathematically. It calls upon more than one aspect of our mathematical knowledge to solve. It asks us to communicate our understanding in different ways and allows us to make decisions about how to proceed. It is important that we experience both types of problems in math: one to hone our skills and the other to hone our critical and creative thinking skills and our ability to apply our mathematical knowledge. *adapted from Smith, Huinker and Bill, 2017, Taking Action: implementing Effective Mathematica Teaching Practices, NCTM.
October 2017 What is Productive Struggle? And, why is it an important part of mathematics? Think of something you have learned to do well. When you first began, you were uncertain, unstable or just couldn't do it very well. Productive struggle is necessary to learn anything. It is the space in between not knowing and knowing. The space where we are curious, ask questions, try different ways and doubt our abilities to ever truly learn something. In order to improve, you needed to practise, reflect on what was going well and what was not working and try different things out. This perseverance was critical to your success. You might have sought out a friend or coach to give you feedback about what how you might improve your performance. Talking about your struggles and your progress helped you make sense of which steps might be next to attain mastery. You didn't give up because you believed you would eventually get better, so you kept trying. This is how we learn, especially if we want to learn something at a deeper level. Unfortunately, many do not apply these principles to the study of mathematics. We seem to live in a culture where it is acceptable to think of ourselves as lacking when it comes to math. "Oh, I'm not good at math", is often the response to a mathematical situation. Or, "I was lousy at math, so I get why my kid is too". This is a culture we need to change, if we expect our children to excel in mathematics, which they all can do with a healthy dose of productive struggle. Here are some ideas you can try: 1. ALWAYS ANSWER A QUESTION WITH ANOTHER QUESTION. Our children have trained us well. They ask, and we answer. By answering their questions immediately, we remove the cognitive load. That is to say, we are doing all the thinking for them. So, the next time a child asks you, "How do you...", try answering this way: "How do you think...?" or "Can you think of a way...?" or "Where might you start to find the information you need to...?" The kids need to do the "heavy lifting" when it comes to thinking. 2. ACTIVATE PRIOR KNOWLEDGE OR EXPERIENCE. Within every new learning situation we find ourselves, we rely on our past experiences to help us make sense of what is new or different. Our prior experiences or knowledge creates a frame upon which we hang new knowledge. As we think about how the new experience or idea changes what we already know about something we are learning. When children are struggling to make sense, try to relate what they are doing to something they might have experience with. This will allow them to make connections between what is known and what is new. 3. TAKE TIME. Deep learning takes time and repetition. Being able to stick with a task is a hallmark of productive problem solvers. New learning does not happen instantaneously, it takes time. We need to try things, think about them for a while, come back to the task and try different things. Brain research tells us that even when we are away from a challenging task our brains continue to work on the problem. 4. ENCOURAGE AND ACKNOWLEDGE. It is important to acknowledge that the new learning is difficult or challenging. At the same time, we need to be sending the message that we believe the child can do it. Just like the Little Engine, we have to believe we can in order to do things that are scary or challenging. |
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October 2018
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