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Igniting Passion In Mathematics Through

Multiple Intelligences

Suriani Othman

Singapore

Fulbright Distinguished Awards in Teaching Program

December 2009

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Table of contents

Introduction ………………………………………………………………………… 3

Background …………………………………………………………………………. 4

Multiple Intelligences in Research Literature…………………………………….. 6

Multiple Intelligences in West View Primary School, Singapore ..……….………9

Multiple Intelligences in the U.S. Schools ……………………………………..… 14

Best Practices: Ongoing Assessments

1. Mathematical Communication …………………………………………… 18

2. Math Journal Writing ………..…………………………………………… 19

3. Project Work ……………………………………………………………… 21

Tips from the expert:

1. Identifying and Encouraging the use of MI in Schools …….….……….. 23

2. Planning MI-based Lessons ….………...…………………………………. 24

3. Dispelling MI Myths ……………………………….……………………… 25

4. Implementing MI …………….…………………….……………………… 26

Conclusion …………………………………………………………………………. 27

Appendix ……………………………………………………………....................... 28

References …………………………………………………………………………. 29

Acknowledgements ……………………………………………………………...… 31

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Introduction

This capstone project is based on a research project that I have developed in

2008 which investigates how incorporating teacher-developed activities based on the

theory of Multiple Intelligences (MI) impacts children’s engagement, motivation,

attitude and achievement in the learning of mathematics in an elementary school in

Singapore.

Many approaches can be used when teaching mathematics to elementary

school children. Whatever method is chosen, however, children’s varied learning

styles, strengths and experiences, and perspectives must be considered. To achieve

this goal, it is important to recognize that not all children learn the same way, and that

children have multiple means of learning.

As part of the Fulbright Distinguished Awards in Teaching Program, I have

sought to learn more about mathematics teaching and learning, especially the

incorporation of MI theory in the teaching of mathematics in the U.S., where MI first

originated. During this Fulbright program, I have visited 8 elementary schools in the

U.S., 2 of which are MI schools. I have the privilege of having observed 30

elementary mathematics lessons and studied how MI strategies are being infused in

the teaching of mathematics in the elementary schools in the U.S.

From these school visits, I observed and attained knowledge about a great deal

of best practices in the teaching of mathematics which I would bring back home and

share with my fellow teachers in Singapore. I hope to put into good practice what I

have learnt from the school visits and make further improvements to mathematics

instruction and assessment in Singapore to ignite and enhance children’s passion in

the learning of mathematics through multiple intelligences.

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Background

Singapore has been ranked very highly in mathematics, top two for the 4th

grade and top three for the 8th

grade (TIMSS, 2007). The standard of proficiency in

mathematics among Singapore children is high and the competition to excel is steep.

As a result, mathematics has become an unpopular subject among the majority of low-

ability children in Singapore schools. These children tend to dislike mathematics as

they are not able to achieve their desired academic scores in the subject. Some

children even develop fear and anxiety in the subject as they believe they will never

be able to do well in it.

Through Singapore’s Ministry of Education (MOE) Teach Less Learn More

(TLLM) Ignite! Project in 2008, West View Primary School school has embarked on

an action research project in the teaching of mathematics through the multiple

intelligences among its Primary 4 children (Othman & Thong, 2009). Through this

project, the school hopes to develop in children a love for mathematics and to help

them see that learning mathematics can be fun and exciting. It is hoped that they will

overcome their fear of the subject and be motivated to excel in it. The project also

hopes to help children perform better in the subject. West View teachers believe that

children have different dominant intelligences, and they can be better engaged if

multiple bridges are used to reach out to them in the teaching of mathematics.

According to the Singapore Mathematics Syllabus for primary schools (MOE,

2009), “the primary aim of the mathematics curriculum is to enable children to

develop their ability in mathematical problem solving. The attainment of problem

solving ability is dependent on five interrelated components – Concepts, Skills,

Processes, Attitudes and Metacognition. Students’ attitudes towards mathematics are

shaped by their learning experiences. Making the learning of mathematics fun,

meaningful and relevant goes a long way to inculcating positive attitudes towards the

subject.” Hence, by addressing the attitudinal aspect in the learning of mathematics,

through the teacher-developed activities based on the theory of MI, children will be

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fully engaged in their learning, understand concepts better and most importantly,

enjoy the learning of mathematics.

