SSTRF_2017_ETD_3 Explore-Useful Learning Math Apps 


Principal Investigator: Lawrence WEE Loo Kang

Co-Principal Investigator (if any): Thong Chee Hing

Woo Huey Ming

Kwan Yew Meng

Samuel Tan

Collaborators (if any): Professor Felix J. Garcia Clemente University of Murcia, Spain



Learning problems in Primary Mathematics for young students could stem from a lack of concrete and personal experiences with mathematical concepts. Therefore, the use of simulations is a technique for practice and learning that is be applied to many different disciplines such as the military (training soldiers in rifle shooting techniques), aviation (training pilots in landing and taking-off of airplanes) and in education, to complement existing concrete hands-on learning experiences. Thus, we argue that simulation can provide valuable learning experiences, especially so with the online portal Singapore Student Learning Space.  

In today’s context, one student to one mobile device can be seen to be pervasive in and out of classrooms, so our simulations will be able to run on these mobile devices in addition to normal desktop computers. A 2017 tech scan on the One Portal All Learners (OPAL)  resource library shows that Primary mathematics makes use of web-based applets which are not compatible with these mobile devices. Even on the internet, many of the simulation applets available are also not localised to our national curriculum (Wee & Mak, 2009).

Thus, we proposed an approach to design and develop open-source Mathematics learning simulations (interactive resources), compatible with almost any mobile devices in an efficient and sustainable manner. To increase chances of organic scaling up these ICT tools, we will be guided by the 3A framework of Accessible (licenses creative commons attribution), Adaptable (open source codes) and Affordable (free of charge).

This SSTRF aims to be a specialist leader in Translational Research, Innovation and Scaling (TRIS) to realise the vision of “Quality Learning in the Hands of Every Learner - Empowered with Technology”, a goal of  the Information and Communications Technology (ICT) Masterplan 4, Singapore.



To explore the design and development of open source Learning Math Apps and website, for use in Android and iOS mobile devices.

Final Report Hack Design Thinking Methodology

Our approach is start with prototype first then to cycle through to understand, define, ideate, prototype and test Math apps tailored to the Singapore Primary syllabus, improved and infused with literature and school-based-research pedagogical features and make them freely accessible on the internet, for the benefit of all in Singapore and beyond. We speculate that the hack design thinking will allow the project to rapidly developed 15 (instead of the initial 4 planned) solutions that actually meet MOEHQ officers’, teachers’ and students’ needs in the one year SSTRF time frame because of the existence of rich Math expert knowledge (we already been empathizing, scoping and ideating all the time) and deep educational technological knowledge to create apps.

To sum it up, we have five stages to our research methodology:

Hack Start Stage 4 (Prototype):

Create working prototypes based on the wealth of resources on OPAL and the internet.

Stage 1 (Empathize):

Understand users’ requirements to develop a deep understanding of the teaching and learning challenge-problem by networking with ETD ICT in Math Learning Community teachers and scanning the internet and literature.

Stage 2 (Scope):

Define clearly the problems to solve. Expand the related scope of what the simulation can do to cover more learning issues across primary 1 to primary 6, foundational to gifted programme.

Stage 3 (Ideate):

Brainstorm potential designs that can be supported by the selected open source tools.

Stage 5 (Evaluate):

Assess their usability and engage in a continuous short cycle of prototyping process to continually improve the design.

Proposed Design Thinking Methodology

Our approach is to empathize, define, ideate, prototype and test Math apps tailored to the Singapore Primary syllabus, improved-infused with literature and school-based-research pedagogical features and free on the internet for anyone to use, for the benefit of all students in Singapore.

In brief, stage 1: empathize aims to develop a deep understanding of the teaching and learning challenge-problem by networking with ETD ICT in Math Learning Community[1] teachers and scanning the internet and literature. If the App is ready by stage 1 (empathize), it will include user (teacher and students) experience. Stage 2: define aims to clearly articulate the problem the project wants to solve as agreed by the team. Stage 3: ideate aims to brainstorm potential solutions using the open source tools selected by the PI and develop the solution using open licensed tools to lower barriers to scaling up these practices using our solutions-apps. Stage 4: aims to design a series of prototypes to test part(s) of the solution and integrate them eventually. Lastly, stage 5: test aims to engage in continuous short cycle of innovation process to continually improve the design.

Key Findings

  1. 1. Technology Magnifies

Case 1: Anchor Green Primary School

The Telling Time lesson conducted by Ms Anna Goh (Anchor Green Pri) was very effective because the practices of pattern recognition on O’ clock and half past where the whole class would sit on the floor in front of the whiteboard and focus on the teacher’s facilitation and guiding questions.

