Project L.A.B Report

Page 1 of 42

L.A.B (Learning Arithmetic Basics) | Project Report

PROJECT REPORT

L.A.B

(Learning Arithmetic Basics) Addition, Subtraction, Multiplication, Division

December, 2014

Prepared for

Teach For Pakistan www.iteachforpakistan.org

Prepared by

M. Aqeel Ashraf Fellow-2014 [email protected]

mailto:[email protected]

Page 2 of 42


1 Transmittal

December 22, 2014

Ms. Maryam Haqqui

Academic Coordinator

Teach For Pakistan, Korangi, Karachi

Dear Madam

Please find enclosed the project report. The report has been drafted on the project

“L.A.B (Learning Arithmetic Basics)”. In this project, four basic arithmetic

operations i.e. addition, subtraction, multiplication and division were taught to

students of grade 3, 4 and 5 at Government Boys Primary School (GBPS), Shireen

Jinnah from 24th Nov to 6th Dec. The report discusses the need of such a project on the

basis of diagnostics assessment results. This is followed by a detailed discussion on

different teaching methodologies applied while teaching above mentioned concepts.

Finally report wraps up on driving conclusions/recommendations based on

comparison between diagnostics and summative assessment results.

Feedback will be appreciated

Kind Regards

M. Aqeel Ashraf Teach For Pakistan- Fellow 2014 Primary Teacher - GBPS, Shireen Jinnah, Karachi Email: [email protected]

mailto:[email protected]

Page 3 of 42


2 Acknowledgment

Author is thankful to

Almighty Allah,

For His unlimited blessings and bounties,

And for keeping him sane, sound and successful;

His parents and co-fellows,

For all their support and trust in him and his aims;

Teach For Pakistan, Training & Support

For teaching him things he knew not;

Shireen Jinnah School Administration,

For their continuous support during his stay at the community and sharing his vision

for his students

And last but never the least

Academic Coordinator

For her utmost help, guidance and time

Which made author able to complete this project

Page 4 of 42


3 Table of Contents 1 Transmittal 2

2 Acknowledgement 3

3 Table of Contents 4

4 List of Figures 5

6 Abstract 6

7 Introduction – L.A.B 7

7.1 Need & Importance 8

7.2 Unique Features 9

8 Diagnostics Assessment 10

8.1 Design Aspect 11

8.2 Result Analysis 12

8.2.1 Major pitfalls 13

8.2.2 Quantitative Aspect 14

8.3 Conclusion 20

9 Project 21

9.1 Objective 21

9.2 Pedagogy Aspect 22

9.1.1 Peer Learning 22

9.1.2 Minor changes-Bigger Impact 25

9.1.3 Practice / Drilling 26

10 Summative Assessment 27

10.1 Result Analysis 28

11 Comparison- Growth Summary 30

12 Conclusion 40

Page 5 of 42


4 List of Figures Figure 1 - A 5th grader’s response in Mid-term exam 8

Figure 2 - Diagnostic Assessments 10

Figure 3 - 4th Grade- Sample Diagnostic Assessments 11

Figure 4 – Major Pitfalls 13

Figure 5 - Shireen Jinnah-Diagnostic-Histogram 14

Figure 6 - Grade 3,4,5-Diagnostic-Histogram 14

Figure 7 - Shireen Jinnah-Mastery-Diagnostics 16

Figure 8 - Grade 3,4,5-Mastery-Diagnostics 17

Figure 9 - Usual classroom structure 23

Figure 10 - Project L.A.B class view 23

Figure 11 - Peer learning through groups 24

Figure 12 - Learning from Senior Students 24

Figure 13 - Simplified INM of Addition 25

Figure 14 - Practice Worksheet -1 26

Figure 15 - Grade 4-Summative Tests 27

Figure 16 - Shireen Jinnah-Summative-Histogram 28

Figure 17 - Grade 3,4,5-Summative-Histogram 28

Figure 18 - Comparison-Scores-Shireen Jinnah 30

Figure 19 - Comparison-Mastery-Shirren Jinnah 32

Figure 21 - Comparison-Mastery-Grade 3 34



Page 6 of 42


6 Abstract

Primary purpose of doing L.A.B project was to increase students’ mastery in four basic

numeracy skills namely addition, subtraction, multiplication and division. The need of this

project was felt after analyzing students’ performance in mid-term exams and diagnostic

assessments. Students achieved mere 5.39 marks on average out of 16 in diagnostic tests.