Schools in Singapore have traditionally favoured children who excel in

linguistic and analytical arenas because these skills are highly valued in our culture.

Unfortunately, this traditional approach leaves certain children behind to stumble

blindly through an educational system which ignores their unique abilities. This is not

to say that the development of linguistic and analytical skills should be abandoned in

favour of non-traditional approaches to education. Rather, traditional and non-

traditional approaches should be combined to formulate a method of education that is

best suited to the children who populate our classrooms.

The traditional approach for learning in mathematics creates passive learners

(Soh & Tan, 2008). In order for children to take an active role in mathematics, it is

important to engage them (Bednar, Coughlin, Evans, & Sievers, 2002). Engaged

learning is an active involvement in the learning process (Soh & Tan, 2008).

According to Fredricks, Blumenfeld and Paris (2004), “engagement is a multi-faceted

construct that includes affective, behavioral and cognitive dimensions.” Affective

engagement refers to children’s emotional reactions and feelings, behavioral

engagement is described as being task-oriented and cognitive engagement includes

motivation and effort. All the three dimensions are interrelated and are equally

important in engaged learning. Examples of strategies to engaged learning include

cooperative learning activities, experiential learning and teaching to the multiple

intelligences (MI).

The theory of MI, developed by psychologist Howard Gardner (1983), offers a

balance which teaches children what they need to know in order to be successful in

our society in a way that compliments the unique abilities that each individual

possesses. This study seeks to show that when the theory of MI is applied effectively

in the mathematics classroom, it may improve children’s engagement, enjoyment and

attitudes toward learning, thus improving academic achievement.

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Multiple Intelligences in Research Literature

Over the past twenty-five years, educators have embraced Dr. Howard

Gardner’s theory of multiple intelligences as a framework for integrating all the paths

to learning into instruction. Gardner’s asset model empowered teachers to build on the

strengths of all learners, promoting a more complete array of instructional strategies

to foster student success.

Gardner’s theory of the MI is a departure from the view that intelligence is a

single, measurable unit (Gardner, 1999). Gardner believed in different learning styles

and identified eight intelligences. According to Gardner (1991), all individuals have a

blend of the eight different “intelligences”: verbal-linguistic – sensitivity to the

meaning and order of words, logical-mathematical – the ability to handle chains of

reasoning and to recognize patterns and order, visual-spatial – the ability to perceive

the world accurately and to recreate or transform aspects of the world, musical-

rhythmical – sensitivity to pitch, melody, rhythm and tone, bodily-kinesthetic – the

ability to use the body skillfully and handle objects adroitly, interpersonal – the ability

to understand people and relationships, intrapersonal – access to one’s emotional life

as a means to understand oneself and others and naturalistic – the ability to recognize

and classify the numerous species, the flora and fauna, of an environment (Hoerr,

2000). Chapman (1993) stated that each person is born with all eight intelligences, but

because of cultural differences some intelligences develop more than others do.

Gardner (1999) stated that an instructional technique or program that is

heavily reliant on one of the intelligences minimizes opportunities for children who

may not possess a propensity to learn in this way. These children, who may not

achieve in the traditional way, may become lost to both the school and the community

at large. Creating opportunities for all children, by enriching the classroom through

MI develops them and brings out their strengths. Children should be taught based on

their ability and ways of learning. Active and involved teaching is a step towards

children’s academic success. Teachers generally carry the belief that all children are

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capable of achieving. MI considers this and indicates the tools, teaching strategies that

will bring forth such success.