Students were invited to ask questions orderly and the teacher used a storybook about time to set the context, and flip paper table to write down their collective responses. The App developed was on the class projector screen serving as a teaching tool.

In the last 15 minutes, students are allowed to practice through the self assessment game of telling time while the teachers goes around the classroom to check on their learning progress.   

Case 2: Henry Park Primary School

The Target Math Addition Game lesson conducted by Ms Theresa Heng (AST MTT) was effective because the practice of the game play was an established practice using physical cards, worksheets and teacher facilitation by Theresa.

Students were paired during the lesson, using a laptop to engage in the game play of taking turns to add using their ‘hands’ of cards (number 1,2,3,4,5) and who reach the target of 20 first, is the winner. In order to win consistently, player 1 and player 2 need to strategize target minus maximum of opponent players card minus minimum of own card.

For example, to win, 20 - 5 -1 = 14, so both players will try to reach 14 first, in order to gain control. Using the same logic, 14 - 5 -1 = 8 and 8 - 5 -1 =2 is deducible.

So to win, adding to 2 first and that player will have control by always adding to 2, then 8, then 14 and finally 20. To our delight, most students were able to come up with their own strategy to win for those challenges set in the worksheet.

The complexity and challenge can be further by selecting different targets instead of 20, even or odd set of cards numbers for players and starting number not equal to 1.

At the end of the lesson, one boy came up to the project team and issued a challenge to play the game using both players with only even cards 2,4,6 for both players.

Thus, 20 - 6 - 2 = 12 and 12 - 6 - 2 = 4, so the boy who is player 1, started by hitting the 4 card and managed to reach 12 and 20 eventually , winning the game consistently.

This is a moment where the magic of student creativity was clearly demonstrated through the student’s mastery of the rules of addition with a gaming element.

The two cases serve as evidence supporting the argument that educational technology can amplify student learning gains measurably, provided there are effective teaching and learning processes.

Figure from A model of teacher professional knowledge and skill including PCK: Results of the thinking from the PCK Summit January 2015 Julie Gess‐Newsome


In other words, educational technology cannot ‘cure’ bad teaching nor poor learning attitudes, but can magnify effective teaching and learning gains but it can also worsen matters in already ineffective lessons.

2 What MOE teachers like

2.1 Accessible

Teachers feedback that the interactive resources are accessible and runs smoothly in operating systems such as mobile Android, iOS and laptop WIndows OS and Mac OS. Having the same simulations as Apps greatly increase the ease of using them in the classroom without strong WiFi as the students can be instructed to download the Android or iOS app where there is strong WiFi.

2.2 Adaptable

Teachers feedback that the strengths of the prototypes is their ability to further customize to suit their pedagogical preferences, such as for use in guided inquiry, self directed learning or demonstration during direct instructions. Thus, most of our apps are designed with 2 modes, one to support teachers’ direct instructions and other existing pedagogical practices and two to support students’ self directed learning and productive exploration.

2.3 Affordable

Teachers feedback that the free prototypes for Google and iOS and the website do indeed make them very easy and convenient to deploy to the students’ own personal  mobile devices or the schools’ devices (laptops and tablets).

  1. What MOE-HQ like

Quality Learning in the Hands of Every Learner

Aligned with the ICT Masterplan 4 goal of “Quality Learning in the Hands of Every Learner - Empowered with Technology”, these interactive resources can be regenerated and deployed as web pages (HTML) for Student Learning Space, mobile Apps (APK and IPA) and even electronic books (EPUB), using the same technology tool called Open Source Physics OSP (Easy Java-JavaScript Simulation, EJSS) modeling tool.


The Apps are available on the Open Source Physics at Singapore digital library website, Android App and iOS App Stores. The table below shows the number of visits and installations as a proxy to our dissemination efforts.

App number and short name

Website visits

Android Store install

iOS Store install

1 Numbers from 1 to 100




2 Telling Time




3 Weighing Scale


8 200


4 Nets of Cubes




5 Net(s) of Square Pyramid




6 Speed for 2 Objects




7 More than Less than Question Generator




8 Target Math Addition Game




9 Comparing Fractions




10 Add and Subtract Proper Fractions




11 Volume of Tank Simulator




12 Symmetry Block




13 Symmetry Letter




14 Symmetry Shape




15 Multiply Fractions








NA - not available

Thus, grand total of website visits, Android installs and iOS installs is


A total of 4 face to face Sharing sessions-workshops were conducted and the URL of the contents of the sharing on each URL below.

1 for 40 teachers

2 for 20 teachers

3 for 30 teachers

4 for 30 teachers

Total of 120 teachers attended our 4 workshops.

