In one question, Sam Shah summarized the frustration I had felt with the accelerated math class I taught for two years. "How does your class move the needle on what your kids think about the doing of math, or what counts as math, or what math feels like, or who can do math?" - Sam Shah in his Call for Presenters for his Virtual Conference on Mathematical Flavors For two years, I had the most wonderful opportunity to teach amazing 5th grade students. Students rode a bus from their home school to spend 75 minutes with me where we delved into rich problems, debated ideas, and created deep connections. Sounds like a dream come true, no? I realized about two weeks into the first year that I was probably not the best person to teach this class. Students had to achieve a particular test score to participate in the class. Mathematics has historically been a "gatekeeper" to opportunity - and I worried about how this class might be sorting students into future "haves" and "have nots". My first year I had 63 amazing mathematicians. My charge was to compact two years of content (5th and 6th grade) into one year so that these students would be ready for the state's 6th grade math test and move into PreAlgebra as 6th graders. It quickly became clear that about 20% of the class could move at a pace that would allow us to meet this goal. I was unwilling to teach "tricks" so I found myself between the proverbial rock and hard place. How to prepare these students while also continuing to build them as mathematicians? I chose to continue focusing on inquiry-based learning and co-constructing mathematical meaning through rich conversations rather than concerning myself with a standardized test. Facilitating these conversations was not always an easy thing to do. Many of my students were brilliant calculators. Speed had taken them far in their mathematics life up to this point. Some were very frustrated when they were asked to explore, invent, and imagine. I was asking them to redefine their view of mathematics. In her book Becoming the Math Teacher You Wish You'd Had, Tracy Zager describes this dilemma: In allowing time for these conversations each day, we eventually built a culture where students made conjectures about mathematical ideas and used reasoning to explain, defend and revise their thinking. By the end of the year, my students used words such as these pictured below to complete the statement "Mathematics is ____." While I felt that I had success in moving the needle for this group of students, I was frustrated by comments made by other teachers. I frequently heard, "Well, of course they can talk about math in those ways. They are the smart kids." I wanted to demonstrate that ALL students can make conjectures about mathematics and reason/debate/revise their thinking about their mathematical ideas. I worried that I was contributing to the idea that mathematics was only for "some" people and I wanted to prove that any student could think deeply about mathematics - not just students who reached a particular score on a test.
This year, I begin my second year as a math coach in a building where I have the privilege to work with grade K-5 classrooms with diverse learners from different countries and backgrounds. I am blessed to work with an amazing staff who wants to eliminate the traditional idea of mathematics as a gatekeeper. Together, we are working to build mathematical thinkers who are creative and willing to test their ideas. I am grateful for the opportunity to expose each and every student to rich mathematical ideas - without relying on test scores to determine which students will access these experiences. I can't wait to see what students notice and wonder this year about mathematics! I know I will learn a lot from them and I am looking forward to a wonderful year!
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"If you could have secondary teachers understand one thing about elementary school math learning, what would that be?" - David Sabol (@Dave_Sabol) As an elementary school teacher and instructional coach, I am so appreciative of this question. And especially that so many teachers from #TMC18 are asking about what we do in elementary school mathematics. I think these conversations are essential in helping us all learn together and provide a more cohesive experience for all of our students. Using and connecting representations is a huge part of our work in elementary school - along with providing many opportunities for conversation to make sense of mathematical ideas. In conversations with teachers, I often refer to the image below from Lesh and his colleagues to show how these representations are connected in making sense of mathematical ideas. Through these multiple representations, students deepen their understanding of the mathematical content. In Ohio, our standards are written so that students move from concrete to iconic/pictorial to abstract/symbolic representations. Some of these ideas build across years - which gives learners the time and space to develop these ideas in a deeper and more connected way. They have the opportunity to build, then draw, and then use symbolic notation to represent their mathematical ideas. Throughout this process, there would be many conversations and writing about their ideas as they connect these different representations. (Let me be clear - this is something we are still working on and I am not claiming that we have it all figured out at the elementary school level! We are improving at making these connections and deepening our conversations about mathematical content.) In the photos below, you can see 1st grade students using blocks, pictures, equations, and apps such as Number Line to represent their ideas about Graham Fletcher's Bright Idea 3-Act Task. Students worked in groups to refine their ideas and then shared during a whole class conversation. In the next example below, 3rd grade students worked in groups to write a story about creating bouquets of flowers. The groups were then asked to draw a picture and write an equation that would match the story. During the class conversation, students were looking to see whether the story, equation, and picture were a match. This video provided a chance to see students working to make sense of what these different representations mean and how they might be connected to the mathematics and context of the problem. In the following example, 5th grade students debate whether the answer to a problem is 4/5 or 4/7. I was fascinated by how what students knew about addition and multiplication of fractions interfered with their ability to make sense of this problem: In a bag, 3/5 of the marbles are blue and the rest are red. If the number of red marbles is doubled and the number of blue marbles stays the same, what fraction of the marbles will be red? I thought this would be a quick warm-up exercise - instead it turned into a debate that lasted 30 minutes and continued to the next day. (Which made for fantastic discussion!) I see these classroom conversations as essential to empowering students to think mathematically. Robert Berry describes this eloquently in his post Positioning Students as Mathematically Competent. What types of conversations are happening in secondary mathematics classrooms? How does what we do in elementary school influence what comes later? What can we do as elementary school teachers to build stronger coherence for our students? I would love for there to be further conversation between elementary and secondary mathematics teachers. We have so much to learn from one another!
