Mathematics Updates
January 2017
"Powerful, Passionate, Accomplished Teachers"
By John Hattie
Visible Learning for Teachers, 2012, pp. 19-20
The messages in Visible Learning are not another recipe for success, another quest for certainty, another masking of untruth. There is no recipe, no professional development set of worksheets, no new teaching method, and no band-aid remedy. It is a way of thinking: "My role, as teacher, is to evaluate the effect I have on my students." It is to "know thy impact", it is to understand this impact, and it is to act on this knowing and understanding. Is requires that teachers gather defensible and dependable evidence from many sources, and hold collaborative discussions with colleagues and students about this evidence, this making the effect of their teaching visible to themselves and others.
Powerful, passionate, accomplished teachers are those who:
- focus on students’ cognitive engagement with the content of what it is that is being taught;
- focus on developing a way of thinking and reasoning that emphasises problem-solving and teaching strategies relating to the content that they wish students to learn;
- focus on imparting new knowledge and understanding, and then monitor how students gain fluency and appreciation in this new knowledge;
- focus on providing feedback in an appropriate and timely manner to help students to attain the worthwhile goals of the lesson;
- seek feedback about their effect on the progress and proficiency of all their students;
- have deep understanding about how we learn; and
- focus on seeking learning through the eyes of students, appreciating their fits and starts in learning, and their often non-linear progressions to the goals, supporting their deliberate practice, providing feedback about their errors and misdirections, and caring that the students get to the goals and that the students share the teacher’s passion for the material being learnt.
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Grade 5 Math Pacing Guide Updated
A committee of fifth grade teachers met before the winter break to make updates to the math pacing guide for that grade level. The revised document is available on the curriculum website and in the shared Google drive folder for Grade 5 Math.
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Lessons, Activities, and Videos from NCTM
Grades K-1
Grades K-2
This collection of lessons gives students experience with many different ways of thinking about subtraction-as-taking-away: on the number line, with manipulatives, and more.
Grade 3
In this lesson, the book, A Remainder of One, by Elinor J. Pinczes, introduces division with remainder. Students will enjoy the story context as they explore different remainder situations and model division with arrays.
Grades 3-5
Students take timed turns racing to the end of each fraction line by moving one or more of their markers to sum to a given fraction value. Game requires students to strategize.
Grade 6
This fast-paced five-minute video links students' informal methods for solving a fraction division word problem to teaching the standard algorithm.
Grades 6-7
Students apply their knowledge of ratios, unit rates, and proportions to sort through the clues and deduce which suspect is the true culprit.
Grades 7-8
Grades 9-12
Grades 9-12
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Growth Mindset: Going Beyond Answer-Getting
By Emily Nuttall
As a student, I was one of those kids who sort of caught on quickly to algorithms. I was “good” at math. As an adult, I realize that had nothing to do with my intelligence; instead, it was - and still is - more of a reflection of my personality. As I come to research and understand more about how learners learn, I have become more reflective of my own learning experience. I reflect in order to keep myself in grounded in “my students’ shoes,” so that I may continue to understand how they learn and what they need from me as a facilitator of their learning. As I learn more about Growth Mindset and put words to what I’ve felt innately, it is clear to me that true learning comes from exploration, questioning, and challenges.
When I learned algorithms, I was not really learning. I was simply becoming really good at imitating steps. The unfortunate thing about that is that I remember being praised for doing so - being called “smart” for getting answers, while watching my peers’ self-esteem plummet because they couldn’t get answers in the same way, or as fast. I remember feeling bad for my friends as they struggled, and as unspoken labels began to pour over them. I heard every “sigh” from a frustrated teacher. I could feel the buzz of nervous snickers from classmates. Classmates who were laughing to hide their own insecurity about their ability to memorize a set order of steps, in order to solve a math problem, and therefore appear to be mathematical geniuses.
