Dyscalculia Book Review

 

Book review by Angela Weeks

Dyscalculia: Action Plans for Successful Learning in Mathematics by Glynis Hannell

In 137 easy to digest pages, Glynis takes the reader deep into the world of the child or adult for whom aspects of mathematics, that we often take for granted, present frustrating hurdles. Through actual conversations with children we learn how a different way of thinking can sometimes lead them astray. We learn how to identify the points of weakness and are presented with practical action plans for overcoming each hurdle.

The book is divided into six sections:

1. Introduction to dyscalculia what dyscalculia is, possible causes and how to identify students with dyscalculia (see box below)

2. Effective teaching – effective learning presents new ways of looking at and assessing difficulties in mathematics

3. Understanding the number system– looks at areas of weakness and offers action plans to address them

4. Understanding operations – looks at areas of weakness and offers action plans to address them

5. Measurement and rational numbers – look at areas of weakness and offers action plans to address them

6. Teacher resources - includes student and parent questionnaires to elicit the child’s feelings about mathematics and their parents’ perspective

Sharon Ellison in her review of this book (SPELD Victoria Journal, June 2006) made the following comment:
I have taught remedial maths for many years, yet have never felt as close to knowing what the child (or adult) is really feeling or seeing as I did after reading this book…(My colleagues) and I agreed that we had never read or heard such enlightening material. Reading this book can only improve one’s teaching technique at all levels.

The following extracts provide a window into the wealth of information and practical guidance covered in Dyscalculia: Action Plans for Successful Learning in Mathematics. This book is recommended reading for every junior and middle school teacher, and all senior mathematics teachers, in particular those who teach vocational maths or Maths A.

Throughout this book, Glynis provides pratical action plans with strategies and activities for addressing areas of difficulty.

The following example is taken from 1. Identifying pupils with dyscalculia (Section 1, page 14) [top]

There are a range of warning signs that a particular child or adolescent may have dyscalculia. Some of them are outlined here.

Slowness

  • Slow to give answers
  • Slow in working comparison with others

Reliance on tangible counting

  • Has difficulties with mental calculation
  • Uses fingers to count simple totals
  • Uses tally marks where others use mental calculation
  • Uses the “counts all” method instead of “counting on” when using fingers or manipulatives for addition.
  • Finds it difficult to estimate or give approximate answers.

Difficulties with the language of mathematics

  • Finds it difficult to talk about mathematical processes
  • Does not ask questions, even when he or she evidently does not understand.
  • Finds it difficult to generalise learning from one situation to another
  • Makes mistakes in interpreting word problems, and instead just ‘Number Crunches’ the numbers in the text
  • Gets mixed up with terms such as equal to, larger than.

Difficulties with memory for mathematics

  • Finds it difficult to remember basic mathematics facts.
  • Has trouble remembering what symbols such as + mean
  • Forgets previously mastered procedures very quickly
  • Has to recite the entire multiplication table to get an answer such as 4 X 6 = 24.
  • Works multiplication tables out by adding on as they recite.
  • Finds mental mathematics difficult, forgets the questions before the answer can be worked out.

Difficulties with sequences

  • Loses track when counting.
  • Loses track when saying times tables: 2 times 3 is 6, 3 times 3 is 9, 5 times 3 is (adds on 3 to previous answer) 12.
  • Has difficulty remembering the steps in a multi stage process.

Difficulties with position and spatial organisation

  • Is confused about the difference between 21 and 12, and uses them interchangeably.
  • Mixes up + and X
  • Puts numbers in the wrong place when redistributing or exchanging.
  • Poor setting out of calculations and of work on a page
  • Scatters tally marks instead of organising them systematically
  • Unaware of the difference between 6 - 2 and 2 - 6, says 4 is the answer in both cases.
  • Gets confused with division is it 3 into 6, or 6 into 3?
  • In tens and units takes the smaller number from the larger, regardless of position.
  • Finds rounding numbers difficult.
  • Finds telling the time on an analogue clock difficult.
  • Is easily overloaded by worksheets full of mathematics
  • Copies work inaccurately

Reliance on imitation and rote learning instead of understanding

  • Can ‘do’ sums mechanically but cannot explain the process
  • Sometimes uses the wrong working method such as treating a ten as one (or vice versa) in exchanging or redistribution.


