The Matific Approach to Pedagogy and Engagement

In Elementary School Mathematics

Matific is a repository of more than a 1,500 interactive games, worksheets, and problem sets,

designed to support the teaching and learning of elementary school mathematics (kindergarten

through grade 6). This document presents the key principles underlying the Matific approach to

mathematics education. These principles are rooted in our vision that mathematics is best learned

through guided activities, hands-on interaction, and learning by discovery.

Matific is field-proven: Matific is presently used in 45 countries, with more than a million activities

performed daily by children around the world. The impact of Matific on mathematics education was

tested in 2016 by the Szold Institute, a public, non-profit research organization. The 127 teachers who

participated in the research reported that Matific has significantly benefitted their teaching,

particularly in terms of student enjoyment level (98%), interest (95%), motivation (86%), and curiosity

and participation (84%). The results of the students attitudes were as follows:

Comparison of student attitudes in classes that used Matific (right bars) with classes that did not use

Matific (left bars). All differences were statistically significant (Szold Institute study, 2016)

The Matific impact was also studied independently by associate professor Catherine Attard, an expert

in primary mathematics education. The Attard study reported an average of 34% increase in

mathematics test results, tracking 8 different schools (video about the Attard study). These results are

supported by numerous testimonials from teachers, students, and parents. Matific has won several

international awards, including the 2016 Codie Award for “Best Mathematics Instructional Solution”.

Episodes are the unique feature that sets the Matific pedagogy apart. A typical episode presents a

visual and hands-on environment, and challenges the student to answer questions or perform tasks

within the simulated environment. For example, one of Matific’s 5th grade episodes engages students

in weighting (and later ordering, by their volumetric weights) objects made of different materials. The

tasks become increasingly more challenging, yet the user experience is always playful, animated, and

encouraging. The software monitors the student’s actions, and intervenes when necessary with

supportive feedback and relevant hints. Each Matific episode entails about 10 to 30 minutes of

interaction, focusing on well-defined, curricular-driven concepts, skills, or insights.

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Epsiode example (5th grade): students use an animated scale balance and a set of weights to measure the volumetric weight of different materials. This episode practices problem

solving strategies, addition, subtraction, and working with decimal units.

Multiple correct solutions are always welcome, since they encourage curiosity, exploration, and

learning by discovery. For example, the solution strategy used by the student whose work is shown

above reflects the equation 1 + 5 x 0.01 - 0.1 = 0.95. Another student can reach the same weight

(0.95) by placing nine 0.1 weights and five 0.01 weights on the scale’s right plate. Multiple correct

solutions stimulate class discussions, promote deeper learning, and support the level of rigor which is

increasingly required by local, state, and national standards.

A typical week with Matific involves a balanced mix of hands-on episodes, interactive worksheets,

and applicative word problems. The episodes promote a deep understanding of the subject matter;

the worksheets build technical competence; the word problems practice application skills. For

example, after performing various weighting games, the student may be asked to solve a worksheet

of algebraic equations with kilos and grams. Next, the student may be asked to solve related word

problems. The exact weekly plan of activities that students perform is curated by the teacher, using

curricular, class-specific, and student-specific considerations.

Matific is curriculum-oriented: when Matific is first configured for a certain school or class, the

teacher can select a given curriculum, program, or textbook’s table of contents. After this one-time

configuration has been completed, teachers can easily locate and choose the episodes, worksheets,

and word problems that support their weekly teaching plan. Teachers who wish to go beyond a set

program are welcome to do so. For example, one can ask Matific to supply episodes that engage

students with digital and analog clocks, even if this material is not part of the standard curriculum.

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Matific is teacher-oriented, featuring hundreds of lesson plans that provide minute-by-minute guides

on how to use activities in the classroom. Each lesson plan includes an opening , suggesting motivation

and context pointers, presentation , suggesting how to use specific Matific activities in the class,

practice , suggesting when and how the students can interact with the activities, discussion , suggesting

applications and extensions, and closing , summarizing what has been learned and what will be

learned next. For example, a typical Fraction Representations Lesson Plan consists of an opening (3

minutes), presentation (12 minutes), practice (12 minutes), discussion (12 minutes), and closing (3

minutes) sections.