Gardner (1999) suggested there are many ways to motivate children,

depending on how they learn. More meaningful material can spark children’s natural

curiosity about the world around them (Mc Combs, 2002). In order to arouse curiosity,

Robinson, Silver and Strong (1995) suggested that two things need to be

accomplished: make learning a mystery to be solved by the children, and have content

relate to their lives. Children become bored if a teacher becomes apathetic with the

subject matter, when children receive work that is not meaningful to them, or if

curriculum lacks variety. The use of MI helps teachers to tap on different children’s

intelligences and interests. The intention to use MI is to use more ways rather than

one traditional method to reach out to children in their intelligences. Presentations

through various modalities provide children with numerous opportunities to learn

through their strengths. Daily activities should be planned around all the intelligence

areas. The logical-mathematical intelligence is not a strength in many children.

Teaching mathematics to the other intelligences will strengthen their logical-

mathematical intelligence (Bednar et al., 2002). Children’s motivation and

achievement will increase when teachers determine what makes them tick.

The teacher’s role in an MI classroom consists of constantly shifting methods

of presentation from linguistic to naturalistic. Teachers are going beyond the text to

reach the needs of all children. There are many ideas on how to implement MI

strategies. Possible teaching strategies for naturalistic intelligence, for example, would

include allowing children to use their five senses in their learning such as using

manipulative or models, allowing learning through real-life scenarios and including

nature in teaching. Music is a venue through which mathematics can be effectively

taught. Different types of music, such as popular jingles, raps, or marches, facilitate

recall through mnemonics. Puzzles provide a unique alternative to mathematical

instruction. Puzzles aid in numbers and operation sense, help children use patterns to

problem solve, and develop critical thinking skills. Games are a fun way to teach

mathematics. Interpersonal intelligence can be addressed through working in groups.

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Children need work that will give them opportunities to interact with others. Children

who work with others become more involved and energetic. Teachers should always

link their instructional objectives to the eight MI. The exceptional teacher can

combine these intelligences in unique ways to create memorable learning experiences.

Hoerr (2002) stated that the effectiveness of MI is supported by the findings of

a study conducted by Harvard’s Project Zero. In interviewing the principals of 41

schools using MI, 78% of them said that their schools had realized gains on

standardized achievement scores and 63% attributed the growth to practices inspired

by MI theory. Not surprisingly, the use of MI paid other benefits in these schools as

well: 78% of the schools reported improved performances by children having learning

difficulties, 80% reported improvement in parent participation, and 81% reported

improved discipline.

Pokey, as cited by Pociask and Settles (2007) claimed that MI can make the

greatest contribution to education. He suggested that teachers expand their repertoire

of techniques, tools, and strategies beyond the typical linguistic and logical ones.

Stanford, as cited by Pociask and Settles (2007) also stated that by incorporating MI

into the classroom, children can experience success and academic growth. Research

suggests that teaching to the MI is very beneficial for educating the whole learner.

Teaching to the MI improved assignment completion, class participation and

engagement of learners (Cluck & Hess, 2003). There is a general trend toward an

increase in children’s motivation and positive attitude through the use of MI (Bednar

et al., 2002). Children who are exposed to MI also show considerable increase in

academic performance compared to those taught using the traditional method

(Douglas, Burton & Reese-Durham, 2008).

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Multiple Intelligences in West View Primary School, Singapore:

An Action Research

Given the numerous benefits in using MI, we have used MI in the planning

and implementation of our Primary 4 mathematics lessons on “Fractions” and

“Decimals” as our research project through TLLM Ignite! in 2008 (Othman & Thong,

2009) in West View Primary School. The primary purpose of the research was to find

out if the use of MI in the teaching of mathematics will result in children’s increase in

motivation and engagement and will have a positive impact on their attitude and

achievement in the subject.

A total of 140 low-ability and average-ability Primary 4 children and 3

teachers were involved in the research project. In the first semester, a project group of

68 children went through a three-week MI intervention in their learning of “Fractions”

and 72 children who were taught in the traditional way served as a comparison group.

In the second semester, both groups were taught “Decimals” through MI over six

weeks. Post intervention data indicated improved attitude and an increase in

children’s motivation and engagement. Children taught through MI also produced

higher achievement scores in their post intervention tests. Results also suggest that a

longer exposure to MI has a positive impact. Teachers have also gained professionally

from this project (Othman & Thong, 2009).

