Katha 2014: Heuristic Alert: Bar Modeling

Minutes of the Workshop transcribed. Speaker Ms. Pauline Mangulabnan

KATHA: DAY 5

Heuristic Alert: Bar Modeling

Ms. Pauline Mangulabnan

De La Salle University

August 16, 2013

Minutes of the Workshop

1. Introduction. The speaker first distributed problem set materials to the teacher-participants and asked them to solve the problems using bar modeling. The speaker did not use any verbal problem algebraic expressions in the material, only bar model graphs for the teachers to answer. She also suggested the use of paper folding in the problem sets for percentages, fraction and ratio integration.

2. Understanding Algebra using Bar Modeling. This approach is applicable to both elementary and high school students where algebra can be easily understood. Big mathematical ideas are required for this approach which makes the students easily understand numbers and variables, make sense of algebraic expressions and visualization connections. The speaker noted that the teachers should not assume that the students’ knowledge is not of the same level as them.

3. Principles of Modeling Construction. The principle dated back in the 1980’s in Singapore, Japan and Korea, where students are able to understand the concepts in math and avoid memorizing formula. The students are required to draw bars to help them answer the questions and let them discover the formula for the problem. This approach may help bridge the mathematical knowledge from primary to secondary students. It helps them to understand the relationship of the given data and deduce the solutions by themselves. It also avoids problem complications.

3.1. Fractional Equations. This bar modeling may also be used in fraction-related problems which may also be integrated in ratio, comparison, multiples and percentages, all of which may be utilized together even though these are considered as difficult topics.

3.2. Problem Set. Problem sets using the bar modeling is also effective for teaching math because the students can easily read and understand the problem, make them underline the question and determine who or what is tackled in the problem. The students may draw unit bars. The speaker discussed a few problem sets on fractions and ratio using the bar modeling method.

The use of bar modeling helps the visually-stimulated students. At the same time they can proceed to more difficult questions; that is, bar modeling can hit two birds with one stone.

3.3. Practices and Conventions. Bar modeling may also be utilized in representing values by units. There are four labels in which bar modeling is materialized: 1) function label 2) quantity label 3) unit label and 4) total label. The speaker gave more problem sets to the participants and solved and discussed each one. The concept of manipulation of units is also being utilized in this method where the teacher can scaffold the questions. Other methods include the use of dashed lines, model length and classifying units by shading.

4. Types of Bar Modeling. There are different types of bar modeling. This include 1) part-whole model in topics such as derivation, representation and comparison 2) comparison model in topics such as fractions, percentages and representations 4) Stack Model in algebraic problems 5) Area Model for length 6) Remainder Subset Model 7) Container and Content Model 8) Multi-step problem in adaptive expertise of letting the students think they own Math; this is also for operations-integration in one problem and division problems. This is also used to make questions more difficult to achieve student critical thinking. 8) Comparison Model where abstract thinking is shifted to concrete ones. Performance questions are required to improve the difficulty of the question. This is also used to  analyze multiple questions. The speaker discussed more problems on this comparison. This is essential to reinterpreting abstract algebraic equations into modeling. The use of tick marks may also be helpful for the problem solving. The speaker emphasized that in high school, both concrete and abstract methods are required for them to fully comprehend the problem sets. It is always necessary to employ checking of answers and when one teacher offering another way of solving the problem. Teachers may present alternative solutions without compromising the students’ own solutions. The speaker illustrated more examples of bar modeling problem sets and emphasized the constant use of tick marks for the same value of the unit in question. This method may be applied for age problems. One teacher-participant raised a concern on the difficulty of the procedure, while others seemed to have a problem on the transition from concrete to abstract algebraic expression. The speaker concluded that it’s all in the method of the teachers using the bar modeling which is easily understood by the students.