Singapore Math Online Resources – Free! (For now…)

Since so many teachers and parents are schooling from home, I thought I’d update some of the resources that companies are offering for free, at least through the end of the academic year.

Dimensions Math and Primary Math

For students:  free instructional lesson videos  Grades 1–4.
These are designed for students to use with textbooks and workbooks to complete their school work. Many of these lessons may be used for students using Primary Mathematics as well; PM students should look here to find the corresponding Dimensions Math chapters.

For teachers: free access to ebooks. Fill out the request form here: https://www.singaporemath.com/at-home-learning

Primary Math and Math in Focus

Marshall Cavendish is providing free access through the end of May to Math Buddies, an online learning tool.

Some of my favorite sites and apps

These are challenging times… How can we help?

The Coronavirus pandemic is impacting society across the globe. Efforts to reduce the spread of the virus are forcing unprecedented disruptions, including widespread lockdowns that have closed many of our schools.

Despite the COVID-19 threat, life goes on. Teachers, who thrive on personal interaction with students in their classrooms, are being asked to deliver instruction remotely. And students are being asked to learn independently.

In these challenging times, we want to help.

Free Dimensions Math Lesson Videos

For students, Singapore Math Inc. is currently offering free instructional lesson videos created for Dimensions Math Grades 1–4. These are designed for students to use with textbooks and workbooks to complete their school work. Many of these lessons may be used for students using Primary Mathematics as well; PM students should look here to find the corresponding Dimensions Math chapters.

Live Online Q & A Sessions

With the COVID crisis keeping me at home, I really miss spending time with teachers. Fortunately, tech tools like Zoom offer an alternative. So, beginning next week, I plan to host live, online meetings to address your questions about teaching math using a Singapore approach.

Are you stuck at home and need to teach your students remotely? Just curious about Singapore Math or Model Drawing? 

This is your opportunity to Ask Me Anything about teaching math the Singapore way. Please register here for the Tuesday, March 31 session. This Q & A will begin at 1:00 PM  Mountain Time (US). Attendance is limited, so sign up today! Canceled due to personal emergency. We’ll try again in 2 weeks!

I’d love your input on times or topics for future sessions; share your suggestions here.

Summer Jumpstart Your Singapore Math Workshop Update

The Coronavirus pandemic has escalated significantly since we announced these workshops three weeks ago. We hope the crisis will soon pass and life will return to something more normal.

We know when that happens, teachers will want training for the next school year. It is too early to know whether it will be safe or proper to hold summer training. We will continue to evaluate the situation and provide updates here.  We will also notify those registered of any changes and offer a flexible refund policy.

Please stay safe in these uncertain times.

Graphing the Holidays

Originally posted 11/27/2018

Teaching between Thanksgiving and the winter break can be a challenge. How do you keep your students engaged in meaningful math learning while embracing the season? Introducing graphing and data analysis might just be the answer.

Imagine starting your day in first grade with a question about favorite holiday treats. Students can answer the question and instantly you have meaningful data that can be organized into a tally chart, picture graph, or bar graph for students to analyze. Or, students can build a bar graph with post-it notes as they make their choices. Then, spend some time analyzing the results.

Ask 5th graders if they traveled over Thanksgiving break. If so, how far? Now use this data to find mean, median, and mode, or to create a histogram for students to analyze. Or, chart the temperatures over the course of a couple of weeks and use this data to create a line graph.

Third and fourth graders could tally the number of candles in their homes for the holidays and use this data to create a line plot. Fourth graders can use their line plots to explore finding the median.

Planning a holiday party? Survey the students on what should be served and what activities should be included. Students can present the findings in a graph and use the results to determine how much and what needs to be donated or purchased to make the party a success.

The holidays are a great time to share family traditions. Why not use that information to meet some graphing and data analysis standards?

For other ideas to keep students engaged in learning read Mental Math Breaks from December 2017.

Who’s doing the talking?

A new school year brings new commitments to improving our practice as teachers of mathematics. One tip I often share with the teachers I coach is, “Ask more and tell less.” Well, that’s easy to say, but what does that look and sound like in the classroom?

Often times, the teacher’s guides are written following a more traditional, lecture-style of teaching. They encourage the teacher to model, or work problems, while the students watch, and then the students are asked to mimic what the teacher did with a similar problem. I challenge you to flip the script and replace the word “show” with “have the students model” and replace “tell” with “ask”. When your teacher’s guide says to show the students the difference or similarities between problems or concepts replace that with, “ask the students what they notice?” It’s these little tweaks that will go a long way toward engaging your students in meaningful discourse and ultimately deepening their understanding.

A fourth-grade teacher from Aurora, Colorado shared her strategies for engaging students in math talk in her classroom.

While this appears to be written for the students to follow, it also suggests some great questions for teachers to ask to generate more discussion.

As students are working through a task ask:

  • How did you solve that?
  • How do you know that’s correct?
  • Can you solve it another way?
  • Can you build a model?
  • Can you use numbers and symbols to explain your model?
  • Is that the best (most efficient) way to solve that?
  • Is your answer reasonable?
  • Do you agree or disagree with your partner’s answer?

So, who’s doing all the talking? Give some of these questions a try and let us know how it goes.

Guest Post – Problem Solving: The Heart of Singapore Math

This article originally was featured in the fall 2018 issue of St. Anne’s-Belfield School’s Perspectives magazine and is republished with both the school and author’s permission.

