Reading and Math. Connected? Connected!

At my school, math problem solving is the main topic of conversation. This conversation spurs many ideas for math pbls. Quite like the math-ish thinking pbl on this blog. We’re missing a key element of math application. Students must read the problems and think like a reader. If we can be math-ish thinkers, then we can also be math-ish readers and writers!

At first, I thought the connection was just with reading strategies. I thought we could use these strategies to help students read in math, too. But then, I thought deeper about the buzz word that flies around with reading… CLOSE READING. We closely read to uncover new details and collect a deeper comprehension.  Students are taught to read and reread. How often do we preach this in math? Many times, our students just glance once at their math story problem. We need to direct students to the mathematical text. What does it say? What doesn’t it say? What’s confusing? We need students to dissect our story problems.

What if math story problems are a genre for our close reading work? What if math was full of interactive read alouds and think alouds?

I write this blog to plan out loud and get your help. What might an entry event look like? How can we engage students in seeing that reading and math are linked? What if the entry event showed math as other genres?  Suggestions wanted.

Once upon a time, there lived a math story that showed numerical characters that changed over time. These characters were giving and mischievous. Sometimes, they worked together and other times they compared themselves to each other. Who’s bigger? Who’s longer? They could be greedy and steal from each other, too. The writers of these stories didn’t always need a setting. The story was all about the characters and their interactions. There are many hidden meanings to be uncovered.

What does the math genre consist of? Numerical characters. Questions. Interactions and changes over time.  This genre asks us to make inferences about the characters. We must deeply look at cause and effect.

A blog on close reading: 5 Close Reading Strategies (Chunk the text, underline and circle with a purpose, look at structue and author’s purpose)  http://iteachicoachiblog.blogspot.com/2012/06/five-simple-close-reading-strategies.html

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Math-ish Art Museum

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Have you wanted your mathematicians to show their thinking?

Have you hoped students would use pictures, words, and numbers in solving a problem?

Have you wished for the highest form of learning through students teaching?

Have you wondered if students could ask questions of each other?

Today, we had an art museum. An art museum unlike any other . It was full of vibrant and creative math. It was full of student voice and choice. Students were proud to share and even inspired by their peers.

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Just by asking the driving question, How can we, as mathematicians, effectively show our math-ish thinking? Students tried out their thinking for weeks. They saw how it could be different for each student and for each new concept. They had many guest visitors show their own thinking. It thread us through many units of math and I’m sure it’s one that will stay with us through the year. Our thinking never ends. Isn’t that what we always want in education?

“Education is not the learning of facts, but the training of the mind to think.” – Albert Einstein

When we shoot for an end product of our pbls, we must shoot for reflection and changed thinking over the molded product. What’s the bigger picture? What do we want kids to do 10 years from now or carry over in their learning later?

In our culminating event, students were able to choose their content / problem. They chose among a list of concepts that they had learned thus far. They then chose their media to solve the problem. They chose how they wanted to show their thinking, solving, and explanations of such a problem. Some drew, crafted, and videoed their thinking. The project came full circle! From an entry event of math-ish art that teachers created and googled into an art museum of their own thinking. The art museum was set up for an hour for visitors to come and look at. It was also set up for questions from students and visitors. The room was loud, but that good type of loud where conversations are had and curiosity is being explained. This is something that could happen every year or even semester. We could take a list of what students have learned and ask them to pick what they want to teach after closing a semester or quarter. A portfolio of math-ish thinking??

Students challenged my own thinking and showed me new methods of solving problems that I hadn’t even taught (partial differences and more). As a teacher, math-ish thinking is vital. If we cannot see the work, we often don’t know how our student got to their answer. Yet, we can’t just tell them to “show their work” without teaching them how. Math-ish thinking was the remedy! As a teacher, I could diagnose where a student was challenged just by looking at their thinking on the paper. They didn’t know that learning to show their thinking would help me learn how to help them. Win- Win!

An added product at the end was to come back to the circles we started in the very beginning. On the very first day or in the entry event, students had to add 3 numbers in a circle. They could add it however they wanted. They had to just show their thinking. While most knew how to show some thinking, many still got the answer wrong. We didn’t worry about that, though. We focused on the thinking and the process. We took the same circles and numbers to be added at the end. Students not only showed their thinking in numbers, but they added with written words and steps. The beauty of these end circles was that almost all got the answer right on their own. Maybe, this was because they had learned to slow down. Maybe, it was because of practicing showing their thinking. They may have known already what steps they were going to take. By training their minds to show their thinking, they ultimately created a well-known – well-traveled – memorable path of solving similar sorts of problems. They had memorized their own unique steps  in solving those problems and ultimately were more effective in gaining answers.