Results showed that about 75% of the students did not have mastery in four basic arithmetic

skills.

Project L.A.B was a 2 week targeted project with a strong growth assessment system. JMP

software was used to analyze the data coming from students. This project used the

technique of making data driven decision to make learning curve steeper for students. Many

new and innovative pedagogy practices were being used to make learning more interesting

and engaging for students. Along with this many old less effective techniques were modified.

After the project, summative test were conducted and results were compared with that of

diagnostics. Results showed that project helped students in a long way in achieving mastery

in these numeracy skills. Mean score increased from 5.39 to 12.4 (out of 16). The results

further highlighted that there is still a big room for improvement in terms of student

mastery.

Page 7 of 42


7 Introduction- L.A.B “You cannot create experience, you must undergo it”

Projects-based learning is a dynamic approach where one has a greater control over his learning. As a

Teach for Pakistan fellow, author feels like analyzing/reflecting on these two years of fellowship’s

performance on yearly basis, just gives too less time and opportunity to a fellow to improve and

experiment with different strategies in a classroom setting. So in author’s perspective, it’s more helpful

to divide even single year of fellowship into one-week to two-week time periods and doing

targeted/objective projects with a proper results monitoring system. This was the basic thought in

teaching simple maths concepts like addition, subtraction, multiplication and division under an umbrella

of a project called L.A.B (Learning Arithmetic Basis).

Basic objective of project L.A.B was to increase mastery level of 3rd, 4th and 5th grade students in four

basic arithmetic skills i.e. addition, subtraction, multiplication and division. In order to achieve this

objective, different strategies in all areas were applied and then subsequent outcomes were monitored.

Author has also taught these concepts previously but the mastery level of students as a result was not

impressive. So that experience also served as a reference point while designing L.A.B project.

Page 8 of 42


7.1 Need & Importance

The need of such a project was strongly felt after the mid-term exams as most of the students were

unable to solve simple problems of addition, subtraction, multiplication and division. Lack of mastery in

these basic arithmetic skills was equally evident across all grade levels. It was necessary to start a

revision camp for these skills with an innovative approach, before moving on to teach higher concepts.

Due to this deficiency, nearly 35% students in each grade level were unable to achieve mere passing

percentage i.e. 33% in Maths mid-term exam.

Figure 1 - A 5th grader’s response in Mid-term exam

Addition, subtraction, multiplication and division are basic numeracy skills which need to be mastered

in order to achieve minimum mastery on the primary level maths curriculum. These skills will further

make students able to solve basic arithmetic problems of their daily life like doing shopping from a

grocery market, calculating family monthly expenditure etc. This will help students to get engaged with

maths curriculum in more practical way.

Page 9 of 42


7.2 Unique Features

Author has already taught concepts of addition, subtraction, multiplication and division to 3rd, 4th and

5th graders. So that experience served as a great reference point for author while designing project L.A.B

(Learn Arithmetic Basis). Certain pedagogy strategies that were applied previously went off the list this

time as student demonstrated below average mastery. Innovative and interactive teaching strategies

were chosen after a through debrief session with academic coordinator in order to facilitate student

learning.

Following are the few unique features of the L.A.B project that differentiate it from the way these

concepts were taught in the first attempt.

Comprehensively designed diagnostic assessments to gauge student understanding of the whole

concept in general and potential pitfalls in particular.

Incorporating strategies in lesson planning to clarify frequent pitfalls that came up through

diagnostic assessments.

Following “Learn by Doing” approach in lesson planning to make content more student engaging.

Applying “Differentiated Learning” strategy in order to make class time equally productive for all

level of students.

Giving away extra practice worksheets as homework

Setting ultimate level of mastery as “able to teach others” in order to enhance peer learning and

feedback inside classroom.

Using charts and other real life items to make content more engaging and appealing.

Comprehensively designed summative assessments to check student mastery.