The findings obtained from this study, resembles other studies which evaluate

MI instructional approach for the children’s success and attitudes. In a study by Cluck

and Hess (2003), results showed improved assignment completion, class participation

and engagement of learners using MI. A similar study by Bednar, Coughlin, Evans

and Sievers (2002) on kindergarten, third, fourth and fifth grade children, results

showed an increase in children’s motivation and positive attitude through the use of

MI. In another study by Douglas, Burton and Reese-Durham (2008) on eighth grade

mathematics children, results showed considerable increase in academic performance

on children taught through MI compared to those taught using the traditional method.

The results from our action research study are also consistent with the larger scale

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research conducted by the creator of MI and its principles, Dr. Howard Gardner which

demonstrates the effectiveness of MI with the noted improvements in standard

achievement scores, performance of children having learning difficulties, parent

participation, and student discipline (Hoerr, 2002).

Due to the length of the current research conducted (Othman & Thong, 2009),

three of the four improvements were observed in our study: improved academic

performance, greater impact on the low-ability children and behavior improvements

namely on children’s attitude and motivation in learning of mathematics. Discipline

problems tend to disappear, as reflected by the project teachers, when children are

excited about learning in a fun filled lesson.

Moving Forward

The success of the project led to a refinement of the prototype and an

emergent model for MI-based lessons in the teaching of Mathematics in West View

Primary School. In 2009, a two-pronged approach has been adopted in West View

Primary School. The school developed by equipping all teachers with practical

working knowledge of using MI through a Key Learning Program (KLP). At the

same time, there was a catalyst group, comprising the specific project teams formed at

Primary 1, Primary 4 and Primary 5, that would systematically use MI to teach

mathematics for selected topics. Overall, the scope has expanded through the

involvement of 210 children and 7 teachers in Primary 1, 280 children and 8 teachers

in Primary 4 as well as 280 children and 7 teachers in Primary 5 (Othman & Thong,

2009).

Children are highly motivated and enjoyed the

MI infused mathematics lessons. To illustrate,

below are excerpts from the journals written by

some children:

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• “We sang a lot of songs about decimals and

fractions. It is very fun and interesting

learning decimals and different types of

methods and using [attractive] power point

[slides] to teach our class.

• I love mathematics! It is really fun to learn!

All the questions [are] like solving mystery

cases! We also played mathematical games to

learn. Our teacher teaches us mathematics in

very fun ways. I love to play more

mathematics games and learn more about

mathematics! The problem sums are really

challenging! Mathematics is now fun!”

• “….The songs help us to remember

[mathematical concepts]. The games are

fun and enjoyable. It is easier for us to

learn (mathematics) because we enjoy the

lessons…”

• “…We can learn a lot through playing

games. The games are very fun and yet very

challenging… The many fun activities make

me like mathematics more… I [am] always

eager to wake up every morning [to] go to

school and learn more about

mathematics…”

• “We did a lot of activities, we sang songs,

played many mathematical games and do a

lot of activities… It is an easy and fun way

to learn. Now my mathematics is improving.

I am looking forward to my END YEAR

EXAM MARKS!”

Feedback from teachers further affirmed the

improvement in attitude and the high motivation

observed in children through the MI infused

mathematics lessons.

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• “The class was highly enthusiastic

which was a dramatic difference from

their usual behavior in class. I can see

that some of them really looked forward

to the lessons. They were engaged and

enjoyed working in groups…It was

really comforting to see a normally

distracted pupil engaged for the first

time …”

• “Children were definitely more engaged

- more activities, more interaction, more

hands-on. As lessons were interesting,

children’s attitude towards mathematics

became better. This positive attitude

helped them to remain engaged even

when doing non-exciting tasks such as

LONG DIVISION!”

• “We all want our children to learn well.

From this experience, we see that

interesting lessons really make a

difference! Children are more interested

in Mathematics, and they enjoy school

more. In this aspect, we have achieved

what we set out to do. We have

succeeded in improving children’s

attitudes and increased their interest in

Mathematics!”

• “I have seen for myself how planning a

lesson that involves multiple

intelligences actually makes the lessons

more exciting for the children. Children

can relate better, recall the learning

points better, and on the whole, they are

more motivated. By getting children

involved through fun activities, songs,

stories, students actually looked forward

to learning.”

