Abstract: This report presents a lesson study conducted with Year 3 students at St Francis of Assisi Primary School (Qawra) focusing on mathematical problem-solving and budgeting skills. The lesson study provided hands-on learning experiences using real money to bridge the gap between abstract mathematical concepts and real-world applications. Teachers collaboratively designed and trialled a lesson in which students engaged in budgeting within a fixed amount, integrating digital tools and cooperative learning strategies. Observations yielded valuable insights into student engagement, the influence of external observers, and the role of technology in mathematics learning. Reflections from both educators and students underscore the importance of collaboration, differentiated instruction, and building students’ confidence in problem-solving. The report concludes with recommendations to improve future lesson studies and enhance student participation.

*Keywords:* Budgeting, lesson study, primary school students, problem-solving, real-life

‘miriam-chetcuti’, ‘amanda-cilia’, ‘natasha-calleja-decelis’, ‘nadine-cauchi-briffa’, ‘daniela-farrugia’, ‘maria-grima’, ‘matthew-joe-spiteri’, ‘christine-tanti’, ‘ruth-vella’, ‘moira-xuereb’

Volume 1 9 , No. 2 , 259 275 Faculty of Education©, UM, 202 5

Enhancing problem-solving in mathematics through

lesson study: Budgeting in the real world

Miriam Chetcuti, Amanda Cilia, Natasha Calleja Decelis, Nadine

Cauchi Briffa, Daniela Farrugia, Maria Grima, Matthew Joe Spiteri,

Christine Tanti, Ruth Vella, Moira Xuereb

Maria Regina College, St Francis Assisi, Primary School, Qawra

*Email: miriam.chetcuti@ilearn.edu.mt

Abstract: This report presents a lesson study conducted with Year 3 students at St Francis of Assisi Primary School (Qawra) focusing on mathematical problem-solving and budgeting skills. The lesson study provided hands-on learning experiences using real money to bridge the gap between abstract mathematical concepts and real-world applications. Teachers collaboratively designed and trialled a lesson in which students engaged in budgeting within a fixed amount, integrating digital tools and cooperative learning strategies. Observations yielded valuable insights into student engagement, the influence of external observers, and the role of technology in mathematics learning. Reflections from both educators and students underscore the importance of collaboration, differentiated instruction, and building students’ confidence in problem-solving. The report concludes with recommendations to improve future lesson studies and enhance student participation. Keywords: Budgeting; lesson study; primary school students; problem-solving; real-life

Introduction

During the lesson, the students applied their 21st^ century skills as they

used their critical thinking skills as they needed to budget their money

appropriately to reach their goal, whilst communicating and

collaborating during the process. The children interacted in teams and

supported each other.

The problem posed was that of creating a ‘Thinking of You’ card (see

Appendix 2), but first students had to ‘buy’ the objects needed to make

this card within a budget of 99c. In this way students had to use their

reasoning skills to choose objects wisely and finding totals and change

from 99c.

The research lesson

The lesson was chosen to expose the students to a real-life situation

utilizing real money. Nowadays children are being brought up in a

society where plastic money dominates real money.

Through problem-solving and mathematical computations, the students

needed to budget the money provided to achieve the final product. This

encompassed 2 tasks using concrete-pictorial-abstract (CPA) approach.

This lesson also enabled the students to use hands-on approach as well

as technological resources.

In this lesson, the teachers sought that students learn about the value of

money and understand the concept of change, whilst planning an

activity within a given budget. The following learning outcomes were

targeted:

I can handle small amounts of money in classroom situations (e.g.

keeping track of money collected from small change for charity

money collections).

I can plan an activity within a given budget (e.g. using tickets,

travel brochures, price lists, menus…).

I can use receipts, simple menus, entrance tickets to work out totals

and change.

I recognise that prices marked as €0.99 are a marketing strategy to

make prices more attractive

I can use assistive technology (e.g. tablets & computers) and other

resources (e.g. array cards, base 10 blocks, Cuisenaire rods, fraction

wall, euro coins, ten frames, Unifix cubes) appropriate to this level

to calculate and to learn about numerical calculations.

The lesson study context

The school

St Francis of Assisi Primary School (Qawra) forms part of Maria Regina

College and is the largest primary school on the Maltese island. It

accommodates around 990 students ranging from early years to year 6

from diverse cultural backgrounds fostering an inclusive learning

environment.

The school strives to give its students a holistic educational experience

through a friendly, safe, fun and eco-sustainable environment. The aim

of the school is to cater for the individual needs of all students

throughout the scholastic year whilst fostering a collaborative

atmosphere where all stakeholders – children, parents and educators –

are given their due consideration. Multicultural experience and a

problem-based approach will assist students achieve their full potential

and nurture the love towards lifelong learning.

The students

The achievement levels in this Year 3 class vary widely, with some

students performing well above the expected grade level, while others

are struggling to grasp fundamental concepts. This division can be

influenced by various factors, including prior knowledge, learning

styles, and external support. For the students who are excelling, maths

can be a source of confidence, and they are often seen helping peers or

tackling more complex problems. On the other hand, those facing

challenges may feel overwhelmed, which affects their ability to keep up.