Conference Paper:

García Clemente, F. J., Esquembre, F., & Wee, L. K. (2017). "Deployment of physics simulation apps using Easy JavaScript Simulations," 2017 IEEE Global Engineering Education Conference (EDUCON), Athens, 2017, pp. 1093-1096.

doi: 10.1109/EDUCON.2017.7942985. arXiv preprint arXiv:1708.00778.

4 Planning and Design

For Criteria for success, we propose measuring the degree of usefulness and willingness to continue using them after the funding period through survey and interviews.As for iterations, the PI will iterate the apps after SSTRF to ensure effectiveness of apps after funding period ends as was done in PI’s other apps found on earlier SSTRF-ETD_2012_01 Gravity Physics by Inquiry[2]

Currently, planned 4 apps, topics will be varied based on school needs (already prototype are time, numbers1 to 100, reading scale, nets of 3D), target audience are primary 1 to 5, schools/teachers involved with be as many as possible, minimum 2 classes per app is desired so that the app is improved to meet MOE’s school needs.

Samples of the designing thinking methodology is already available here as the project members empathize, define, ideate, prototype and test Math apps during and before-and-beyond the funding period. 


A total of 15 (instead of the intended 4) interactive resources are developed as Website and Mobile Apps, accessible, adaptable and affordable on the Open Source Physics at Singapore digital library. The list below is based on chronological order of date when first prototype is made and attributed with where the initial idea came from.

1 to 100 for learning Odd, Even, Multiples and Factors based on ideas from Thong Chee Hing (ETD SS) and teachers in our workshops.

  • Teaching mode shows odd, even, multiples and factors up the number 100, great for teacher demonstration (direct link)
  • Practice mode affords for student exploration with automatic targeted feedback
  • Colour-coded factor pairs for pattern recognition such as 1x24, 2x12, 3x8, 4x6 = 24

Telling Time based on ideas from Anna Goh (Anchor Green Pri) Theresa Heng (AST MTT) and teachers in our workshops (direct link)

  • Game mode affords for a random time to be set to the nearest half an hour or 5 minutes and dragging the both clock hour and minute hands to correct position for feedback with sound.
  • Practice mode affords for student exploration with automatic targeted feedback.
  • Teaching mode shows time in O’clock half past, and quarter to and past, great for teacher demonstration

Mass or Weighing Scale based on ideas from Rachelle Lee (Yio Chu Kang Pri) and teachers in our workshops (direct link)

  • Teaching mode shows a weighing scale in 1, 4 and 5 kilograms used by the teacher. The apple, coin and pineapple are example objects to give practical usages and typical masses of common objects.
  • Practice mode affords for selecting the correct mass in either whole number grams (lower primary) or decimal kilograms (upper primary)
  • Able to zoom in and out via pinching the screen of the handphone for better interactivity, great for projector usage by teachers.

Nets of Cubes and Cuboids based on ideas from Thong Chee Hing and teachers in our workshops (direct link)

  • Teaching mode shows either isometric and realistic three dimensional view of a cube or cuboid folding and unfolding in a total of 11 ways of which there are patterns A (1,4,1 squares in a row), B (1,3,2 squares in a row), C (3,3 squares in a row)and D (2,2,2 squares in every row) for pattern learning  
  • Added an input field calculator feature for cost per unit area, for a more authentic case of building a swimming pool with only 5 sides and a open top.
  • Colour-coded for ease of noticing the 6 faces of the cube or cuboid.

Net(s) of Square or Rectangular Pyramid based on ideas from Thong Chee Hing (ETD SS) and teachers in our workshops.(direct link)

  • Teaching mode that shows realistic three dimensional view of a square pyramid folding and unfolding into a net

Speed for 2 Objects based on ideas from Lye Sze Yee (Teck Whye Pri), Cynthia Seto (AST PMTT) and teachers in our workshops (direct link)

  1. teaching mode shows adjustable town A and town B distance apart, with a bus and a car with adjustable speeds and starting positions
  2. a drop-down menu of different scenarios for ease of exploring concepts
  3. the bus and car can U-turn or stop at town B or town A, making this simulation fully customised to Singapore teaching practice and examples found in OPAL lessons.

More than Less than Question Generator based on ideas on website and teachers in our workshops (direct link)

  • practice mode comes with 3 different sets of possible questions and when student gets something wrong, hints appears in the form of bar models in part (BLUE) add or subtract part (RED) to get the whole (GREEN)
  • colour coded the model bars and the question numbers used to aid pattern recognition.

