Contents
- Why is Math important in early years?
- Why is research and testing needed for learning solutions?
- What is Magrid?
- How is Magrid different from apps and games?
- How does Magrid work?
- How are the tasks in Magrid selected?
- How does the Magrid program empower teachers?
- Is Magrid really effective?
- Conclusion
1. Why is Math important in early years?
Although developing mathematical skills is key to succeed in educational systems, their importance is not limited to school. Quality of life as well as the financial situation have been shown to be related to mathematical achievements at school. This is because mathematics is intertwined into every element of our lives in both direct and indirect ways. Mathematical abilities at the beginning of elementary school are strongly predictive of achievements later in life.
“Mathematical knowledge begins during infancy and undergoes extensive development over the first 5 years of life. It is just as natural for young children to think mathematically as it is for them to use language, because “humans are born with a fundamental sense of quantity” (Geary, 1994, p. 1), as well as spatial sense, a propensity to search for patterns, and so forth”
-(Clements, Sarama, & DiBiase, 2004).
Thus, children who fail to acquire sufficient knowledge of basic mathematics during the preschool years, such as counting and number knowledge, will not have a strong foundation to build up the more advanced math skills later on. This is due to the hierarchical nature of the development of mathematical skills.
For instance, to solve the calculation “3+2=5”, a student should have knowledge of: (a) the symbolic numerical system, (b) the sign “+” meaning adding and (c) the fact that adding two numbers leads to an exact number which is the sum of two operands.
2. Why is research and testing needed in learning solutions?
The swift development and uptake of information is the landmark of information societies. Technology, as we know it today, permeates every aspect of our modern times. It is part of how we interact, work, play, and learn.
Especially after the onset of covid, the number of such solutions in the education technology space has skyrocketed. Teachers and schools tried to onboard multiple solutions to bridge the gap between classroom learning and classes on video calls.
However, many of these solutions appear as games or just apps. In many cases, these apps are without any science or research backing the learning methodology. The effects of this lack of thorough research and testing ranges from no improvement in the child’s learning to over-dependence on the tool, which leads to learning problems in the short to long term. Because children interact with such apps only using a tablet, there could be health demerits too.
Therefore, it is essential for educational institutions and professionals to use programs which are scientifically proven, peer- reviewed and thoroughly tested. This process helps understand both the positive and negative effects of long-term use of the solution.
3. What is Magrid?
Magrid, or Math-on-Grid, is a scientifically proven pedagogical training and learning program, which has been developed to foster early mathematical skills for early learners (3-9 years old).
The main aim of implementing the Magrid application is to foster young children’s early mathematical abilities without relying on any language skills. Magrid presents visuo-spatial and mathematical tasks and concepts visually, and allows children to have an interactive exploration to find the solution for the given task. Finally, it verifies the user’s solution and provides real-time feedback on the solution.
Magrid includes a large number of different tasks targeting different aspects of early mathematical abilities to maintain young children’s interest and to provide them with a profound and flexible understanding of basic mathematical concepts.
All training tasks have been developed in accordance with established developmental models of numerical cognition and further findings from empirical research on visuo-spatial and numerical development.
4. How is Magrid different from apps and games?
Magrid has a number of distinguishing features:
- Language neutrality
- Combination with external materials,
- User Handling and Task Management
- Scientifically designed tasks
- Built-in monitoring system
To the best of our knowledge, although there are a few academically motivated pedagogical training applications on early mathematical abilities, there is no application that offers all capabilities of the Magrid program together.
4.1. Language neutrality.
The exclusively visual design of the application is independent of any language requirements such as text or voice-overs. This is possible by visualizing the mathematical concepts and ideas, and by providing real-time feedback on the users’ action while they try to solve a task and guiding them towards finding the solution. The experience includes visual hints and sound effects, which assist the user without depending on any text.