The most prominent challenge in this class seems to be a lack of

foundational understanding for some students, which creates a barrier

to mastering more advanced topics. Additionally, there are often

individualized attention or differentiated instruction can find it hard to

keep pace with the curriculum. These gaps in learning may be a result

of inconsistent instruction, differing home environments, or various

learning difficulties. Maths anxiety also plays a significant role, as

students may develop negative feelings about the subject due to past

failures.

This class was chosen for its dynamic mix, providing a unique

opportunity to observe how students at different achievement levels

interact with the material and each other. By focusing on this group, it

becomes possible to develop and implement strategies that cater to a

range of needs whether it’s providing extra support to those struggling

or offering enrichment for advanced students. The goal is to foster a

more inclusive learning environment where all students can experience

success and begin to build more positive associations with Maths.

The team members

Name Role at school Role in lesson study Miriam Chetcuti Head of Department (Maths) Facilitator Amanda Cilia Maths Support Teacher Facilitator Nadine Cauchi Briffa Teacher Team member + taught the 1 st^ lesson trial Natasha Calleja Decelis Teacher Team member Daniela Farrugia Teacher Team member Christine Tanti Teacher Team member Matthew Joe Spiteri Teacher Team member + taught the 2nd^ lesson trial Ruth Vella Teacher Team member Maria Grima Deputy head of school Team member Moira Xuereb Deputy head of school Team member Connie Bonnici Digital Literacy Support Teacher Knowledgeable other Marica Saliba Head of Department (Digital Literacy) Knowledgeable other

The lesson study process

The meetings

Date Points discussed

19/11/2024 (^) • Discuss rules and roles

Discuss the ‘research focus’ and identify ways of gaining a better understanding of the focus
Explore what is teaching through problem solving

25/11/2024 (^) • Discussing and deciding upon the teaching through problem solving aspect to focus on during the lesson study 26/11/2024 (^) • Make a timeline

Distribute roles
Discuss the ‘research focus’ and identify ways of gaining a better understanding of the research
Go through the lesson plan template

03/12/2024 (^) • Discussing the research focus

Deciding on the task/problem to use for the lesson study

04/12/2024 (^) • Identify the class in which the lesson study will take place

Go through all the ‘research focus’ and decide which is the most suitable for the selected class
Discuss the possibility of having a videographer during the delivery of the lesson

10/12/2024 (^) • Discussing the main activity.

Discussing the steps to follow in the lesson plan

08/01/2025 (^) • Continue working on the Lesson Plan 09/01/2025 • Meeting with Ms. Marica, Digital Literacy Support Teacher, to work on Task 2 activity 16/01/2025 (^) • Discuss and go through the digital task created by the digital literacy support staff 21/01/2025 • Going through the online task – is there a need to repeat the physical and online task?

Suggest giving one tablet per group, students work simultaneously using tablet and physical worksheet.
Going through the Lesson Plan 23/01/2025 • Working on the lesson plan and amending as per feedback sent by Ms. Amanda and Ms. Miriam.
Amending the worksheet as per feedback sent by Ms. Amanda and Ms. Miriam

24/01/2025 (^) • Discuss online game and worksheet

Add lesson details

The problem-solving task

The lesson plan

Phase 1: Introduction How will the lesson be introduced? What will you say and/or do to get them interested? Initiate the lesson by enquiring the students if they ever used money in their real-life and their experiences with it.

Have you ever used real money at a shop?
What was your experience whilst using it?
Those that didn’t use real money, tell us why?
Do you usually spend all your money or less? (stay within budget). Think-pair-share their experiences. Following, the students’ feedback the teacher will lead the lesson into the scenario. The scenario will be introduced by viewing a short 30 second video clip about the Children in care homes. The video will expose the students to the life inside one of the children care homes in Malta. Following this, it will explain to them how we can make them feel more loved and included in the community. The educator will exhibit and explain the learning intention on the PowerPoint as well as the whiteboard:
The value of money
The concept of change
Planning an activity within a given budget Consequently, the Maths word-problem will be presented and discussed with the class. Furthermore, the problem will be written on the whiteboard and shown on the PPT.