The author, Sara Kronstain, has almost a decade of experience guiding elementary and middle school mathematicians to become critical thinkers and problem solvers.  She teaches fifth-grade math and is the Kindergarten-6th Grade Math Department Chair at St. Anne’s-Belfield School in Charlottesville, Virginia.


Problem-Solving: The Heart of Singapore Math

When I was in school, my math classes were typical of what one would expect a “traditional” math class to look like. I remember sitting in my elementary and middle school classes, watching as my teachers modeled problem after problem. The class would listen and then practice many of the same types of problems in our notebooks. While this type of teaching may achieve the immediate goal of learning a mathematical procedure, it does not guide students to reach an integral part of learning mathematics: problem-solving (Cai & Lester, 2010).

Singapore Math is comprised of a framework with problem-solving being the center of learning mathematics. This framework is built around five key components – metacognition, process, attitudes, skills, and concepts – all being of equal importance in developing mathematical problem solving in students. Whereas traditional math classes may place primary importance on developing skills and concepts in students, the additional three components of metacognition (self-regulation of learning), process (reasoning, making connections, and applying knowledge), and attitudes (perseverance, confidence, interest) are all key to developing critical thinking and problem solving skills in students (Ministry of Education Singapore, 2006).

A typical Singapore Math lesson is taught with a concrete-pictorial-abstract approach. Where many of my lessons as a math student began in the abstract stage (solving equations), the concrete and pictorial stages allow students to create and solidify their own understanding of a topic. The concrete stage refers to using hands-on materials to model a mathematical situation.  The pictorial stage consists of diagrams and other visuals, thus building students’ learning in a tangible way (Maths No Problem!, 2018). The concrete and pictorial stages allow students to understand why math works the way it does before learning the procedure of how to solve using an algorithm.

Most Singapore Math lessons begin with an anchor task, allowing students to explore these three stages. The anchor task is a question that allows students the chance to deeply explore a topic and develop multiple methods for solving a problem (Ban Har, 2013). Let us say, for example, a group of fifth graders were posed the problem, “The distance of a race is 3km. Lily ran two-fifths of the distance. How many kilometers did Lily run?”  Students would be given the opportunity to freely explore this question by using manipulatives such as fraction bars, fractions circles, or paper (for folding) along with writing materials. Here are a few examples of possible student responses to this question:

Method: Repeated Addition

Add ⅖ + ⅖ + ⅖Students may use fraction bars, fraction circles, or pictures.  Students become familiar with the phrase “3 groups of ⅖”.

            

Method: Bars

Three boxes are each split into fifths. Two of each of the fifths in all three boxes are shaded in.  The shaded parts are added together.

      

Method: Bar Model

A bar with the length of 3 wholes can be split into five parts.  Each part has a value of ⅗. Then add ⅗ + ⅗ .

Method: Addition with Fractions

Three boxes are split into 5 equal groups, first by placing one half in each group. Then, split the leftover half into five parts (tenths). Each group will have one half of a whole and one tenth of a whole. Combine two groups by adding two halves to two tenths.

      

In this example, the repeated addition method reinforces addition with fractions, while the last method has students thinking about and manipulating fractions in a much more complex way.  Thinking back to the five key components of Singapore Math, students in this example are refining their process of learning operations with fractions by making connects across operations.  It is powerful that these responses are coming from students, as they are building their understanding of math through collaboration with their peers. In sharing methods, listening to other’s methods, and processing others methods, students are also developing their metacognition. This question could also be modified and challenge students to problem solve in an even deeper way. “What if the total distance was ½ km?  What if the total distance was 3 ½ km?”  Students can then go back to the concrete, pictorial, and abstract stages and continue to build on their problem-solving abilities.

At the end of the day the primary purpose of this math lesson, or any math lesson for that matter, is not simply to learn how to multiply fractions by a whole number. The most important takeaways are the critical thinking, questioning, collaboration, and problem-solving that happens among students. Teachers are not preparing students to go out into a world where they will simply be asked to recite an algorithm. While a goal is for each child to develop a deep love of math, the biggest hope is that students learn to ask questions, logically think through problems, and make sense of the world around them.

 

References

Ban Har, Yeap.  (2013, June 13).  Singapore Math at the Blake School, Hopkins, MN.  Retrieved from http://banhar.blogspot.com/search?q=anchor+task

Cai, Jinfa, & Lester, Frank. (2010, April 8).  Problem Solving. National Council of Teachers of Mathematics.  Retrieved from https://www.nctm.org/Research-and-Advocacy/Research-Brief-and-Clips/Problem-Solving/#brief

Kaur, Berinderjeet.  (2018, March 29).  Building the Maths house: Singapore’s curriculum framework.  Oxford Education Blog.  Retrieved from https://educationblog.oup.com/secondary/maths/building-the-maths-house-singapores-curriculum-framework

Ministry of Education Singapore.  (2006).  Mathematics Syllabus Primary.  Retrieved from https://www.moe.gov.sg/docs/default-source/document/education/syllabuses/sciences/files/2007-mathematics-%28primary%29-syllabus.pdf

Maths No Problem! (2018). Concrete Pictorial Abstract.  Retrieved from https://mathsnoproblem.com/en/the-maths/teaching-methods/concrete-pictorial-abstract/

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