Sunday, December 4, 2011

Review of MathTappers: Numberline

MathTappers: Numberline is a game that challenges players to find the locations of numbers on a number line.   This game is designed to help players to develop their understanding of our number system and their proportional reasoning skills (with whole, integer and decimal numbers).  MathTappers: Numberline is one of a group of educational apps designed to help children master mathematical concepts and skills.  Search for MathTappers on iTunes and download them all (they are all free and have no ads or upsells).

The development of this app has been supported through grants received from Constructivist Education Resources Network (CER-Net) and the University of Victorias Faculty of Education Centre for Outreach Education (CORE), along with the generosity of HeavyLifters Network Ltd. who have sponsoring the development and publishing of the MathTappers app collection. Visit www.MathTappers.com for additional information.  I’m one of the designers on these apps, so this review might be a bit biased, but I’m still doing my best to help you see the learning potential of various math apps. 

Playing the game:
The goal of this game is to accurately and efficiently locate the positions of numbers on a number line.

At the start of each round the player estimates the position of the requested number on the number line and taps on it, if the position they chose is correct (within +/- 2.5%), then the number is tagged, full points are awarded and the next challenge is presented.  If the estimated position is not close enough, the screen zooms in around the position selected, marks the location selected with the value, adds the nearest benchmark values, and gives the player a second chance to select the correct location.  If the number line currently presented on the screen is not centered on the proper range of values the player may simply swipe a finger along the line to shift it.

Ten rounds (numbers) are presented during a game and progress is marked on the bottom of the screen.

Useful Options
The app has six types of number lines. In each case the accuracy is set to the number of decimal places shown in the range. 

There are three levels of tick marks on the number line that you can choose between to assist you in estimating the position of numbers. 
  • None - means that the only tick marks are those that appear under the two referent numbers on either end of the line.  Additional major ticks and referent numbers appear when you zoom in so that there are always two referent values available on the screen.
  • Coarse provides a second level of tick marks that divide the space between the two referent numbers into obvious subdivisions (as the learner figures out the value of the tick marks they are assisted in efficiently estimating the position of the challenge numbers). 
  • Fine tick marks subdivide the spaces between the coarse tick marks.  These are designed as training wheels - once the player understands the positions associated with these tick marks, then process of finding the right position can be reduced to counting.

Assessing progress
The Progress tab allows you to review the progress of players using the app.  Sliding the player name allows you to switch between players while the Clear button provides you with the ability to clear the database for that person. The Report button allows you (the parent/teacher) to forward all of the results to your own email address for further examination.  The Research button inside of the Report option allows you to forward a report with more comprehensive player action information to a second email address. The designers of this app encourage parents, teachers and other researchers to use this feature to support their own investigations.  No data is sent without the explicit action of the parent/teacher/student, and then it is only sent to the email addresses entered.


Advice for Parents and Educators:
The development of number sense is linked to the development of an accurate mental model of the number line and this model can be effective in keeping number sense alive as children master skip counting, fact retrieval, estimation tasks, arithmetic algorithms, proportional reasoning, measurement and fractions. A good grasp of a number line model also helps children to develop and use a wider variety of problem-solving strategies and better judge the reasonableness of solutions.

Even after mastering the counting to 100, young children placing numbers on open number lines from 0 to 100 typically plot values in a logarithmic pattern (i.e. distances between smaller numbers are exaggerated relative to distances between numbers closer to 100). As children gain experience with the number system, their number line placements become more linear and they start to manipulate numbers more accurately. In late primary grades children start to think proportionally about the number line and learn to use round numbers (benchmarks) to aid their placements.  This incremental process of refining their internal number line model repeats up through the grades as students develop their mastery of the numbers through 1000 (i.e., on a 0 - 1000 number line) and beyond and then again with decimal numbers, integers and real numbers.

The MathTappers: Numberline app has been designed to provide players with useful experiences as they explore a dynamic number line and receive automated feedback and encouragement through game play.  Don’t try to push learners faster than they are ready to go -  start with 0-100, then monitor progress.  At each level ask children to explain what they are doing as they select positions to confirm the current difficulty setting is accessible and appropriate.

Guiding beginning learners
If a child is unable to make sense of the number lines you are presenting, they may need to do further preparatory work with counting, comparing numbers and physical representations of number lines. Some activities to support the development of understanding of number lines might include having a child count out 30 or 50 pennies and line them up without gaps - then mark off where the line starts, where first group of ten pennies ends, and similarly for the second group of ten, etc. and followed by labeling the points on the resulting number line. Children will also benefit from examining, playing and working with rulers, measuring tapes or meter sticks and measuring objects of varying lengths. 

Accuracy first, fluency second
It is important to emphasize to children that we all learn differently, that accuracy is more important than speed and that the goal of this learning activity is not to have a race between students, but rather it is a challenge each of us to improve as individuals. The emphasis should always be on mastery of the concepts along with capturing the strategies or processes required to find the answers. 

Encourage learners to take their time to find the correct answers as they play the game.  Supervise children initially and challenge them regularly to give reasons and explain their strategies.  If at first they choose to count the ticks on the numberline to find their answer that is OK, but challenge them find and share additional, more-efficient strategies that also work for them.     If the challenge is too onerous (takes too much time), find an easier level - remember success breeds motivation.

Using this app in the classroom
This app may be used in several ways to support learning in the classroom. 
  1. On an iPad connected to a data-projector it can be used as a tool to support introduction and class discussion.  Start with a physical number line, then move to the app.  Have the students share their strategies for making sense of the number line and finding numbers on it.
  2. With an appropriately designed discovery learning worksheet a paired activity can be helpful.  Challenge the students to identify and articulate their understandings and strategies, then share their discoveries in a class discussion.
  3. After completing lessons on a particular range of numbers, this app may be used at an activity center, or recommended to parents for home practice and discussion to support and reinforce the understanding that the learners are developing and to revisit previously learned relationships and strategies. 
  4. In later grades this app, along with some moderate supervision and appropriate tutoring support, may also be effective review for students seeking to build/rebuild/remediate foundational skills.

A small set of iPod Touches (or even just one) with a variety of learning apps installed for individual practice can be an excellent and productive resource for learners to use during breaks between their other learning activities.   You might provide learners with a road map linking apps and levels within apps to curricular goals (from both current and prior years).  This may encourage children to take some responsibility for their own learning progress. Ask learners to use unique player names, and use the progress reporting function to assess individual growth and needs.

Summary
Obviously, as one of the designers of the app I am inclined to think that it is useful.  I believe that it can be used in the classroom or at home to support learners as they master different aspects of number, and that it offers something that you can’t do as well with paper and pencil.  Ultimately all I can say is – there is no cost to giving it a try.  I think you will like it too.   BTW, with this and indeed any other app, if you like the app, help the raise the profile of the app by giving it a good rating (and even a comment if you can spare the time).