Since the beginning of school, I have been a part of many discussions across grade levels about the value and purpose of homework. Using our homework policy as a guide, teams have developed homework that helps consolidate learning, is rooted in inquiry, allows for a degree of choice, and integrates IT in transforming how homework is communicated and completed.
At the end of last school year, I posted about Dan Meyer’s work on how to engage students in inquiry-based mathematics through open-ended problem solving. This past week, the Grade 2 team put this into practice while inquiring into how they can organise numbers by using a big bag of Gummi Bears packets. Following this lesson, they created a video of the lesson and posted it on their blogs to support parents in understanding what is going on in the classroom; allow students to articulate their learning; and create engaging ways to extend learning beyond the classroom.
This led one student bringing in several boxes of Hubba Bubba for the class to explore just as they had with Gummi Bears. Below shows the progression of the lesson they developed using Dan Meyer’s Three Acts of a Mathematical Story:
Act 1: Engage All and Lower Barriers to Entry
They presented the students with a visual that pushed students to question, wonder, and had very few words. It was something that connected to the students and would engage them in mathematical thinking that they might not have thought of before.
Students in Grade 2 were asked to pose questions about this box of Hubba Bubba. Rather than just posing the question yourself, students are able to formulate their own thinking, which also greatly increases engagement.
The teachers then asked students to share their questions and then focused on the question that will help support the standards they are focusing on as a class. “Great. Love these questions. I hope we get to all of them. Here’s one I’ll need your help with first: How many pieces are in the box? Now estimate and give an answer that is too low and an answer that is too high." This allows all students to focus on developing their estimation skills and gives access to all students.
ACT 2: Determine and Overcome Obstacles
Students began to figure out what they need to know and solve the problem. “What information would be useful to know here?" After students have listed all the information they need in order to solve the problem, they document their exploration to answer them.
"How big is a piece of gum?"
"How many pieces are in a pack?"
"How many packs are in the box?"
"How can we easily organize these to count?"
"How else can we group these?"
Students then took time to organise their mathematical thinking on paper.
ACT 3: Resolve Conflict and Extend
The students then were shown the original box, again and discussed and reflected on how they solved the problem. Whose estimates were the closest? How did they figure out their estimation? How did students solve the problem? Are there any other questions that weren't answered?
"Yes, you can each have a pack of gum." :-)
Problem Solving in Mathematics
Recently, the teachers at MIS watched a TedTalk by Dan Meyer on teaching mathematics: Math Class Needs a Makeover.
Over the past several weeks, the math curriculum team has been working to put together guiding principles for how we teach mathematics based on much of his work of focusing on teaching math reasoning and patient problem solving. While researching, we came across some more of Dan Meyer’s work on engaging students in inquiry-based mathematics.
He has developed a model that he uses with students in Grades 5-12; however, it could be adapted to the younger grades. He calls it the Three-Acts of a Mathematical Story.
Act 1: Engage all and lower barriers to entry.
Present a visual that pushes students to question, wonder, and has very few words. It should be something that connects to the students and will engage them in mathematical thinking that they might not have thought of before. Students are asked to pose questions based on these visuals. Watch this Act 1 using what we all love to pop: Bubblewrap, and allow your brain to wonder.
After watching, ask students to share their questions. Then focus on the guiding question on the standards you are trying to accomplish. “Great. Love these questions. I hope we get to all of them. Here’s one I’ll need your help with first.” Tell students you hope we’ll get around to answering all the questions on their list.
Act 3: Resolve the conflict and set up a sequel/extension.
Show the students the answers. Show the same visual but now with the answer. Ask students to see if their questions were answered. Whose answers were the closest? How did they guess? Allow time for discussion and reflection. Here are the videos below revealing the answers to the large and medium sheets of bubblewrap:
Dan uses these bubblewrap sheets during breaks for himself and believes they’re soothing. He has developed these problems for high school and middle school students by examining the world through mathematical glasses. There are many other examples that involve Starburst (candy), caffeinated drinks, taco carts, sugar in soda, cutting Lucky Cow cheese evenly, which are all part of his Bank of Lessons from his blog: Dan Meyer Blog.
Where can we find more examples like this for Junior School students where students can engage in authentic, real-life inquiry? And, can we make our own?
All resources retrieved from Dan Meyer's Blog and used through his Creative Common license agreement. blog.mrmeyer.com/
YouCubed: Mathematical Fluency Without Fear
Over the past several years, Jo Boaler, Professor at Stanford University, has developed YouCubed, a website dedicated to promoting inquiry- and concept-based mathematics instruction. In her most recent publication, Fluency Without Fear, she posits that a focus on fluency in mathematics is important; however, fluency is often misinterpreted as rote memorization of math facts without any number sense.
Hear Jo speak about the importance of conceptual-based mathematics teaching and learning for all our students, particularly with our students who struggle the most.