That Day We Added It All Up 那一天，我们聚在一起学数学
As teachers, we continue to learn new approaches to explore mathematics and are faced with new opportunities to provide the best learning experiences for our students. We are constantly participating in different professional learning to keep our teaching practices in line with the most up-to-date research on how students best learn. We collaborate constantly with fellow teachers, administrators, and instructional coaches to learn from each other, and to make sure our classrooms are true learning environments.
I am also a parent of twins in elementary. As parents, we want to be informed and involved in our child’s education, so we can help at home. We engage with our kids asking questions about what they learned at school at every dinner conversation. We want to be a positive influence on our kid’s emotional and academic life.
These first meetings were about sharing with our parent community that recalling facts, procedures, and formulas is merely arithmetic, and while it seems to “work” for elementary and middle school, it does not prepare students to solve real mathematical problems, which is the main goal of mathematics: to solve “messy” or “unfamiliar” complex problems. Mathematics is about making connections and solving problems by making sense of numbers, by using numbers flexibly, by using concrete and visual representations to build understanding. When students truly understand a concept and they can visualize it, use a model or representation, and can explain it, then they are ready to make a connection to a new math concept where they can apply their knowledge accordingly to solve the new “messy” problem.
Parents continued to want to learn more about this conceptual approach to learning mathematics, so we invited them to participate in four sessions called “Math in March.”
We started by showing the progression of addition and subtraction strategies our students use to build understanding in solving problems. Parents were engaged using a variety of CONCRETE manipulatives, to make sense of place value when adding and subtracting without the need to use any rules or tricks such as “carry” or “borrow”. They were able to use place value strategies to understand how to make tens, or how to “unbundle” a ten when subtracting. They continued to use PICTORIAL representations such as tape diagrams or number lines to model the problems. They understood the difference between modeling and fake modeling (which is just drawing an answer found by an algorithm). Using visual representations is how we really MODEL a problem, then we can choose other strategies to help us solve.
We moved onto ABSTRACT strategies and then expanded into multiplication and division, and in later sessions into fractions. (Fractions were a hit with the parent community. They were so excited to use fraction tiles, unifix cubes, number lines, area models, and tape diagrams to understand how to add, subtract, multiply and divide fractions conceptually!)
The constant sounds of “ahhhhh” and “ohhhhh” were just fabulous when parents were shown a visual representation of what ½ x ¼ looks like! Parents were able to see past the formula and tricks and able to see in a new, clearer way what one half of one fourth really looks like, and why the product is one eighth. The room was loud, Chinese and English language, iPhone flashes, unifix cubes everywhere! Our parents were doing mathematics!
当看到 ½ × ¼ 的直观表示时，家长们发出了一阵阵的惊叹声。家长们能够透过公式和技巧以更加清晰的全新方式看到四分之一的二分之一到底长什么样以及乘积为什么是八分之一。家长们议论纷纷，有说中文的，也有说英文的。大家纷纷拿出手机拍照，到处都是方块积木。看哪，家长们在学数学！
Annie Barnard, mother of 5th grade and kindergarten students, said of the experience, “Most of us were impressed with simple questions we had been taught in the past and knew how to do, but never got to understand why. You taught us to visualize the math. Seeing the answer make sense in front of our eyes really gave us a good vibe for the first time, and got us wanting to learn math again. We’re now helping each other understand how to solve math problems without worrying about not being able to remember the right way – because there isn’t one way to solve math, there are many ways.”
What can parents do at home to support their child to feel successful in mathematics?
*If you find a mistake in their homework, instead of saying, “That is the wrong answer, do it again.” Try saying, “guide me through this problem, how did you get that answer?” Most likely, when explaining their strategy, they will catch their own mistake.
*When doing homework, ask: “Can you think of a different way to solve that?”
*Play with numbers, for example: find all the different ways to make 24, or all the different ways to solve 16 x 9.
*玩数字游戏，例如：找到得到24的所有方法或解答16 × 9的所有方法。
*Solve math puzzles.
*Play math games to practice fluency, fun games, not flashcards!
Across both campuses, at SAS we use a balanced approach to teaching and learning mathematics. Teachers and students not only focus on concepts and procedures, they focus on the use of visual representations to model real-world situations, they problem solve, they communicate and reason in their thinking, and make connections to their future learning.
ARTICLES FOR PARENTS:
Jo Boaler, Standford University
To read the whole article, click on this link: https://bhi61nm2cr3mkdgk1dtaov18-wpengine.netdna-ssl.com/wp-content/uploads/2017/03/teacher-article-youcubed2.pdf
Steve Leinwand, American Institutes for Research
To read the whole article from Steve Leinwand, click here: http://steveleinwand.com/publications/
More resources to help your child at home:
To access this resource, click here: https://padlet.com/caty_romero/o281lgfyj2dx