Matific is modular: each year from kindergarten to grade 6 is supported by a portfolio of hundreds of

Matific episodes, worksheets, and word problems. These grade-level portfolios are highly modular,

richly indexed, and recombinant. Every week, teachers select Matific activities that support their

teaching plan, and make them available to the class students. Teachers can start with default weekly

plans (which are curriculum-driven), and then modify them to determine the exact mix and order in

which the activities unfold to their students. In addition to the activities assigned to the entire class,

teachers can create customized learning pathways, designed to support individualized instruction.

Part of the Matific teacher dashboard, showing activities that the teacher assigned to a group of students (which may or may not be the entire class), as well as personal activities assigned to

individual students (not shown here).

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Matific is student-friendly, featuring a treasure hunt theme in which the assigned activities come into

play in a vivid and sensible order. Each student follows a map that lists his or her assigned activities

for the current week. By scrolling the map up and down, the student can move between the classwork

activities and the homework activities assigned by the teacher.

Typical student view of Matific (scrollable), featuring the weekly activities assigned by the teacher (see the teacher’s dashboard in the previous figure).

In this particular example the student sees two classwork activities and four homework activities. Completion of any activity results in various rewards, shown on the left.

Matific can be used in any class. Many teachers use Matific in classrooms that are equipped with a

single PC or tablet, and a projector. If the class has no computer equipment, Matific still provides a

complete off-site solution that can be used when learners have access to lab or home computers.

Each student gets a Matific username and password, and can connect to his or her personalized

learning plan from any device. Matific also supports multi-user settings in which several students

share a single device, taking turns. Field experience shows that this form of collaborative learning

develops not only mathematical proficiency, but also social skills like patience and tolerance.

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Matific is adaptive. The most pressing problem in traditional mathematics education was that all the

students in the class normally got the same treatment, resulting in significant knowledge gaps. For

example, students who don’t fully understand common denominators are forced to progress to

fraction arithmetic, simply because they must keep pace with the rest of the class. The students may

be able to follow procedures and solve fraction exercises correctly, but they don’t understand the

underlying mathematics. Instead of developing into intelligent thinkers, they act as calculating

automatons. This is typically the point where “math phobia” takes hold, undermining the student’s

confidence and building a lifelong resentment to mathematics, and, by extension, to quantitative

sciences. With Matific, each student's performance is continuously monitored, analyzed, and reported

to the teacher. When the child's work reveals that he or she needs to strengthen a particular area,

Matific proposes more basic activities that provide the missing building blocks. The result is

personalized instruction, allowing each student to progress adaptively, according to his or her

individual needs.

Matific accommodates entire classes, individual students, and groups of students. Quite often,

teachers wish to create groups of students that merit different tiers of intervention. For example, it is

quite possible that the teacher will want group A learners to work on multiplying fractions, group B on

adding fractions, and group C on identifying common denominators -- all within the same class, and

during the same week. In Matific, teachers can easily create and manage such groups. Moving

students from one group to another is a simple action, and so is getting timely information about the

performance of each student and group.

Matific reports are central to the teaching and learning process. Each student’s and group’s

performance is continuously monitored, analyzed, and presented on the teacher's dashboard.

Teachers get timely information about the class as a whole and about groups and individual students,

highlighting their progress over time and viz-a-viz the rest of the class. The reports also identify

advanced students who make good progress. If the teacher chooses to do so, Matific can engage

these students in more challenging work. The result is a formative, data-driven approach to

mathematics education, treating each student according to his or her intervention level.

Matific is versatile, engaging students in numerous practical tasks that unfold in common settings:

counting animals, hanging balloons, decorating cakes, planting flower beds, connecting pipelines,

filling water tanks, blending colors, hanging laundry, sorting socks, launching boats, driving cars, and

so on and so forth. Importantly, we believe in teaching the same abstract mathematical theme using

many different concrete metaphors. This is done in order to develop generalization skills and

general-purpose problem solving strategies. In particular, we seek to improve the student's ability to

decide which abstract mathematical tool is applicable to which concrete problem, and to hone their

ability to apply the tools correctly to the problems at hand. The best way to develop such analytic

skills is to engage students in many concrete and practical manifestations of the abstract

mathematical themes.