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• “Children enjoy the lessons tremendously.

There is a lot of excitement and

productive buzz in the various classes as

the children were highly stimulated.”

• “They learn to grasp concepts quickly by

playing games and singing the lesson

songs.”

• “Children enjoy working in groups and

many of them could perform the group

tasks assigned very well.”

• “Children had learnt well. More

importantly, they become active learners

and they look forward to mathematics

lessons.”

Overall, the implementation of MI infused lessons in West View Primary

School had positive results for both teachers and children. It was an enjoyable

experience in the eyes of both. There was an increase in engagement, motivation,

positive attitudes, and greater passion towards mathematics among the children who

were exposed to MI. In closing, the most beneficial aspect of our research is that it

takes into consideration human differences within the classroom and teaches the

subject matter in a variety of ways appealing to all learners (Othman & Thong, 2009).

Our next step is to focus on how we could monitor our children’s learning of

mathematics through MI particularly in the form of creative ongoing assessments. The

Fulbright school experience in the U.S. has provided me with a better insight in the

teaching approaches of mathematics through MI. To further improve on the use of MI

in mathematics, I would like to adopt best practices that I have observed in the U.S.

schools that I have visited. I would learn to design more exciting MI lesson activities,

craft more creative ongoing MI assessment tasks to monitor children’s progress and

achievement through MI more effectively.

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Multiple Intelligences in the U.S. Schools

The 30 classroom visits I have made in all the 8

elementary schools during this Fulbright program

(Appendix) have been a very enriching

experience for me. I have observed a great deal

of good practices in the teaching and learning of

mathematics in all the classes. In a nutshell,

regardless of whether the school is a public,

private or an MI school, all the teachers have

actually incorporated MI strategies in their

Mathematics lessons.

Generally, teachers have been observed using

authentic materials, bringing real life scenarios

into their lessons, hence addressing the

naturalistic intelligence. They carried out a lot of

mathematical conversation and got their students

to present their answers to the mathematical

problem, explaining, clarifying and justifying

their solutions, hence addressing the verbal-

linguistic and mathematical-logical intelligences.

Many teachers conducted pair-work, group-work,

cooperative learning as well as individual

assignments within the lesson, hence addressing

the interpersonal and intrapersonal intelligences.

In many occasions, students are assigned to write

their reflections and thoughts about the problems in their math journal, hence

addressing students’ linguistic and interpersonal intelligences. Many teachers have

also been observed using jingles, raps, songs and dance, incorporating music and

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movements into their mathematics lessons, hence

utilizing the musical and bodily-kinesthetic

intelligences.

The use of MI strategies in the teaching and

learning of mathematics observed in the U.S.

schools is inevitable if teachers must comply to

the Principles and Standards for School

Mathematics set by the National Council of

Teachers of Mathematics (NTCM, 2000). Of the

10 standards, five are content-oriented and five

are process-oriented. The process standards

include Problem Solving, Reasoning and Proof,

Communication, Connections, and

Representation. They actually serve as a

framework for utilizing the multiple intelligences

that children bring to mathematics learning. Thus,

mathematics lessons and activities that I have

observed in the U.S. schools have been designed

to capitalize on children’s use of the seven

intelligences of learning.

Adams (2001) provides a very comprehensive

relationship between the five process standards

(NTCM, 2000) and MI. He explains that

reasoning means using available information and

prior knowledge to make sense of an idea or

phenomenon. Estimating, questioning,

hypothesizing, and conjecturing are some of the

components of reasoning. Adam (2001) suggests

that one of the best ways to improve children’s

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reasoning skills is to create opportunities and

situations that encourage them to use reason. In

addition, children should be encouraged to justify,

or “prove”, their reasons and explanations relevant

to a mathematical situation. Children will

definitely need to use their linguistic and logical

intelligences as well as other multiple

intelligences when going through this process

standard.

Adams (2001) also highlights that communication

is a key component of an effective classroom.