I've been using Jon Gordon's One Word to set a goal for myself each year. This year's word is CONNECT. Spending 4 days at Twitter Math Camp (TMC) this past week allowed me so many ways to live my word! The event was in Cleveland, OH and I was fortunate to be going with two amazing colleagues from my district (@brendaboring1 and @kellykir02). Sharing this experience allowed us to connect at both a professional and personal level and I'm looking forward to how we might share what we have learned throughout our district.
It was incredibly powerful to spend time with like-minded educators who are working to provide the best possible opportunities to help students learn mathematics. We had conversations around equity, engagement, content, pedagogy - along with some time for fun! I'm still processing all of the information we discussed but I know our conversations will deeply impact my work this year. Some ideas I want to remember are the powerful message shared by @DingleTeach about measures of center and how we can make ALL feel welcome and valued. I also want to remember the importance of being a teacher leader (thank you for the inspiring message that we ARE enough, @jreulbach) - which is important in working to push forward actions of inclusion and equity. I loved meeting new people close to home (@MrKisselMATH, @minor_math, @sail2pib and @MrsArnoldPlus1) as well as from across the country and beyond (@MsSpinato, @bstockus, @madisonsandig4, @robertqberry, @saravdwerf, @gfletchy, @jryske, @beske3, @davidpetro314, @MFAnnie, @joshchanyh, @Kidsmathtalk and so many others). Having the opportunity to talk in person will enrich the connections and conversations we have on Twitter. A heartfelt thank you to @lmhenry9, @Dave_Sabol, @crstn85 and all of the organizers of #TMC18. I know it is a tremendous amount of work to organize a conference and I am so appreciative to have had the opportunity to participate in this transformative experience! Thank you to @batty314 for sharing about #TMC17 - you were right about TMC being the best PD ever! If you are looking to engage with educators passionate about the learning of mathematics, I strongly encourage you to follow the people I've mentioned. They are just a few of the amazing people who make up the #MTBoS community. I'm looking forward to continuing to connect with this community! Thank you for your energy and commitment to mathematics education! Too often, we miss opportunities to connect with the families of our students. Parents want to be involved in their children's education and our students will benefit when parents and teachers work in partnership. Math might be intimidating for some - especially when the focus is on justifying ideas or asking questions - since this way of thinking is very different from how many people experienced school mathematics. Our school has held family math nights and our classroom teachers communicate regularly with families. We are continually looking for ways to improve this partnership. This past school year, our staff watched Dan Finkel's TedTalk "Five Principles of Extraordinary Math Teaching". It is one of my favorite messages for teachers and parents alike. The message emphasizes the importance of play in mathematics and provides practical advice. As educators, we have spent time working with parents about having books available and reading with children at home. Many parents feel comfortable reading with their child and talking about books. We have not, however, always provided specific ideas and support for parents in regards to mathematics. In our grade level teams, we brainstormed ways families could interact with math at home. Our ideas included picture books, real-world applications, and games. A website seemed an efficient way to share the information with families that would allow us to update information and expand on our ideas over time. We included a weekly challenge so that the website changes each week - there is new information for families and a reason to return. Click on the image below to see our work. I would love to hear your thoughts about our website and ways that you partner with parents!
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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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