Friday, December 31, 2010

Addition Coach - a simple app to encourage the exploration of addition

With this app there is no stress and no failure, just success. This app is ideal for children from Pre-K through grade 1, although it can also be useful as a support for older children who are still struggling with mastering number and basic addition facts.   In presenting an ‘equation’ of block sets with the total presented in numerical terms, the app helps to introduce the idea of the symbols for addition and equals and their use in arithmetic expressions and equations.  

Playing the game
The child is presented with a number to create and a menu of colored block sets (1, 2, 3, 4 & 5 blocks), and is able to manipulate the block sets on the screen by tapping on them to add them to and take them away from their collection.   Big fingers may be a little frustrated by the narrowness of the target space for the block sets, but this will not be an issue for most children (for special needs - try it on an iPad!).

 As a child taps on a colored set from the menu on the bottom of the screen, it is added to their new collection in the centre of the screen (an expression with a series of block sets added together) and a new total is calculated and presented numerically on the right hand side.   If they choose to tap on a block set already in their collection, it disappears, and the total is adjusted again.  This process continues until the total in their collection matches the total in the challenge (top right) at which point there is a celebratory cheer and everything disappears in a flash of sparkles.  The app nicely starts with full size clones of the block sets and scales the collection down if room is needed to allow for up to 10 sets of blocks to be combined – although the child can create a sum as high as 50, the challenge values don’t seem to go higher than 15.

Helping children to learn
Before working with this app, parents/teachers might invite a child to play with some beans (or some other convenient counter), challenging them to count small sets (up to 5, then 10 then 15), and confirming that they are able to count correctly.  If they have not yet mastered counting small sets, it may be better to spend some additional time with physical counters, or some other app to build up this understanding before introducing this app.

As a child begins to play with Addition Coach, parents/teachers might first focus on helping the child understand how the blocks can be added to the collection and removed from the collection and then focus on supporting the child in making sense of what is being presented.  Ask the child to tell them how many blocks are in each set in the menu and help them to recognize number as an attribute of each set (just like color is an attribute).  Then, as they add sets to their collection, ask them to count the total number of blocks in their collection.  Guide them to recognize that number beside the collection is the same, and discuss that equals means the same as. 

Addition Coach could also be effectively used with a small group in an activity centre. Invite one child at a time to manipulate the app on the screen and encourage the group to discuss what happens.

Suggestions for the authors.
This is a great app, but it would be helpful if the authors could provide some options to allow parents/teachers to choose the level of difficulty and information presented to the child. Although, given the limited screen space, some of these suggestions may be difficult to implement.

For instance it would be great to be able to choose the challenge range or maximum challenge value  - very young children could start with sums to 5, then 10, etc..

It would be nice to have the option to have a symbolic expression/equation presented either in concert with the blocks or at the end before the blocks disappear.  Similarly it would be helpful to allow the sum to be represented as a complete collection of blocks to allow the child to see how their collection of block sets might be represented as a whole – perhaps grouped in sets of fives or tens.

It might also be helpful to have the option of choosing where the equal sign and the total is presented (right or left – to reinforce the idea that the equals sign is used to signify a relationship rather than an operation).

An option to require a double-tap or ‘tap and dwell’ or ‘tap and drag’ to add or remove a set of blocks might help reduce the frustration of some children who like to touch the blocks as they count them.

Finally it might be nice to have the name of the app fade away after the first round to reduce the clutter presented on the screen – but it is already fairly subtle, so that is just a minor quibble

Final word
Addition Coach is a fun app to support children in exploring the nature of addition – and it is free!  I recommend it to parents and teachers – both as a tool to support guided exploration in the classroom and as a tool to support anytime anyplace microtutoring. It is a great app and deserves to be much farther up the list in the app store.

Wednesday, July 14, 2010

Building fluency and learning problem solving with KENKEN

KENKEN captures the fun of a Sudoku logic puzzle and augments it with arithmetic making it a great game to support learners as they build fluency with basic facts and mental math as well as develop logical thinking skills, problem solving strategies and perseverance.

There are 3 versions of KENKEN on the AppStore - and the are all based on the same puzzle – here I am focusing on the $0.99 version by Capcom.


Playing KENKEN:
In a nutshell you are presented with a grid ranging in size from 3x3 to 6X6 (up to 9X9 on paper versions) and like Sudoku you are challenged to place a numbers in the cells so that no row or column contains any duplicate numbers.  The unique twist with KENKEN is that the grid is broken up into a series of cages (connected cells marked out with bold lines) which are marked with a goal value and an operation (left out in the hardest cases).  The challenge is to make sure that the numbers used within a cage combined with the operation produce the goal value. 

As you complete your first 3x3 grid, KENKEN may appear to be quite easy – but very quickly you will find yourself drawn in to puzzles that are very challenging.  Make sure you make use of the note feature to keep track of plausible values in each cell to support you in your puzzle solving endeavors.

Keeping it simple:
The game is easy to get into, all of the controls are intuitive, you don’t get lost, and it is nicely focused on a single puzzle type

The options page allows you to manage the music, change the visual theme (all of which are visually appealing and not too distracting), reset the game and choose a language (English, French, German, Italian and Spanish).

The quick-start ‘how to play’, rules, control descriptions and other help features are an easy read and straightforward.

Learning math with KENKEN:
Although players can start right away with a few free-play puzzles at any level, they need to go through the academy to unlock each of the levels before they will have access to all of the puzzles.

Guess and test can be a good way to start, but players (you and/or your children/students) will get a lot more out of the puzzles if you have an opportunity to think through and talk about the choices you are making and elaborate on your strategies.    Look for a KENKEN buddy, use a notebook, or work in a group.  When working with others, ability levels don’t need to be the same.  Like-ability players can be very productive in co-generating strategies, but unlike-ability players will also benefit from collaboration.  The ‘masters’ will benefit from thinking through, articulating and explaining their strategies, and the ‘strugglers’ will benefit from being able to ask questions and having a buddy to check their moves, provide clues and guide them when they are stalled (preventing excessive frustration). 

The ‘Academy’ provides a nice short series of three lessons and an exam for each level of difficulty.   If you are already a master of the arithmetic and pick things up quickly, you may dash to the ‘Master’ level – in a few hours.  But if you are a leisurely player who prefers to refine your mastery of each new skill, you will appreciate that there are dozens of puzzles at each level to practice on in the ‘free play’ section

I suggest that if you find that you (or your children/students) are getting too frustrated by puzzles at a given level, then you might back up to the preceding level, review the strategies again and practice some easier puzzles.  Success with appropriately challenging puzzles will breed motivation and encourage perseverance – but too much frustration is not helpful. 

Suggestions for the authors:
The app takes 5 seconds to load on a 2nd generation iPod Touch – if removing the (non) talking head would reduce this by 1 second it would be worth it.

The numeral 4 is a bit difficult to read in the markers and totals – the tall stroke shouldn’t diminish in the middle above the horizontal stoke.

The arithmetic that you are practicing does not get very difficult until you are fairly far into the game – to make it more useful for motivating the mastery of basic facts it would be great if the numbers used in the grids could focus on higher number values at lower levels (i.e., I don’t believe there is any reason not to make a KENKEN 3X3 with 7, 8, 9 as the selectable values)

Accomplishments are tracked for only one individual and only by game board – it would be nice if there was an easy way for a parent or teacher to easily review the progress of multiple players.

Final word:
I recommend this game – both as an entertaining pastime and as an educational tool to support the mastery of some basic facts (see note above about improving this) and mental math skills along with encouraging logical thinking and problem solving.