While teaching my 5th graders a couple of years ago, I was looking for a way to challenge their thinking about multiplication. Many of them "just knew" the traditional algorithm and were able to accurately compute products. However, our conversations seemed lacking. I ran across a method of multiplication that involved drawing lines and challenged my students to notice and wonder about the process. I intentionally left the sound turned down so they would actually have to watch what was happening on the screen. Students were intrigued and asked to watch the video multiple times. Sparking this curiosity led to great conversations involving the meaning of multiplication and procedures with an emphasis on place value. Several of my students wanted to explore further and tested this algorithm of drawing lines with other problems. This experience led me to create additional videos to engage students' curiosity. What do you notice in each video? What do you wonder? What numbers would you try multiplying? Will it work with only whole numbers - or could it work with decimals? What other things would you want to explore? How might you revise this work and show it in a different way? I hope these videos unleash your curiosity!
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Jo Boaler has released yet another thought-provoking resource for us to consider: her video titled "Rethinking Giftedness". The messages provided by students within the video are powerful. In education, we spend a tremendous amount of resources (time and money) identifying students by labels. Are these labels helpful? Harmful? Should it concern us that gifted students (at least in my experience) tend to come from higher socioeconomic backgrounds? What opportunities are afforded to those with a gifted label? And, in turn, what opportunities might be denied to those without a gifted label? How might education look different if we eliminated labels and focused on knowing our learners, embracing their individual strengths, and empowering to own their learning in a meaningful way? Click the image below to watch the video:
The best mathematical questions often come from real life situations. One day, Mr. Truske posted on social media about a book he received from Amazon. The single book was sent in this box: When I saw the photo, I replied, "That looks like a math problem." And I was thrilled when he replied, "Yes - let's plan it!" Mr. Truske had actually received a total of 6 books from Amazon - all books arrived on the same day but were sent in 3 different boxes. We decided to use the idea to launch a notice/wonder at the beginning of the year. Our intent was to involve students in a conversation around mathematics that wasn't specific to content. We opened the discussion by defining a problem as something for which we did not have a clear solution path. Mr. Truske and I then introduced the first slide to students and asked them to describe what Calvin and Hobbes might be doing. Answers included "noticing", "wondering", and "thinking". Several students raised their hands to share that they had used notices and wonders the previous school year - they were eager to share about the packaging dilemma when they saw the next slide! For the upcoming school year, I am shifting from a classroom position back into a coaching role. I am excited to work with staff and students but have wondered about how I might retain the elements of a classroom most important to me. During our staff retreat, we worked on vision boards. This work helped me refine my ideas about what I'd like to accomplish this year.
EMBRACE: It is important to me that every person - whether student, staff member, parent, etc. -feel welcome and safe. One way to build this environment is to accept others with an open mind and heart. Get to know people for who they are - rather than who you might assume them to be. In mathematics education, we encourage productive struggle, risk-taking, and a growth mindset. As a classroom teacher, I wanted my students to feel that they could ask questions and challenge assumptions. I intend to continue to develop this safe environment as a coach. ENGAGE: Once students feel accepted and know you care, it is important to engage with them to build a shared understanding of mathematics. The mathematics that students learn should be relevant to their personal lives. This goes beyond personal interests - as educators we need to listen to understand how others approach a problem, assumptions they make, and what prior knowledge or experiences they bring to the situation. Listening to students as they share their ideas, their notices, and their wonders develops their engagement. They realize that what they have to say matters! And, I find I always learn so much from others when I listen - I can't wait to learn from the students as they discuss their mathematical thinking! EMPOWER: As my ultimate goal this year, I want students (and teachers) to feel empowered to continue growing as a community of learners. I consider myself blessed to have this opportunity to work with a fabulous team of students, teachers and support staff! It's going to be an amazing year! Interference. A big word with many meanings. In this case, interference was causing my students to misunderstand what I anticipated to be a simple problem: "You have a bag with 5 marbles. Three of the marbles are blue. The rest are red. If you double the red marbles, what fraction of the marbles will be red?" I gave students a couple of minutes to start this problem individually. As I walked around observing their work, I jotted down their solutions. Most students were finding an answer of either 2/5 or 2/7. I posted these two possible solutions in the room and asked them to stand by the answer that best fit their thinking. As part of our routine during class debates, there is a section in the room for those "still thinking". Once students have made a choice, they are to talk with the people in their group about why they made this choice and work to convince others in the room why their choice is correct. For those at "still thinking", they are to think of a question that will help them come to a decision about the answer. After each group has time to share, students may revise their thinking and change groups. This particular episode fascinated me because only two students initially chose the correct answer. As I listened to their reasoning, I understood that many were thinking about what we had learned with fraction multiplication - that 2 x 2/5 would equal 4/5. Even with other students modeling the problem with blocks and drawing pictures, some of the students were firm in their belief that the correct solution must be 4/5. The debate lasted for approximately 25 minutes (although the video is condensed to about 7 minutes). At the end of the debate, many students still were at the incorrect solution so we waited until the following day to discuss the solution. After having the evening to think more about the problem and talk with others, all students came to agreement that the correct solution was 4/7. While this was a time-intensive activity, the time was well spent. Students did very well with the unit about ratios and had a clear understanding of when they might be able to use fraction operations and when they needed a different approach. To have given the solution to quickly would have cut off the students' opportunity for sense-making and reasoning about the mathematics. |
AuthorSharing what I'm learning from others. Collaborative experiences and communication are essential in building a shared understanding of mathematics! Archives
September 2018
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