Bar Modeling – Introduction, History, and Theoretical Underpinnings
What Are Bar Models?
Strip Diagrams, Tape Diagrams, Tape Models and others, are all names for the same thing – Bar Models. But as a dear friend and colleague of mine cautions – don’t have your kids Google “Strip Models,” that is unless you want to spend a few months in meetings.
Beyond the many names, Bar Models are an elegant and highly effective process of translating word problems into visual representations. They help students better understand how the quantities in a problem are related and give them the flexibility they need to manipulative the given quantities. Most importantly, they help students learn to reason and deduce their way to a solution. Bar models are also a wonderful way to provide students with opportunities to communicate their understanding to others and build metacognitive skills that will serve them for the rest of their lives.
If you want a “nuts and bolts” description of bar models, they can be best described as rectangles used to represent the known and unknown quantities in a word problem. The sense is made of these rectangles with brackets, sizing, and carefully placed labels. And like anything in mathematics, there needs to be conventions, terminology, and processes to communicate, teach, and learn with bar models.
The History of Bar Models
The Bar Model Method of teaching students to solve problems is widely used in classrooms around the world. It has been adopted in some form or other by most of the major education publishers. This widespread use, along with the variations in the name, has led many educators to wonder where the Bar Model Method originated. Make no mistake – the Bar Model Method was created and developed in Singapore. It is a key component of the Singapore Primary Mathematics Curriculum.
The Ministry of Education in Singapore developed the Bar Model Method as part of a plan to solve a nationwide problem in the 1980s – their students’ poor performance in mathematics.
After gaining independence in 1965, Singapore, with its limited natural resources, quickly learned that to be successful and prosperous, they would have to educate their people well. In response to this realization and the newfound push for higher quality education, the Ministry of Education investigated the mathematics learning of their primary students. They found that at least 25% of their students did not meet minimum levels of numerical literacy. Several years later, their research found that almost half of their Primary 2 to 4 students couldn’t solve word problems that didn’t contain keywords like ”altogether” or “left.” They had quite a lot of work to do, and so they began their education makeover.
Singapore established the Curriculum Development Institute of Singapore (CDIS) in 1980, and the CDIS contained separate project teams. One of these teams was the Primary Mathematics Project (PMP), led by Dr. Kho Tek Hong. Dr. Kho and his team were given the job of creating instructional tools, strategies, and professional development models to improve mathematics teaching and learning. Their mission took them to around the world and more than ten countries, and they would eventually find their key learning theories in America (this is why you’ll hear us suggest that there is no such thing as “Singapore Math”). Educational psychologist, Jerome Bruner, emerged as a favorite, and Bruner’s theories were chosen to drive much of their new approach to teaching mathematics. Bruner suggested that students learn mathematics best when starting with concrete objects and when ready, bridging to an abstract understanding with visual representations. This has become known as the “C-P-A” method of instruction, and bar models became one of the bridges that Dr. Kho and his team would build for the students of Singapore to achieve high levels of mathematics learning.
It’s probably no news to you that Singapore did significantly increase the mathematics achievement of their students, but many people don’t realize just how much. At the time Dr. Kho and his team set out on their mission, Singapore’s students were a full grade level behind the average on international measures of student achievement. During the 1980’s many reforms took place as the team continued their research and hard work, and in 1995 it became evident that their efforts were not in vain. Singapore’s students had not only shown considerable improvement, but in 1995 when the results of the TIMSS (Third International Mathematics and Science Study) were released, the world was shocked to find that Singapore’s students had skyrocketed to ranking first among all the countries that participated. It can’t be overstated how astounding these results were, and equally as impressive were their subsequent outcomes. They had continued to lead the world in mathematics achievement during all of the subsequent administrations of the exam except in 2007 when their 4th-grade students ranked second, and their 8th-grade students ranked third, and in 2011 8th-grade students ranked second. The TIMSS has been administered every four years to 4th and 8th graders around the world since 1995, and Singapore has ranked first almost every time. Truly amazing and a testament to their efforts and methods, like the Bar Model Method developed by Dr. Kho and his team.