From my own experience as a young learner, I now understand the burden and pressure of being labeled the “smart kid,” as well as the damage and self-esteem robber of being silently labeled as “not as smart.” It brings to mind the recent, and powerful, video from Jo Boaler and the team at YouCubed: Rethinking Giftedness. When I became a teacher, the reality of both experiences flooded my mind as I watched some of my students catch on quickly to the mathematics, while at the same time other students struggled to make sense of it. Throughout my years as a teacher, I noticed that all students genuinely wanted to be successful.
As an educator, I am driven by the notion that all of my students need to (and deserve to!) maintain that desire to be successful. I know from my own teaching and learning experiences that all students are capable of learning. However, just as each person is unique - with a unique personality - each student learns differently. We need to shift away from the practices of rewarding students whose learning style and personality are compatible with algorithms, following steps, and getting-answers. Instead, we should celebrate students’ ability to reason through their thinking - regardless of correct or incorrect answers. It is essential that we support and develop each individual student’s path to discover and understanding mathematical concepts, which includes celebrating and encouraging many mistakes. Getting answers does not support conceptual understanding; in fact, these students do not achieve true understanding or depth of knowledge on which they can build and connect ideas. We need to shift to Growth Mindset teaching and learning practices in order to reach all learners.
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January Math Professional Learning Opportunities
9-12: Enhancing Instruction with Technology
Essential to 21st century learning is that instruction should be student-centered, education should be collaborative, learning should have context, and schools should be integrated with society. Technology is a tool that helps achieve these goals. Kym Giles and Kristin Harris have collaborated this year on incorporating technology into their mathematics classes to enhance instruction. In this session, they will share ideas from their work. Participants are asked to bring their Chromebooks.
Tuesday, January 16, 2:50 - 3:30 p.m. - Webinar
K-2: Developing Quality Math Assessments
In this webinar for K-2 teachers and administrators, considerations for item development will be discussed. Items will be analyzed for content complexity, and universal design, vocabulary/language, and standards alignment will be examined. A blueprint template will be shared. Register by noon on January 16 at https://goo.gl/forms/2zUQsfV6aBe82gPO2 to receive a link to join the session.
Thursday, January 18, 2:50 - 3:30 p.m. - Webinar
3-5: Developing Quality Math Assessments
In this webinar for 3-5 teachers and administrators, considerations for item development will be discussed. Items will be analyzed for content complexity, and universal design, vocabulary/language, and standards alignment will be examined. A blueprint template will be shared. Register by noon on January 18 at https://goo.gl/forms/lRxzUxbFrfoJHDsj2 to receive a link to join the session.
Wednesday, January 24, 4 p.m., Madras Middle School
6-8: Teaching Math Using a Flipped Classroom
Jessica Keegan will share her experience implementing a flipped classroom with her math students. Benefits, pitfalls, and expectations will be shared along with suggestions to help others who are considering implementing this instructional models be successful. Participants are asked to bring their Chromebooks.
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Research base
Looney, S., & Carr, K. (2016, May). High five for mathematics. Teaching Children Mathematics, 22(9), 532-537.
National Council of Teachers of Mathematics [NCTM]. (n.d.) NCTM Illuminations. Reston, VA: Author.
Nuttall, E. (2017, December 15). Growth mindset: Going beyond answer-getting. [Blog]. MyNCTM. Retrieved from https://my.nctm.org/blogs/emily-nuttall/2017/12/14/growth-mindset-going-beyond-answer-getting
Szydlik, J. E. (2015, May). Mathematical conversations to transform algebra class. Mathematics Teacher, 108(9), 656-661.
Szydlik, J. E., Parrott, A., & Belnap, J. K. (2016, March). Conversations to transform geometry class. Mathematics Teacher, 109(7), 507-513.
Wells, P. J. (2015, December). Mathematical exploration (classroom-ready activities): Understanding linear functions and their representations. Mathematics Teaching in the Middle School, 21(5), 308-317.