Page 10 of 42


8 Diagnostic Assessments

Diagnostic assessment is a type of assessment which examines what a student knows prior to a learning

program being implemented. Before starting the project, it was necessary to take diagnostic

assessments for following reasons:

To get information about student's prior knowledge about the concepts.

To narrow down the points of common misconceptions among students about the concepts.

To provide a baseline for understanding how much learning has taken place after the project is

completed.

To plan for appropriate pedagogy and targeted learning to more effectively scaffold the learning

needs of students.

Figure - 2 Diagnostic Assessments

Page 11 of 42


8.1 Design Aspect

Diagnostics assessments were comprehensively designed in order to gauge students understanding.

They were scaffolded from easy to hard. Furthermore all types of questions related to all rigor level

were included to check both breadth and depth of the student understanding. Copying/cheating during

diagnostics assessments was a major reason of data unreliability which eventually leads to a false

conclusion. To overcome this problem, author designed at least four different diagnostic tests for a

particular grade level and they all were same in their basic layout but different in terms of problems.

Following represents two of the four different diagnostic tests given to fourth graders.

Figure 3 - 4th Grade- Sample Diagnostic Assessments

Page 12 of 42


Referring to the diagnostics assessment on the previous page:

“Q#1 (i)” was designed to check student ability to add to different numbers without carrying. Unequal

number of digits in both numbers checked the student knowledge of writing same place value digits

above one another. Next problem i.e. “Q#1 (ii)” was to check student understand of adding numbers

with carrying. Similarly two problems of division were designed in such a way that they must present

every type to case to students for example situation were dividend is less than divisor etc.

Shortcoming: Despite of taking extra care while designing diagnostic assessments, yet one shortcoming

that author came to know later was that multiplication section of these assessments did not checked

the student understanding of multiplying any number with zero.

8.2 Result Analysis

Results from diagnostics assessments were compiled and analyzed in such a way so that they

provide answers to following set questions:

Q#01: What were the most common errors done by students while solving problems?

Q#02: What scores each student scored out of total i.e. 16?

Q#03: How many students in each of the grade have mastered addition, subtraction, multiplication

or division?

Q#04: Calculating common parameter that would help to compare these results with summative

like mean score etc.?

Page 13 of 42


8.2.1 Major Pitfalls

Following were the major pitfalls / points of misunderstanding as they came up through diagnostics

results:

1. Place value concept: Majority of the students didn’t write

same place value digits one above another while solving

addition & subtraction problems.

2. Knowledge of Signs: Many students did not know the

mathematical signs for addition, subtraction,

multiplication & division.

3. Starting point: Many of the students were starting

solving problems from the left hand side rather than the

right hand side.

4. Concept of carrying: A portion of students did not know

to carry one to the next place value when sum exceeds 9.

5. Concept of borrowing: A portion of students did not knew

to borrow one to the next place value when upper digit

is smaller than the lower one at same place value.

6. Tables: Majority of students have not memorized

multiplication tables. Few of them who did, not actually

knew the rational/logic behind forming those tables.

7. Division: Many of the students failed to identify dividend

and divisor in a division problem.

Misconception # 01

Misconception # 02

Misconception #04

Figure 4 – Major Pitfalls

Page 14 of 42


8.2.2 Quantitative Aspect

A total of 85 students (after omitting students who either missed diagnostic or summative) were

monitored in this project. This sample size included 33 students, 24 students, 28 students from

grade 3, 4 and 5 respectively. Software used for this purpose was JMP.

Shireen Jinnah - Overall

Figure 5 - Shireen Jinnah-Diagnostic-Histogram

Grade - 3

Figure 6 - Grade 3-Diagnostic-Histogram

Page 15 of 42


Grade - 4

Figure 6 - Grade 4 --Diagnostic-Histogram

Grade – 5

Figure 6 - Grade 5 --Diagnostic-Histogram

NOTE: A histogram is a display of statistical information that uses rectangles to show the frequency of data items

in successive numerical intervals of equal size. In the most common form of histogram, the independent variable

is plotted along the horizontal axis and the dependent variable is plotted along the vertical axis.