Math success! Pictures below. Photo cred @ams_lee

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Math PBL for all!

Hello,

I haven’t taken much time to keep up this website. I write today to reflect and share a new pbl that is being experimented with in a couple classrooms at my school. Recently, a coworker and I planned and started a math pbl. We were searching for more knowledge and experience with pbl in math in order to coach other teachers at school. We were very hesitant to preach math pbl when we hadn’t done one ourselves. So, we set out to learn!

This pbl began with brainstorming math solutions in a leadership meeting. What are the biggest needs in math? What areas need to be concentrated on? We kept coming back to problem solving. We found that many times our students wanted to show their answer, but not their work. Rush, rush, rush! We thought thoroughly upon how we were teaching students to “show their work and thinking,” but also what does that even mean. What does it mean to “show your work” in math? How do we show our thinking? Why do we keep asking them to show their work if we haven’t properly explained and explored those terms? AHA! That’s our driving question, How can we, as mathematicians, show our math thinking effectively? We soon listed what we as teachers needed to know and what we already knew.

What does it look like? What does it sound like? What tools and parts of speech can we use? Showing your thinking involves showing the steps and the plan you made to solve a problem. Metacognition thinking stems need to be used. It means slowing down… thinking critically, sharing your ideas, and gaining feedback.

We use Everyday Math at our school. We needed to see how this could be thread through a curriculum that spirals through different concepts each lesson. We had to ask ourselves: Can this fit into each concept? Can it show up everyday as we explore something new or old? YES! Whether you’re extending a pattern, creating a shape, using an algorithm… we’re always thinking something. The question is how can we verbalize and show that thinking?

Our entry event theme: Math is Art! Have you ever read “Ish” by Peter Reynolds? This book is about art, but is greatly founded in the idea of perfection, creativity, and thinking “ishly.” How many of us come to math with the anxiety of perfection or that just right answer? Did you know that high anxiety causes a lower function of the math sense in the brain?  We read “Ish” to students and emphasized the connections they might make between math, art, and the young character in the book. How many of you think you’re a mathematician? Do you think your math could be framed? What might math look like in a frame? What frustrates you in math and what motivates you? What does it mean to think “ishly”? What does it mean to make something “look right”? Students began thinking about our driving question. How can we, as mathematicians, show our math-ish thinking effectively? In the beginning, students thought very broadly for their Knows and Need to Knows. “It looks like our ideas. It looks like math.” Few questions were raised. We planned ahead for such thinking…

Then, we unleashed the exploration! Students needed a better idea of what this could look like. We had an “art museum” set up for them. Black table cloths were on student tables. Frames and “paintings” were created with math thinking. Some frames had math thinking stems. Some frames showed several solutions or algorithms to a problem. Some frames showcased problem solving steps of circling, boxing, and highlighting among word problems. A student favorite said, “Math is art. Live in the numbers.” They walked around this museum in awe. They noticed the key words and deep quotes. They were thoughtful about the numbers and words being shown. Students were able to come back to our Knows and Needs to Know with a fresh perspective. These frames strategically had math thinking that we as teachers always dreamed to see.

We then dove into the lesson in our curriculum… solve and add 3 to 4 two digit numbers. We came at these problems abstractly. We created problems for students that allowed them to think for themselves and in the order they wanted. Many times, as math teachers, we set some numbers down in a set column or row. This strategy often creates an environment where students think they have to use the order we wrote it in. Instead we placed 3 numbers in different areas of a circle with the instructions: Add these numbers, however you like, but show your math-ish thinking. Students really took off! They were drawing arrows and lines and showing algorithms. Some used words. Some added all numbers at once and others added two numbers first and then the third number. They practiced on a few problems. Some got to stand in front of the class and share.

Finally, we sent them off with their very own artistic circle of numbers (as an assessment). Add these numbers, however you choose, just show your math-ish thinking. Do it all by yourself. Students posted these circles on our own mural of thinking. Upon reflection, all of the students showed their thinking. Some students got the answer wrong, but we were able to see why they came to their answer because they had shown their thinking. Why do we show our thinking? We gain a better understanding of the steps we take and we gain feedback on how to improve. If students had just shown a right or wrong answer with no thinking, how would we know what to do to help them?

The students have been so affected by the fact that math is art. They write this phrase sometimes around their new found math-ish thinking. They shout out in lessons, “Can I show you my math-ish thinking?” As readers, I challenge you to think about two questions. How can you model your math-ish thinking for students? How can we, as math teachers, think more abstractly in order to allow for more creativity in math? To be continued…