Target Math Addition Game based on ideas from Theresa Heng (AST MTT) (direct link)

  • game designed for 2 player playing on the same device/laptop through turn taking.
  • customised to suit teachers request of adjustable deck of number cards, even or odd sets and different starting card numbers and final addition target, for a great variety of possible card play.
  • appropriate feedback is given when player 1 or player 2 reach the target (WIN) or exceed target (LOSE)

Comparing Fractions based on ideas from two Primary 3 lessons in SLS and teachers in our workshops (direct link)

  • teaching mode through dropdown menu shows 1. equivalent fractions in SLS video 12=36 and questions, 2. greater or less than related fractions 45>35, 3. greater or less than of unrelated fractions 25>310with a make equal parts for the denominator for conceptual understanding
  • shows 1. circular parts of a whole, 2. horizontal bars of a whole and 3. vertical bars of a whole for multiple representations and synergistic learning
  • drawing (solid line and dotted line), colour scheme(RED and GREEN with transparency helps productive noticing when the 2 shapes are dragged to overlap or played ) and position of start of fraction piece are based on rigorous tech scan of available resources

10 Add and Subtract Proper Fractions based on ideas from Primary 3 lesson in SLS and teachers in our workshops (direct link)

  • teaching mode through dropdown menu shows 1. additional of  same denominator fractions in SLS video 411+511=? and questions, 2. subtraction 56-16= ? with automatic solver to show simplified answers 9/11 and 2/3 respectively. The green piece move to the red piece position now different from the earlier simulation to aid teacher instruction
  • shows 1. circular parts of a whole, 2. horizontal bars of a whole and 3. vertical bars of a whole for multiple representations and synergistic learning
  • drawing (solid line and dotted line), colour scheme(RED and GREEN with transparency helps productive noticing when the 2 shapes are dragged to overlap or played ) and position of start of fraction piece

11 Volume of Tank Simulator based on ideas from Khoo Ghee Han (Jing Shan Pri) (direct link)

  • teaching mode comes with pre-defined examples from worksheet by teacher question 1 to 13 where the three dimensional water tank can get filled up via a tap above and lose water via a bottom tap. Students can visualise exactly at which time the changing height of the water level, what amount gets poured into or gets drained out of the tank
  • practice mode comes with input fields for length, width and height of tank, current water height, amount of water to be added, and rate of water in and out of tank for a full suite of possibilities to suit most Singapore complex word problems involving volume of tank

12 Symmetry Block based on ideas from Thong Chee Hing (ETD SS) and Yeo Teck Wai (CPDD) (direct link)

  • teaching mode comes with 4 different (horizontal, vertical, 45 degree and -45 degree to x axis) symmetric lines, selectable draw straight lines, click boxes and free hand draw.
  • practice mode supports student clicking on a number of boxes and check if their answers is indeed symmetrical about the line of symmetry
  • in the free hand mode, different colour also help students visualise their instantaneous lines and their symmetry

13 Symmetry Letter based on ideas from Thong Chee Hing (ETD SS) and Yeo Teck Wai (CPDD) (direct link)

  • teaching mode comes with 2 different (horizontal, vertical, symmetric lines to a predefined 26 letters in the alphabet that shows a folding about the symmetric line.
  • practice mode supports student clicking on either horizontal or vertical skewing that animates the letter with the new selected skew, which helps student explore if it is indeed symmetrical and if not, how it looks like

14 Symmetry Shape based on ideas from Thong Chee Hing (ETD SS) and Yeo Teck Wai (CPDD) (direct link)

  • teaching mode many options such as circle with infinite symmetric lines, square, rectangles, pentagon, ladybug and butterfly and their correct lines of symmetry that shows the folding and unfolding about the symmetric line.
  • practice mode supports student clicking on the hotspots to fold the shape and the symmetric line darkens after being selected.

15 Multiply Fractions based on ideas from Sharon Ong (ETD) and an existing Geogebra applet (direct link)

  • teaching mode comes with selectable the 4 dropdown menu (numerator and denominator of the 2 fractions) that shows the interaction of the 2 fractions as the visualise representation of the effects of multiplying 2 fractions
  • the final simplified answer is also shown to help calculations

The screenshots below aim to provide the basic 3 or advanced 4* stage-approach of one such app.

  • Stage A: Knowledge acquisition by watching video tutorials
  • Stage B: Knowledge formation by inquiry/activity 
  • Stage C: Knowledge construction by practice/discussion
  • Stage D*[may be implemented where appropriate] : Knowledge extension by application/production

For this development project to be useful and relevant (Wee, Lee, Chew, Wong, & Tan, 2015), the apps will be open sourced[3A ICT scaling up framework] , so that other educators as well as students can modify, build on and re-share the refined versions of the apps for the benefit of all.