Page 16 of 42


Shireen Jinnah - Overall

Figure 7 - Shireen Jinnah-Mastery-Diagnostics

Page 17 of 42


Grade – 3

Figure 8 - Grade 3-Mastery-Diagnostics

Page 18 of 42


Grade – 4


Page 19 of 42


Grade – 5


Page 20 of 42


8.3 Conclusion

Diagnostics result were ALARMING as only 6% (i.e. 6% of 85= 5 students) of the whole Shireen Jinnah’s

students population had mastery in four basic arithmetic skills – addition, subtraction, multiplication

and division. More than 75% of the students at Shireen Jinnah didn’t know subtraction, multiplication

and division. Furthermore results showed that understanding level of student decreased as we go from

addition to subtraction to multiplication to division.

These results confirmed the urgent need of the project L.A.B.

Page 21 of 42


9 Project L.A.B

9.1 Objective

Following were the objectives of the Project L.A.B (Learning Arithmetic Basis).

Primary objective:

To increase the mastery level of students in four basic numeracy skills i.e. addition, subtraction,

multiplication and division

Secondary objectives:

To expose students to a variety of teaching methodologies in order to figure out what works

best for them

To make author able to track the learning curves of students from start to end of the project

and be able to apply innovative ideas to make this curve steeper.

Improving author’s understanding of designing diagnostics, INMs (Introduction to New

Material) and summative.

Note: JMP is a statistical analysis software developed by SAS. JMP combines powerful statistics with dynamic graphics, in memory and on the desktop. Its interactive and visual paradigm enables JMP to reveal insights that are impossible to gain from raw tables of numbers or static graphs

Page 22 of 42


9.2 Pedagogy Aspect

Steepness of the learning curve inside classroom depends upon teaching & learning methodologies.

Pedagogy is "how" teaching and learning occurs. Author feels that there must be variety in teaching

methods in order to reach to all the students in the class.

Many new techniques were applied in the L.A.B project so that learning benefits must reach to the

weakest student in class as easily as they reach to the strongest. These techniques focused on extracting

maximum advantage out of the classroom time. Furthermore these teaching methods were designed to

counter the common pitfalls student faced while attempting diagnostics.

9.2.2 Peer Learning

Peer learning is an educational practice in which students interact with other students to attain

educational goals. As these concepts of addition, subtraction and division have been taught earlier. So

this time round the basic thinking behind L.A.B project pedagogy was to make academically weak

students interact with their academically strong peers to achieve required academic goals. Peer learning

was accomplished through following two means;

Classroom Structure

Previously author used to deliver complete lessons standing in front of the black board and students

going through all the 5 steps of the lesson planning. This approach was proving to be too passive for

Page 23 of 42


students. Also this approach was making difficult for the

author to quickly spot the students who didn’t get the

concept as lesson was being driven forward mostly by

the correct responses from strong students. So in order

to make the best use of class time and to provide

customized learning solutions for weak students, whole

class was divided into groups of 5 led by an

academically strong student. Author chose 5-6 students

in each grade who were academically strong and made

them leaders of the group. Lesson used to happen in a

way that all students individually listen and comprehend

first two steps i.e. opening and INM (Introduction to

new material) part then they were divided into group

and each group used to start work as an independent

class. Where, first of all, group leader used to repeat

briefly the INM part and then they used to do remaining

three parts of the lesson plan i.e. GP, IP, Exit ticket. In

the meantime, author used to roam in the class and

check the working of different groups. At the end, group

leader present report to the author about how many in their group perfectly got the concept. In this

way, author quickly came to know about the student who didn’t get the concept and then special

combined remedial class were arranged for grade 3, 4 & 5. This technique proved to be really helpful.

Figure 9 - Usual classroom structure

Figure 10- Project L.A.B class view

Page 24 of 42


Guest Speakers

Senior students are always a great help for junior students. Author thinks that inter-grade learning

should also happen along with intra-grade learning. That is why during project L.A.B strong students

from upper grade were invited to lower grade classes as guest speakers. They explained one of the

four numeracy skill to the students. This further enhanced peer learning.

