It’s no secret that TWA has long been a fan of appp media UG. Their newest release, Understanding Math - Addition and Subtraction is the second in the Understanding Math Series. This is a well-crafted and comprehensive approach to learning addition and subtraction. There are 6 mini games that engage the senses by bringing sight, sound, and proprioceptive/kinesthetic awareness onboard. This not only makes learning fun but creates multiple connections or avenues to help kids access the material when needed.
Gameplay is based on J. Bruner’s Learning Theory of the “Three Modes of Representation,” which are inactive, iconic, and symbolic. The enactive representation is the first mode. Here the child is actively engaged in a task. It is tangible and concrete. Challenges involve open experimentation, trial, and error, and are “just right” meaning that a child is largely successful to reinforce continued play but given enough challenge to be stimulated. This is a hard balance to find, but appp media masters this challenge seamlessly.
The iconic model uses a visual representation where kids begin to recognize the interplay of objects in a bigger schematic. The third stage of representation is symbolic, where the interplay of tangible and intangible becomes possible in a dance of language and meaning. It allows for organization and represents a common reference point in which to communicate ideas, and delineates the integration of the presented material. Bonuses for educators are the ability to track unlimited users, watch their progress, and learn where they may get stuck. This is an opportunity to tailor strategies to each child. Is your student progressing well in the first few games, then getting stuck? Well then pull back and use more tangibles to get numeric correspondence. Are they getting the use of the placement bars, but can’t stop at the correct ones and tens placement? Try using an abacus, Legos, or coins in a container of ten or twenty in play.
Let’s take a look at the mini-games and view Understanding Math in action. Remember the enactive representation? Here it is in playing the first 3 games. The first game is a visual and kinetic game, which begins to marry concrete thinking to the abstract. In this first game, kids are presented with an equation and must tap the screen with their fingertips to achieve the answer. The user imitates the equation in a sequence of two taps as it is written (forward or reverse) to be successful. And that kinetic input by using the sense of proprioception (input into joints and muscles) helps kids know what exactly 4 + 5 = 9 feels like. Reinforcers are plentiful, colorful and just plain fun by changing the graphic after you’ve finished a level in the mini games, and that includes making ducks to balloons with a tap. Each mission unlocks a new graphic and one is able to “pop” the graphics once achieving the correct answer.
The next 2 games use number rods/beads or an abacus-like feature which again bridges the concrete to abstract operational thinking. The rods teach place values of ones and tens, and these games explore addition and subtraction on an inactive, visual and symbolic level. If an answer is incorrect, one simply moves on to the next equation. I think that this is one of the things that make Understanding Math - Addition and Subtraction such an incredibly well thought out design for keeping kids engaged. Kids are recognized for achievements and not necessarily for being wrong. Wrong answers are identified, but not overly emphasized. Students are simply prompted to try again. The lifelong lesson: is to recognize errors and continue on, try, or ask for help.
The fourth game, “Training” uses the operational icons of math…. + - = etc. combining both addition and subtraction challenges. Increased demands for motor control and precision are presented by having the student write the answer directly on the iPad. By using handwriting, every stroke is reinforced and the information is retained by bringing on board proprioception and kinesthetic awareness. These are powerful sensory receptors throughout the body. In this way, kids not only see and think about mathematical operations but begin to recognize the feel of it. And on this level, information has started being integrated on a much more automatic level. In other words, kids don’t have to think about 2 + 3 = 5 and are starting to “know” that 2 + 3 = 5 because of the established rhythms of body, mind, and space.
In the “Duel” mini game, integration comes full circle and adds the element of timing and competition. By upping the complexity of the challenge, kids need to respond quickly and that promotes integration. If you do not know 1 + 3 = 4 at this level, you surely will in order to beat your classroom nemesis, Bobby! Levels of play can be adapted depending on your skill level. I love the thoughtfulness of grading competitors, in that kids of varying abilities can play together. The little sun-like button that sets the game in motion also helps kids to focus and synch with each other before they start. While observing someone who is mastering play…and I mean the ability to compute addition and subtraction fluently, it sets a bar with peers that help students want to achieve that level of play.
The last game involves free play with numbers and equations. By simply imagining what ifs, kids begin to anticipate answers, and it is another way to promote the integration of material. Free play with numbers provides space for finding patterns and creates sparks of possibilities.
I cannot recommend Understanding Math – Addition and Subtraction enough. The team of Kristin Heitmann and Jan Massberg is really an educational duo that sets the bar to the highest standard. The plan and programming of the material are flawless. I love how the graphics pop by using a black background. This keeps focus on the game and glare and refraction that contribute to eye fatigue are eliminated. There is a teacher’s manual available for download, that helps educators get the most use out of the app, and the app is designed to work within any school’s curriculum. It is Coppa compliant, has the ability to track multiple student’s progress, and there is a discount for schools buying in volume.
Jo Booth has been an Occupational Therapist for over 30 years and currently works in Pediatrics with early intervention. She sees kids newly diagnosed on the spectrum as well as medically fragile kids. She loves to move, explore and play every day; so that “her kids” grow up to be healthy independent learners.