4.2. Combination with external material
Magrid is not just a standalone program. It comes with external material, namely (paper) booklets. Booklets are supplementary physical books containing the templates of different tasks. The use of external material augments the visual support provided during the learning activities. Moreover, it becomes suitable for the classroom context. This approach allows teachers (or parents) to actively guide children’s learning progress by providing them with the activities they consider the most appropriate.
4.3. User Handling and Task Management
To use the application, each user needs to have a Magrid Identity card (ID card) containing a unified Quick Response (QR) code. The ID cards will be used for user management and user identification. Users log in to the system by putting their ID card in front of the camera of the device and then they can start or resume solving tasks.
This enables children to login to their account without typing any usernames or passwords. This is of critical importance for the usability of the training application, as our main users are pre-schoolers who are not yet able to read or write.
Each training task has also an ID card with the corresponding QR code printed on it, so a user can start a task by scanning the ID card of the desired task.
4.4. Scientifically designed tasks
The present application includes 32 different number-specific (from non-symbolic tasks to symbolic tasks and mapping between different representations of numbers) and simple arithmetic task types.
Beyond that, it provides 16 different visuo-spatial task types focusing on different aspects of visuo-spatial ability that have been linked to mathematical development (visuo-motor integration, visual perception, spatial visualization, shape recognition and differentiation).
Each type of task comes with different difficulty levels.
Overall, the number of task instances amounts to 2500+ tasks which makes MaGrid a comprehensive and long-term training program.
4.5. Built-in monitoring system
Due to its built-in logging and monitoring system, it can also be used as an assessment application. Teachers and parents can evaluate child usage in different visuo-spatial or mathematical tasks by monitoring their activity and their progress through the realtime monitoring mechanism.
5. How does Magrid work?
Magrid contains the central functional element of the system in which all mathematical tasks are implemented: the grid. A grid is a set of nodes (10 columns, base-ten system) that gives the child (user) the possibility to draw or delete lines on it.
Here’s a screenshot of an empty grid:
Children can draw a line on the grid by connecting any two points on the grid (grid nodes), delete a drawn line from the grid, move a drawn shape over the grid and delete a selected shape from the grid.
The grid is used to visualize the base-ten system and to better structure the space. Furthermore, the use of the grid for drawing activities reduces the motor-demand of drawing, as they only need to connect the dots on the grid. As fine motor skills are still developing in young students, this approach should help them to complete the visuo-spatial tasks. The grid facilitates the drawing process for more complex shapes in young children as well. In some of the tasks, the grid nodes are partially or completely invisible, so they may not be seen in all of the application’s screenshots.
6. How are the tasks in Magrid selected?
A large number of different tasks were designed and developed in the Magrid application. These tasks target different aspects of early visuo-spatial abilities that have been linked to math development and mathematical abilities. The tasks that Magrid contains can be categorized into two main categories: visuo-spatial and numerical tasks.
6.1. Visuo-Spatial Tasks.
Our visuo-spatial training tasks tap into different aspects of visual and spatial abilities. These tasks have been designed under the Magrid program. Most of our tasks in this category focus on different aspects of visual perception. Besides visual perception tasks, the program contains a number of visuo-motor integration (VMI) tasks (characterized by the task’s motor component). In addition to visual processing of information, VMI tasks require the motor output and the coordination between the two. Their role for math achievement has been highlighted in multiple studies.
Visuo-Spatial Tasks examples:
6.2. Numerical Tasks
The number-specific tasks target different aspects of basic math competencies. The theoretical framework for designing and developing these tasks has been set by the four-step developmental model of numerical cognition. In this developmental model, four different forms of number knowledge are distinguished: quantitative knowledge, verbal number knowledge, Arabic number knowledge and sequential knowledge.
Numerical Tasks examples:
6.3 Free Play mode
Magrid also has an additional component called “Free Play mode”, apart from the visuo-spatial and number-specific tasks. In this mode, the user has an empty grid to draw and delete lines and shapes without any limitations to explore the basics of the application. In addition to the event logging mechanism, which is always activated in this application for recording user activities, the application takes screenshots of users’ drawings in this mode as shown below. This mode can either be used to make the students familiar with the functioning of the grid or to study students’ behavior in an unguided situation.
