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Red Oaks Updates Math Curriculum with Singapore Math
The most recent Trends in International Mathematics and Science Study, an assessment carried out every four years, showed that the tiny country of Singapore is leading the world in 4th and 8th grade mathematics. What can we learn from Singapore? To find out, this past summer Red Oaks faculty attended seminars to learn more about the rationale and methods behind Singapore Math, and how they might be applied here at Red Oaks.
The truth is, we often think of reading and writing as creative, but math is creative, too. It's a matter of learning math as a flexible and creative subject. Singapore Math employs model drawing as a methodology for revealing and reinforcing mathematical relationships, place value, and concepts that promote the development of mathematical thinking and literacy. Through problem-solving, students discover new ways to play with and manipulate the math concepts they have learned using our concrete Montessori materials, materials that were developed over a century ago but which are nearly identical to Singapore Math materials, developed quite recently.
It's a perfect fit for Red Oaks. Both Montessori methods and Singapore Math take understanding from the concrete to the abstract; Singapore Math adds an additional, middle step called visualization.
Singapore Math employs three key strategies to to promote superior math literacy skills: model drawing, mental math, and place value. These strategies are reinforced through problem solving, particularly word problems. Students learn to ask questions that help them map out a word problem thereby achieving a visual representation of the math concepts involved. The primary mapping model in Singapore math is the unit bar.
Here is an example of a third grade math problem:
Nora had 4 times as much money as Pedro. Melinda had 3 times as much money as Pedro. If Melinda had $30, how much money did Nora have?
Traditionally, we might solve the problem algebraically:
3x = 30
x = 10
4x = 40
Singapore Math directs us to first ask the question, "Who are we talking about?" In this case, we are talking about Nora, Pedro, and Melinda. Then we ask the question, "What are we talking about?" (their money). Next, we direct students to draw a unit bar of equal length for Nora, Pedro, and Melinda. Students are then directed to read the problem, step by step, and at each step to use the model drawing to record the information that is given.
In this problem, a student would see that the first sentence tells us that Nora had 4 times as much money as Pedro. The teacher would say something like this: "Do your unit bars show that Nora has as much money as Pedro, or more? " Since the drawing always begins with one unit bar of equal length, the children would conclude that the model without alteration shows that they have the same amount of money. Then the teacher might say, "But the problem tells us that Nora had 4 times as much money as Pedro. How can we show that?" The children quickly see that they need 4 unit bars for Nora, compared to one for Pedro.
Now, the teacher would direct the students to the second sentence, "Melinda had 3 times as much money as Pedro." Careful questioning would help children understand that Melinda needs 3 unit bars. In short order, the next part of the problem would be read aloud, "If Melinda had $30..." That gives the student an important fact: Melinda had $30 dollars. And then the thinking comes in: If Melinda has 3 unit bars and $30, each unit bar must be worth $10. And if each unit bar for Melinda is worth $10, so too is each unit bar for Pedro and Nora.
Finally, the teacher would ask the children, "What question are we being asked?" Often, when solving word problems, children answer the wrong question! So in Singapore Math modeling, we have them visually highlight the question with a bracket and a question mark.
Now the children are ready for computation to solve the problem!
10 + 10 + 10 + 10 = 40
4 x 10 = 40
Having solved the stated problem, students might be asked to apply inverse operations (in this case subtraction) to find out how much more money Nora had than Pedro.
"Singapore Math uses models, as tools of visualization, to create a bridge between mathematical concepts and abstract algorithms, or equations - going from concrete to abstract. It's what we do with the Thinking Maps program and it's exactly what Dr. Maria Montessori was talking about over 100 years ago," says Head Marilyn Stewart.
In the meantime, here are a few more problems for you to try, and if you find you're having trouble, you could ask one of our students for help.
1. Megan and Brianna worked at the diner after school. On Monday they earned a combined total of $35 in tips. If Megan earned $5 more than Brianna, how much money did Megan make in tips on Monday?
2. Sarah collected 7 more seashells than Brian. Brian collected 11 seashells. How many seashells did they collect all together? |
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