Thursday, December 31, 2009

Review: ‘Column Subtraction’


If your goal is to help your child to master the traditional subtraction algorithm then Column Subtraction may be the ideal App. I first became aware of this app a couple of weeks ago after reading an article and searching out a news release on prMac.com. In the release the developer, Esa Helttula, explains that he could not find any apps which would support his daughter in practicing column addition, and as a result set out to generate apps to provide users with an opportunity to practice of traditional algorithms for column addition, column subtraction and long multiplication. He explains that his focus was on minimizing button presses and not penalizing wrong answers. This review focuses on only the Column Subtraction app – but the other apps appear to have similar construction, behaviors, benefits and limitations.

The interface is clean – perhaps even sterile – but that is not such a bad thing if you are working one-one with a child and trying to discuss the important details (and a good thing if your child is easily distracted). A reference copy of the question is presented at the top of the working space in horizontal format and then on the right side a working version is presented in a vertical format, finally the current sub-operation is presented at the bottom of the working screen. Below the working screen there is a ‘borrow’ button and buttons for 0-9. The feedback is minimal but adequate – when your child selects the borrow button and borrowing is appropriate, then an animated borrowing occurs in the vertical/working version of the expression and when a numerical value is selected then it is shown at the bottom of the white space and only floats up into the answer space if it is correct. Thus your child is generally provided with feedback that their response was registered and they are given immediate confirmation if it is correct.


The learning
If your child is familiar with the traditional subtraction algorithm they will likely be able to improve their mastery of the procedure using this application. With the ‘show current operation’ option turned on, they are constantly reminded of the next step, which can lead to efficient practice of the procedure. Then by turning off the current operation your child is able to practice remembering the steps on his/her own. Because no wrong entries are allowed the app provides a passive form of positive reinforcement and your child will likely improve in both confidence and competence with respect to the procedure. However, to support learning and understanding in mathematics you need to take an active role in assessing understanding and challenging your child to explain their thinking.

You can support your child in using this application, by first confirming that they have an understanding of subtraction (see caveats), then working through a couple of examples with the current operation showing. By working through a series of questions with you at their side - challenging them to explain what the question might mean (understanding with a context), estimating the outcome, and then showing and discussing each of the steps and checking the answer - your child can have a productive and positive learning experience. Once your child seems to be comfortable using the application and is able to correctly identify when borrowing is necessary, then it would be best to turn off the ‘show current operation’ option. Sitting with your child and asking them explain their thinking will allow the parent to assess whether any further support is needed for them to master both the concept and the process. Once the parent is convinced that the child has mastered both the concept and process, then continued independent use of the app will allow your child to improve their fluency with the operation.


Besides allowing you to turn the current operation on or off, the settings page allows you to choose to have 2 or 3 numbers in each expression presented and 2, 3, 4, or 5 digits in each number. In the BC curriculum guide children are expected to be proficient in subtracting whole numbers up to 10000 in grade 4. Thus the app supports a reasonable progression of starting with 2 digit numbers and moving up through 3, 4, and 5 digit numbers as the child demonstrates mastery (i.e., is able to understand, estimate, complete and check the answer in a moderately efficient manner with sub-operations feature turned off and your quiet observation). I don’t see any particular value in using the 3 values option (it's adding too much complexity for young children and a distraction), and would steer you (parents) away from it unless your child is particularly comfortable with mathematics.

A recommendation, some caveats and suggestions
As a parent I like the potential that this Column Subtraction app has to help my child to master the traditional subtraction algorithm, but I have some caveats and suggestions to add to my recommendation. I urge you (parents/tutors/teachers) to support your children as they use this app and confirm that your child is understanding the process, that they are able to efficiently estimate and check the results and that they are able to visualize an appropriate context for the mathematical expression. I also encourage parents and teachers to investigate and discuss alternative approaches and algorithms with their child.

It is important that children understand what they are doing before learning rote procedures – otherwise the learning achieved will be unconnected to other knowledge, fragile and irrelevant to their lives. Children should be able to represent and solve subtraction related problems in the physical and visual (i.e., pictures) realms before they are pushed to begin manipulating symbols. To check this, ask your child if they can come up with a reasonable story or two to interpret the symbolic expressions presented in the app, and see if they can show you the process with some physical representations (beans, base-ten blocks, etc.). If they can’t easily generate an example, provide them with some and then spend some time helping them to make sense of where these expressions might come from (e.g., given 73-58 the child might say “I have earned $73 doing chores over the past month and spent $58 on a LEGO set – how much do I have left over?”).

Finally, in many regions the use of the traditional algorithm is not mandatory and other processes are equally valid. If your child is frustrated in their attempt to master this traditional algorithm and cannot master it for 2 digits easily, you may want to consider refocusing your efforts toward further building up ofestimation strategies and using alternative algorithms (e.g., Partial difference subtraction)

1 comment:

iDevBooks said...

Hello,

I'm the author of Column Subtraction and I would like to thank you for your kind review.

You mentioned alternative algorithms and I have now two new apps for subtraction that use alternative algorithms: Partial Differences Subtraction and Trade-First Subtraction. For addition I have one alternative algorithm: Partial Sums Addition.

There is also a new Long Division app that uses the traditional algorithm.

Thank You,

Esa Helttula, idevbooks.com