HAMMAD (4th grader) L.A.B Group

YOUNUS (4th grader) L.A.B Group

ADNAN (5th grader) explaining addition to 4th graders MUHAMMAD (4th grader) explaining subtraction to 3rd graders

Figure 11 – Peer learning through groups

Figure 12 – Learning from Senior Students

Page 25 of 42


9.2.3 Minor Changes – Bigger Impact

There were few basic errors in the way author was delivering his math lessons. Those errors were

corrected while designing lesson plans for project LAB. Amazing results were by doing just these

adjustments. Two of such correction are listed below;

Improved INM (Introduction to New Material) & Blackboard usage

There were flaws in author’s execution of INM part of lesson plan in class. Basic shortcoming was that

INM was not being translated on the black board in a student friendly mode. Student friendly mode

means that students should be able to take notes of that INM and can refer to them at their homes.

Special attention was given to this aspect and it was made sure that students must take notes of the INM

written on the board. Further it was observed that students at primary level have very short

concentration time. So writing INM in this way helped to pick up from where they left more easily.

Figure 13 – Simplified INM of Addition

Page 26 of 42


MATH Notebook

It came to spotlight through diagnostics that students struggled with the concept of place value while

solving problems of addition and subtraction. Majority of the students had that problem. While

brainstorming solutions, it was decided to just change the type of math notebooks students were

using. This small change resulted in solution of a very big misconception. Before this project, student

used to use lined copies for math subject (same as that for Urdu). But now all of the students have

shifted to boxed copies for maths work.

9.2.4 Practice/ Drilling

Maths requires lots of practice and that aspect was

totally absent as students were not revising concept

at home that were being taught in class. During this

project, it was made sure that students solve

numerous problems of addition, subtraction,

multiplication and division. For that many practice

worksheets were given to them that they either

completed at home or at school. This helped them to

memorize the procedure for solving these problems.

Figure 14 – Practice Worksheet -1

Page 27 of 42


10 Summative Assessment

Summative assessments were used to evaluate student learning and academic achievement at the

conclusion of the L.A.B project.

These tests were used to determine whether students learned what they were expected to learn. In

other words, what makes an assessment “summative” is not the design of the test, per se, but the way

it is used—i.e., to determine whether and to what degree students have learned the material they have

been taught. The design of summative tests were the same as that of diagnostics test with a slight change

as boxed space was provided for student response instead of lined space.

Figure 15 - Grade 4 – Summative Tests

Page 28 of 42


10.2 Result Analysis

Shireen Jinnah – Overall

Figure 16 - Shireen Jinnah-Summative-Histogram

Grade – 3

Figure 17 - Grade 3-Summative-Histogram

Page 29 of 42


Grade – 4


Grade – 5


Page 30 of 42


11 Comparison-Growth Summary

Following statistical visualizations represents the comparison of diagnostics and summative results.

Figure 18 - Comparison-Scores-Shireen Jinnah

Shireen Jinnah

Page 31 of 42


Page 32 of 42


Shireen Jinnah – Mastery level - Comparison

Figure 19 - Comparison-Mastery-Shireen Jinnah

Page 33 of 42


Grade 3

Page 34 of 42


Grade 3 – Mastery level - Comparison

Figure 20 - Comparison-Mastery-Grade 3

Page 35 of 42


Grade 4

Page 36 of 42


Grade 4 – Mastery level – Comparison


Page 37 of 42


Grade 5

Page 38 of 42


Grade 5 – Mastery level – Comparison


Page 39 of 42


Page 40 of 42


12 Conclusion

Based on the results, it was concluded that project L.A.B helped students in a great way in learning basic

numeracy skills. Mastery level of students increased substantially across all grade levels. Students were

exposed to different learning methodologies which made possible for them to approach a particular

concept in number of ways. It was also observed that students having improved understanding of basic

arithmetic skills started to perform better in other concepts like finding HCF & LCM, solving word

problems etc.

Author learned in the process of this project that how to use data to monitor students understanding

level & subsequent growth. It also helped him to learn how to make data-driven decisions to improve

effectiveness.

Another important point that came to spotlight just because of monitoring this data was the number of

students who still didn’t achieve required mastery level for example 31.8% and 43.5% of all the Shireen

Jinnah students didn’t have mastery on multiplication and division respectively as per summative results.

Page 41 of 42


FEEDBACK

Page 42 of 42


Plot 333, Korangi Township, Near Pak Refinery | Karachi | Pakistan

Documents

Project L.A.B Report