This MOE SSTRF is position more as an exploration to develop high quality Math Apps, focusing on getting the learning features/designs ‘relevance’ right, less on the social experiment to be ‘rigor of gold standard’. Thus the relevance of findings will be based on case studies of student’s feedback/interviews to improve the learning designs of the Math apps instead of control/experimental learning trials using the apps.


Research Objectives

  1. Develop and refine families-series of mathematics app based lessons for Primary students using design based research[1] methodology. 
  2. Educate all CPDD-AST-ETD primary mathematics educators about the design and use of these apps through Professional Network learning 

Potential Applications

  1. Strengthen curriculum (interactive) resource development capability in MOE, usable research in Student Learning Space (SLS). 
  2. Enhance pedagogical understanding of curriculum (interactive) resource developed extending from the works of Singapore-UNESCO Prize for the Use of ICTs in Education[2] [3]. 
  3. Inform policy about 3A scaling up ICT practise framework of Accessible (Licenses creative commons attribution), Adaptable (Open source codes) and Affordable (free of charge) approach. 




Research a Technological Breakthrough - Publishing Simulation Mobile Apps

Using a suite of software like ionic framework,  node js, android studio, cordova, Xcode and Easy JavaScript Modeling Tool, this technology breakthrough is now shared publicly, thanks to our Spanish collaborator Professor Felix and our project team. Ordinary teachers and students can now use a step-by-step guide to publish their own mobile simulation apps in the Android Store (USD\(25 lifetime) and the Apple Store (USD\)99 per year) if they choose to distribute their apps via these 2 stores.

Alternatively, we also recommend sending the Android APK file to students devices, making them installable under the trusted source option on their phones. We do not recommend creating IPA files as students will not be able to install them on their iOS devices, unless the teacher-publisher pays an annual subscription fee of USD$99 per year collected by Apple Inc. Thus, ,we recommend using the mobile iOS Safari app to visit the Open Source Physics at Singapore digital library website.   

Design Thinking Hack

The top design thinking hack used in our project is to focus and start on the Stage 4 (prototype) first before the other stages. With a ‘do-it-yourself with research assistants’ methodology, the project team was able to serve a wide variety of HQ officers, school teachers and students, typically difficult when using a traditional outsourcing production methodology.

Every opportunity and feedback given (Stage 1,2&3 empathize, scope and ideate) was immediately fed back to the prototype and a better Math App updated, ready for more field testing through networking with ETD ICT in Math Learning Community teachers and Stage 5 evaluation.

Power to Create is King

The top reason for the success of the project is our ability to create (prototype) useful tools. Pushing the depth of creation, the Math Apps are open source (recipes of how to make them is clearly documented and codes recyclable) thus making them, reusable in Student Learning Space, to suit and adapt to different lesson intents, flow and design.

Why Research and Development, where is your evidences for effective learning (is Educational Research the answer in a one year project?) ?

Apps used everywhere, our answer to relevant and usefulness of research.

We invite anyone and everyone to try using our well designed Apps (note that earlier part of the report mention total of website visits=29000, Android installs=9828 and iOS installs=20748, making a grand total of 59576) to experience and provide personal evidences to the effectiveness of such tools developed by this SSTRF. When everyone is using the Apps developed by our SSTRF, the question on effectiveness of better learning will be more than adequately answered as everyone will be a data point of evidence.  

We argue that focusing all our attention on the pre-post clinical experimental-control group trials and creating poorly prototyped apps, is likely to yield inconclusive findings.


This project SSTRF_2017_ETD_3 Explore-Useful Learning Math Apps has demonstrated with evidences that this resource development methodology, when using a design thinking hack and an open sourced advanced technology tool such as Easy JavaScript Modeling tool, was able to create 15 high quality and interactive apps in a more sustainable and recyclable manner.  

Through this SSTRF, we hope to inspire others to embrace an open educational resources sharing of Public Service products so as to serve (accessible, adaptable and affordable) every citizen of Singapore, while giving hope for a better world tomorrow.


  1. Wee, Loo Kang, Lee, Tat Leong, Chew, Charles, Wong, Darren, & Tan, Samuel. (2015). Understanding resonance graphs using Easy Java Simulations (EJS) and why we use EJS. Physics Education, 50(2), 189. 
  2. Wee, Loo Kang, & Mak, Wai Keong. (2009). Leveraging on Easy Java Simulation tool and open source computer simulation library to create interactive digital media for mass customization of high school physics curriculum. Paper presented at the 3rd Redesigning Pedagogy International Conference, Singapore.


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