Updated: Sep 21, 2021
Many of us grew up learning math the traditional way-- watch the teacher work a few examples, then turn to page 49 in our textbook to do all odd problems #1-31. Lug the heavy book home to finish the rest for homework. Check it together in class tomorrow. Test on Friday.
Repeat, repeat, repeat.
Our “old school” math education was based mostly on rote memorization, and carrying out standard procedures step-by-step.
But Math looks a little different than that at Hess Academy.
Over time, our understanding of how brains develop mathematical understanding has come a long way! With that new understanding has come updated teaching methods. (Know better, do better, right?)
Every profession and field of study evolves over time as technology and research push progress forward, and mathematics education is no exception. Just as we expect doctors to replace outdated medical approaches with the latest advances, we educators also hold ourselves accountable to keep our approaches on the cutting edge of best practice.
One thing we’ve learned is that while traditional methods got us by, they didn’t lead to very deep or thorough conceptual understanding. They didn’t often lead to quicker mental math abilities. And they didn’t work for all learners.
At Hess, we’ve paired our hands-on approach to learning with a Singapore Math curriculum to create a math experience that’s engaging, accessible, and effective for ALL kinds of learners!
What is Singapore Math?
“I’m from Singapore, and over there we don’t call it Singapore Math. We call it math.” :)
- math education expert and teacher training provider Yeap Ban Har joked
Singapore is a known global leader in mathematics, and it is largely due to the highly effective approach they’ve developed for math education. Their program is based on a few key components:
An attitude that everyone is capable of doing math well, and that doing math well is essential
The “concrete → pictorial → abstract” concept progression
Mastery: concepts are explored deeply and sequentially, such that all new learning builds upon past understandings
“Number Bonds” for conceptualizing number relationships
“Bar Modeling” for visualized problem-solving
Emphasis on mental math: the methods lead to quicker, more automatic numerical sense-making
Rather than just defining each of these components, let’s take a look at what they look like in action in Hess classrooms!
“For math in our African Studies Unit, we’re finding patterns in Kente clothes, animals, and jewelry as natural explorations of this important math skill. We will also compare sizes and explore measurement during this unit. A giraffe simply begs to be measured!”
Patterns are such an essential element of math education that Mathematics itself is sometimes defined as “the study of patterns.” Many later math concepts-- skip counting, multiplication, and even functions, for instance-- build upon a foundation of pattern recognition.
Starting pattern recognition early in Pre-K, especially in an authentic and engaging context, sets students up for mathematical success.
“During math tubs, students made shapes on the geoboard and counted the sides; built pattern trains and pattern block designs; played a dice game; and measured letters in their names with different materials like bears, paper clips, and blocks.
The first graders focused on solving puzzles out of a 100 chart-- more than 10, less than 10, 1 more, and 1 less. The students learned a comparing game called Bears and Blankets, using dice and a ten frame to compare the number of bears to the number of blankets. They also solved problems using a counting pattern by drawing.”
The Singapore math progression goes from concrete materials, to pictorial visualizations, to abstract representation with standard math symbols.
In the early grades, getting their hands on plenty of concrete materials helps students build a deep conceptual understanding rather than settling for just surface-level procedural knowledge.
“This week, students continued working on addition and subtraction through 20 and using higher numbers to add and subtract across place value. We also practiced fact fluency and breaking numbers apart in different ways. We are noticing how addition and subtraction are related. We have practiced using the Part-Part-Whole strategy (and early Algebraic thinking skills!) to solve equations such as (12 + ___ = 18 )”
Another key component of a Singapore Math approach is called Number Bonds, which is a way of picturing and understanding the way numbers relate to each other. Numbers can be combined to make new numbers, or broken down into the parts that made them.
Building fluency in working with number relationships increases mental math speed.
“Our Math lessons continued in measurement this week - collecting data and creating bar graphs. We are working toward answering challenging questions about the graphed data. We'll be continuing that concept this week, and will soon move onto the study of angles.”
Singapore Math is focused on mastery, so students spend time mastering one concept before moving on to the next. The curriculum is refined to the most important concepts, and the narrow focus allows for greater depth within each. Students also build confidence as mathematical thinkers when they experience mastery of concepts they’ve explored deeply.
“Mathematicians in Ricci's class will tackle word problems with fractions throughout the week, mining questions for important information and using bar modeling to visualize and solve.”
For anyone reading this who used to become flooded with dread anytime “word problems” were mentioned growing up like I did… might I recommend to you: Bar Models?
As an educator, when I learned to teach word problems using bar models, a lightbulb lit up. It was like someone handed me the key to unlocking the lifelong mystery that were word problems. Bar models give students a tool and a method for unpacking the language of a word problem and translating it into a visual.
Change is never easy. Our human brains are wired to be change resistant, so it can be hard to adjust to the new way students are learning and practicing math these days. Not to mention how difficult all of this can be when it comes to homework help at home!
Here’s a video to shed a little more light on how and why math education has changed over time:
And here are a few resources for math help at home:
“Math Antics” is a go-to Youtube channel for breaking down lessons in easy-to-follow, engaging (and yes, a little cheesy :) videos
Check out these videos on how to teach Bar Modeling, Number Bonds, Mental Math strategies, & more info on what Singapore Math is all about
Virtual math manipulatives for a “hands-on” experience, in a pinch. These can be a great bridge between the Concrete and Pictorial stages!
Bar Modeling galore! Virtual manipulatives, practice problems, and how-to videos
- - - -
What worries you about your child learning math differently than you did? And what excites you about it?