The following example is taken from Section 2, pg. 31, Understanding the Purpose of Mathematics [top]

ACTION PLANS FOR SUCCESSFUL LEARNING

Making mathematical connections

  • Make explicit connection between what you teach and the children’s everyday lives. Always introduce a new skill or topic by linking it to the children’s own experiences and lives.
  • Look at how the children play and use mathematics in their everyday lives and build on that in the classroom. Make real-life experiences the beginning and end points of the mathematics that you teach.
  • Take the mathematics that you teach in the classroom out into the playground, the environment, the sports field and the home.
  • Emphasise choosing and using as vital mathematics skills. Children do not only need to know how to ‘do’ mathematics, they must be able to know which mathematical process to choose in a given situation and how to apply it in real life. What sort of maths should we choose to work out the teams for sports day? What is the best way to find out how much paper we need for our display table? How can we work it out? Why couldn’t we use the times tables for this one?
  • Model estimation and approximation as important mathematical thinking skills in real life mathematics. Teach the pupils to make a distinction between when approximation and exact mathematics is needed. Could we guess the number of tickets we need on the train? Could we estimate what time we have to leave for the swimming gala?
  • End each day with a recap of what the children have learned in their formal lessons. Have a ‘Maths Wrap Up” every afternoon to highlight what they have learned or used informally: We added up today when we worked out and how many tickets we need form the office We measured today when we put the books on the shelf. We used fractions today when we shared our paints with Mr. Jolly’s class.
  • Always teach a new concept or skill in multiple contexts, across the curriculum. Find ways to link learning in other subjects with your mathematical curriculum.
  • Always make the mathematical connections between what you are teaching and learning explicit. You remember that we were doing doubles and halves in maths the other day. Look in this book: It says that the pigmy mouse is half the size of the regular house mouse. So if a house mouse is 5cms long, how long do you think a pygmy mouse would be?

There are 3 parent information sheets with practical ideas for developing mathematical understanding on the home front.

The following example is a selection taken from section 6, pg 127, Parent Information Sheet: Maths on the move [top]

Did you know that you can turn the car, bus, train or ferry into a great maths classroom for your children?

Maths is not just about ‘doing sums.’ Maths is about thinking mathematically, seeing numbers around you, and understanding what those numbers mean.

LOOK OUT THE CAR WINDOW

  • Is the car ahead a higher or lower number than you?
  • What is the highest number you can see today?
  • What is the lowest number you can see today?
  • What numbers can you see on the large vehicles around you? What do numbers mean? (You might see the company's telephone number, the weight limitations, the engine size, the number of passangers it can carry, its model number etc)

LOOK INSIDE THE CAR

  • Look at the displays on the dash. What do all the different numbers mean? Watch how the display changes as you travel; see how the numbers change 3794.7, 3794.8, 3794.9, 3795.0, 3795.1.
  • How far has this car travelled altogether? How far has the car travelled each year?
    How much fuel do we have? Is the gauge full, half full, quarter empty?
  • What does the manual say about how far we can drive once we have reached ‘red’ on the fuel gauge?
  • What does the manual say about how much fuel we can put in the car?
  • How much would this cost us?
  • About how far could we travel on a full tank?
  • Do we have a car licence? When does it run out?
  • What does the car manual tell us about tyre pressures?
  • What is the maximum weight the car can carry or tow?
  • How often do the windscreen washers wipe the screen in one minute?

DISTANCES AND MAPS

  • Look at the distances on road signs.
  • Set the distance trip to 0 and see how far you travel on a journey.
  • Time how long your journey took.
  • Estimate how far you travel in a week, a month or a year.
  • Look at the map, where are we now?
  • Use the index to look up your street. Use the page and grid reference to find it on the map.
  • Find your school by page and grid reference.
  • Can you see the route you usually take?
  • Is their another route?
  • Can you see the distances shown on the map?
  • What does the grid square mean? Can you find the key that tells you?
  • Are all the maps in your road atlas the same? Are some on a different scale?

STOPPED ON RED

  • How many cars go past in the other direction before the lights change?
  • What is the most common colour for a car?
  • On average how many people in each car?
  • What positions are we at the light? First? Third? Tenth?
  • How long do the lights stay red?

PARKING

  • How many cars are parked altogether in this car park?
  • Look at the parking restrictions. How long can we stay? When can we park?
  • Look at parking fees. How much to stay for one hour? Two hours?
  • How long can you stay in the car park if you only have $3.00 change?
  • What coins can you use to pay for parking?

The book Dyscalculia: Action Plans for Successful Learning in Mathematics by Glynis Hannell is available through the SPELD SA Shop for $61 

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