7. How does the Magrid program empower teachers?
Magrid is a scientifically designed program and thus is highly effective in improving early math skills in early earners. The program is designed to help teachers maximize learning for children.
7.1. Training
To begin with, training and support are integral parts of the Magrid program. It is important to make sure teachers are trained effectively to get the most out of the program, but it the training is also geared towards empowering teachers to thrive in their jobs. All education institutions using Magrid receive ongoing support to make sure the solution is continuosly optimized for their needs and to make sure they are fully up to speed with new features and updates.
7.2. Task Selection
The program is designed to seamlessly integrate with classroom settings and augment learning for children. The Magrid program has more than 2500+ tasks available spread across multiple difficulty levels. This gives teachers the flexibility to choose from a vast pool and actively guide children’s learning progress by providing them with the activities they consider the most appropriate.
7.3. Progress Monitoring
Next, the built-in logging and monitoring helps teachers to track progress of every child and measure improvements in real-time. Teachers can benefit from this application for evaluating behavior in different visuo-spatial or mathematical tasks by monitoring their activity and their progress through the Realtime monitoring mechanism.
8. Is Magrid really effective?
The Magrid solution has been used in two main research studies to survey its scientific effectiveness.
8.1 First Study
In the first study, the Magrid application was deployed in a study aiming to assess the effects of the visuo-spatial training tasks on preschoolers. In this study, children from five classrooms worked with the Magrid application twice a week over a period of ten weeks. We have presented our effect sizes using Hedges’g, as our sample sizes in the intervention group and the control group were not identical.
Results of First Study
Results revealed that children who were a part of the Magrid program over this period made significant gains in visuo-spatial abilities with effect sizes (Hedges’g) ranging between 0.62 and 0.74., compared to children from classrooms who were not a part of the program. These results were the first empirical evidence, not only for the effectiveness of the training application, but also for the feasibility of implementing this application in an authentic school setting. Check out the published research paper here for a detailed description of the study design and results.
8.2 Second Study
In the second empirical intervention study, the Magrid program was at the core of a comprehensive language-neutral mathematics training. This study assessed the training’s effects on young second-language learners’ early mathematical abilities. As mentioned before, second language learners are at risk of lagging behind their native peers in basic mathematical abilities, already during preschool. For this purpose, a randomized-controlled trial design was implemented over the two years of preschool to investigate the effects of this program. 186 children were a part in this study, of which half participated in the language-neutral mathematics training, whereas the other half participated in a language intervention and was considered the control group.
Results of Second Study
After these two school years, children who participated in the early mathematics training performed significantly better on several different measures of early mathematical abilities. Results revealed significant intervention effects on different measures of visuo-spatial abilities with effect sizes (Hedges’g) ranging between 0.37 and 0.47 and on number specific skills with effect sizes ranging between 0.30 and 0.46 (these effect sizes can be considered small to medium).
Considering the results together
Taken together, these empirical results are promising and show that the Magrid program is effective for all pre-schoolers, including traditionally under-served populations such as second-language learners. It can also be effectively used by teachers in a classroom environment.
9. Conclusion
The impact of early numerical abilities on mathematics achievement in future is clear. Magrid uses current technologies to visualize early numerical concepts and provides real-time feedback on students’ actions. These features empower teachers to enable intuitive learning by children.
The above-mentioned experiments provide concrete evidence that the Magrid program is an effective method to foster early mathematical and numerical skills in preschoolers. Magrid’s innovative approach is primarily characterized by language-neutral property (using visual tools) and the proper use of tablet devices in school (using QR codes. These studies further prove that this new approach is effective and can be integrated into everyday school life. It is especially promising for schools with a heterogeneous student population with diverse language backgrounds. This early math learning solution helps these schools provide equal access to effective math education to all students.
If you are interested to know more about what we do or have a discussion around the above, feel free to get in touch with us here.