Maths word problem You need to create a ‘Thinking of You’ card (see Appendix 2) for the children in care homes. You have a budget of 99c to be spent on stationery to design the card. Find the total cost of the items chosen and write the answer. Work out the change from 99c. What difficulties might students encounter? Some of the students might have never been exposed to real money, but mostly plastic money or nothing at all. They might not know the actual value of the coins. The total value of the coins against the quantity of the coins. To be able to choose the best value for money and stay within budget. How do you intend to address these difficulties? Use prompting questions:

How you decide which coins you should use?
What will you do if you notice that you do not have enough money? Expose the students to real money while doing hands-on Explain the value of the coins (visual of coins on the ppt, coin flashcards, coins in a container and poster) Showing them a jar with coins of 1c versus a jar with 10c coins and emanate the answers from the students Whilst arranging the coins from smallest to largest in pairs

Phase 2: Students’ work How will students work? Will they be involved in individual work? Or will they be asked to work in pairs or within a small group of 3 or 4 students? Explain how this will be done. The students will be doing the tasks in 4 separate groups. Each group will have 4 students of mixed abilities and whom will be working collaboratively. The task will have an approximate time of 15 minutes. First each group will be given a learn pad, and the students need to scan QR Code 1. The QR Codes will be both presented in the PowerPoint. The online game will reflect the hands-on activity. The teacher will explain and demonstrate the rules of the game. The game will consist of:

Selecting the stationery items that they wish to use for the ‘Thinking of You’ Card. Such items need to be dragged to the trolley side.
The items that are not needed for the card will be dragged to the shop side.
The students will have a budget of 99c, and they cannot exceed it. During the activity the students need to use the whiteboard to work the Maths problem and to refer to it for QR code 2. As soon as the activity is completed, each group needs to take a screenshot of their work. Following the above, the group will scan QR Code 2. This will consist of an online worksheet, which the group must fill in according to the items chosen in QR Code 1 (refer to their whiteboard). They need to fill the quantity, the total cost per item, the total cost of the card and the change. The workings can be done on the mini whiteboard. A screenshot will be taken again to be presented during the discussion stage. Following the online task, each group will go for the hands-on activity. The group needs to select any stationery items that they have on the desk to assemble a ‘Thinking of You’ card for the children’s care home. The stationery chosen can be different than that chosen in the previous activity. A sample of the card will be shown to the kids.

The group will have all the stationery on their desks, with price tags. They need to choose the best value for money when buying the stationery within their budget. They will have real money to use. In the purse they will have a budget of 99c – made up of different coins. A team member will be selected to act as a cashier and handle the purchase of the items, whilst the entire group discuss and handle the change. The group will use the white board to add or subtract the items chosen to be able to purchase them and calculate their change. A worksheet will be utilised for the kids to tick the items, insert the quantity per item, insert the total quantity and check if they will have any change. All workings will be shown. The worksheet will have a challenge box. This will include a picture of a real receipt, and the students need to draw the coins to show the amount on the receipt, using the least possible number of coins. Page 2 of the worksheet will consist of a task in which the students have to choose different stationery using the same amount of money. This task will be targeted for the high ability students. Questions during the main task:

What do you need to keep in mind while choosing the stationery items? Why?
Is it important to check the price tags? Why?
Can you give less money than the total price? Why?
Can you give more money than the total price? Why? To conclude the tasks, each group will have to present their online work as shown from the screenshot, as well as their hands-on worksheet activity. The educator will write the totals and change of each group on the whiteboard to demonstrate to the class if there are any mistakes. Additionally, they will explain their outcome. What difficulties might students encounter with the set task/s as they start working on it? The challenge of the value of coins, during the online game and the hands-on activity. Maths computations, whilst adding the coins and subtracting for the change, as well as to understand the word problem. Some students might need very basic instructions to be able to follow through with the tasks given.

Teamwork; communication; collaboration (highflyers will take over the students with lower abilities). More time might need to be allocated to the task for some students to be able to finish the activity. Not all the students might agree on the design and items chosen to create the ‘Thinking of You’ card. Over excitement when using the learn pad and whilst playing the online game, especially since they are in year 3 and they do not yet have a learn pad. Technical difficulties, such as faulty learn pad, no internet connection or issues arising with the QR Codes. They might be shy to present their work, due to fear of public speaking. How do you intend to address these difficulties? What kind of help do you intend to provide? Pre-done activities and explanation will address the challenge of the value of coins and using real money. Maths computations: assistance will be provided by the class educators whilst the students will be working in a team and supporting each other. Problem solving strategies such as the bookmark resource (see Appendix) will be used in each group. Teamwork: Outspoken students might hinder the proper collaboration and teamwork; hence the educator will set up the groups with mixed abilities for better sharing of skills. The educator will constantly monitor smoother collaboration within the team. Time: the educator will show a timer on the interactive board as well as reminding them verbally. Design disagreement: the educator encourages the skill to compromise and reach a solution, by posing some suggestions. The educators must demonstrate the use of the learn pad during the explanation. Furthermore, the students will have been exposed to other online games on the same learn pad. If technical difficulties arise all groups will do the handson activity and complete the task 2 on the worksheet. The educator will facilitate the process, with constant support and motivation, as well as support from their team.

Phase 3: Summary and closure How do you intend to bring the lesson to a closure? The educator will use the exit cards. Consequently, the educator will ask: The conclusion will take around 5 minutes. What difficulties might students face during this phase of the lesson? The students may demonstrate that they didn’t understand parts of the lesson. How will you try to address these difficulties? The educator will ask the students to re-explain and demonstrate any difficulties mentioned, while facilitating the process to address such challenges, with constant support and motivation.