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Matific uses many different metaphors to teach the same mathematical skill, insight, or technique. For example,

fraction addition is motivated and practiced using many concrete settings, four of which are shown here.

Matific is simulative, engaging students in numerous tactile actions like cutting, pasting, rearranging,

dragging, dropping, tossing, pouring, grouping, ungrouping, and assembling all sorts of objects. These

actions are animated meticulously by Matific, using natural graphical gestures and physics engines.

The aim is to facilitate hands-on exploration of math concepts and insights within a playful and

realistic learning environment that features numerous virtual manipulatives. Outside the activities

proper, the student experience is gamified using avatars, badges, surprise awards, sticker albums, and

a quest game context. These motivators create a strong sense of progress, and incentivize students to

do well in the assigned activities.

Matific is hands-on. Child developmental psychologists, most notably Jean Piaget, observed that

learning mathematical concepts and skills is best done by tactile and self-guided manipulations of

concrete objects. These actions help children form mathematical concepts and operations using their

own cognitive devices. Matific uses computer technology to accelerate and enrich these learning

processes by administering hands-on interactions with numerous simulated objects and

environments. Obviously, it is unrealistic to expect teachers to prepare, and bring to the classroom,

thousands of physical artifacts ranging from birds to beads to boats. Instead, teachers use Matific to

render the interaction with such artifacts using engaging and realistic computer simulations.

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Hands-on manipulations: in this particular episode, the task is to create a target set of shapes from a given set of shapes. Using scissors and glue, the student carries out a series of geometric transformations that yield the

desired shapes. As usual in Matific, trial-and-error and multiple solutions are encouraged.

Matific supports spiral learning. When learning a new mathematical operation, it always helps to

relate the new operation to another operation that has been mastered and internalized. For example,

one way to motivate, or explain, x + y to young children is to count up to x , and then add 1 to the

result, y times. Thus, the ability to add is related to, and builds upon, the more fundamental ability to

count . With that in mind, Matific uses variants of the same theme to introduce, and motivate, new

mathematical concepts. For example, when learning counting , Matific presents tasks like "create a

necklace using x beads". When learning addition several weeks later, Matific presents tasks like

"create a necklace using x green beads and y yellow beads". When learning multiplication a year later,

the task becomes "create a necklace that has x times as many green beads as blue beads”. And so on.

The ability to apply new operations to familiar settings helps to boost confidence and promote

comprehension. Further, it serves to highlight the implicit relationships between different

mathematical operations, resulting in deep learning. This gestalt and layered view of mathematics is a

central theme in the Matific pedagogy.

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Matific often uses a familiar theme to teach new mathematical operations.

For example, the same string-a-bid metaphor recurs in various aspects of counting , arithmetic operations , fractions , and percentages .

(side comment about Matific’s user experience: note that the necklace on the right is heavier; as the user adds more beads, the necklace bends gravitates closer to the table).

Matific is multilingual, and is presently available in 26 different languages. The Matific contents is

carefully localized to different countries and cultures, and is particularly suitable for multilingual

student populations. Depending on the school’s needs and policies, students can interact with the

same classroom and homework activities using different languages, across and within classes.

Matific is available in www.matific.com. Readers of this document are welcome to select their

country/language version, sign up as teachers, and explore Matific. Please contact us for any question

or issue.

The Matific team includes 100+ mathematicians, computer scientists, software engineers, gaming

experts, artists, teachers, support personnel, and country managers. We are excited to be able to

focus this combined experience on turning mathematics into a fascinating and rewarding field of

study that any child can enjoy and master. We strongly believe that quantitative competence can help

children develop into rational, confident, self-reliant, and productive citizens. This, in a nutshell, is the

ultimate goal of Matific.

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