Oral discourse, written work, and dramatization

provide opportunities for children to share with

and learn from others. Communication also offers

an opportunity for children to be part of an active

community of learners, wherein each child’s input

is valued and respected. This process requires

children to utilize their interpersonal,

intrapersonal, verbal-linguistic, mathematical-

logical, bodily-kinesthetic and naturalistic

intelligences.

Making mathematical connections within

mathematics, and between mathematics and other

disciplines (NTCM, 2000), it is important to help

children view mathematics as an applicable tool. Because children learn differently

and benefit from operating within the strength of one or more intelligences,

mathematical connections can help children view mathematics from different

perspectives.

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Adams (2001) adds that children also need to gain

a perspective of mathematics as a body of

knowledge that is related to other subjects in

multiple ways, and he suggests that curriculum

integration is one tool for making these

connections explicit.

Mathematical knowledge and information can be

represented in a variety of ways. How children

perceive, interpret, and create these

representations is an important issue. For example,

children benefit from being able to use various

representations for solving problems, engaging in

projects and discussions, and exploring the world

of numbers. Teachers must encourage children to

use and create representations that not only make

sense to them, but also are efficient means of

completing a mathematics task (Adam, 2001).

Realizing the relationship between children’s

multiple intelligences and the NTCM standards,

teachers naturally pay attention to children’s

varying abilities, interests, and intelligences to

enhance the quality of mathematics curriculum

and instruction. Teachers may want to consider

the different ways in which a mathematical

concept, skill, or procedure might be approached in light of the different multiple

intelligences, while also acknowledging that many of these approaches and multiple

intelligences overlap. A thorough exploration of the related possibilities can lead to

successful and rewarding mathematics teaching and learning experiences in the

classroom (Adam, 2001).

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Best Practices – Ongoing Assessments

1. Mathematical Communication

What impresses me most in mathematics classrooms in the U.S. is the

mathematical communication that goes on throughout the lesson. Every child’s

contribution is valued and teachers are skillful in reframing, initiating, evaluating and

responding to children’s responses throughout the lesson.

I find the teachers’ role as stipulated in NTCM Standards very useful (NTCM,

2000). It states that the teacher of mathematics should orchestrate discourse by:

• Posing questions and tasks that elicit, engage, and challenge each student’s

thinking.

• Listening carefully to students’ thinking.

• Listening carefully to students’ ideas.

• Asking students to clarify and justify their ideas orally and in writing.

• Deciding what to pursue in depth from among the ideas that students bring up

during a discussion.

• Deciding what to pursue in depth from among the ideas that students bring up

during a discussion.

• Deciding when and how to attach mathematical notation and language to

students’ ideas.

• Deciding when to provide information, when to clarify an issue, when to

model, when to lead, and when to let a student struggle with a difficulty.

• Monitoring students’ participation in discussions and deciding when and how

to encourage each student to participate.

These can only be effectively accomplished in a safe and conducive classroom

discourse and norms which the teacher establishes within the classroom. Teachers

need to be nurturing, encouraging and unassuming. Teachers need to respect

children’s input and create a comfortable environment such that children feel safe

and appreciated even when they make mistakes. Mistakes are learning

opportunities which can be positively utilized.

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2. Math Journal Writing

I have observed that math journal writing is being practiced very extensively

in all the schools I visited. This is a very good form of assessment tool as it helps

children to assess on their learning and understanding of mathematical concepts. I

have observed in the classrooms how journal writing helped children stretch their

thinking and make sense of mathematical problems. When children write in journals,

they examine, express, and keep track of their reasoning, which is especially useful

when ideas are too complex to keep in their heads.

By reading their journals, teachers can evaluate their

progress and recognize their strengths and needs.

The math journal thus becomes a useful

teaching tool for the teachers.

How the mathematics journals have been used vary

in different classes. In the third-grade class of a

particular school, “Math Journal Thinking Trail”

was designed where children do story problems

given by the teachers, typed and pasted into their

journals to reduce writing time. They have a

“thinking box” where children draw the way they

manipulated tools or numbers. Children then

produce the number sentence to solve the problem

and they are then required to explain how they

derive their answers. They are also encouraged to

reflect on their understanding and specify their

confusion or question.