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"If God is sovereign, then his lordship must extend over all of life, and it cannot be restricted to the walls of the church or within the Christian orbit." Abraham Kuyper Common Grace 1.1.

Saturday, 3 March 2012

Revealing Arithmetic - a review

Revealing Arithmetic
Math Concepts from a Biblical Worldview
Katherine A. Loop
Fairfax, VA: Christian Perspective

In a sense this book fills out some details and builds upon Loop's earlier book Beyond Numbers . This is not quite a full-blown Christian mathematics curriculum but it provides hints and helps towards a Christian approach to mathematics education. Loop describes it as 'a supplemental handbook', it focuses on elementary arithmetic. It will be invaluable to home-schoolers and Christian educators.

Four main 'tactics' are used to develop a Christian approach:

  • Rewording the presentation
  • Sharing the history of the concept
  • Applying the concept in a real-life situation
  • Using the concepts to explore an aspect of creation.

Each chapter follows a similar format. There is an introduction, usually looking at historical examples and thus emphasising, rightly, that the symbols or names we give concepts are only one way to express things. This helps undermine the idea that maths is a human creation. The emphasis is continually on the idea that we can only do mathematics because God has created a consistent universe and that God is faithful in keeping his covenant. Maths is seen as a God-given tool, dependent upon God and not as independent facts.

The teaching suggestions and ideas have an objective and specific points to communicate. Usually one of these is to stress the idea that mathematics is dependent upon God and not independent of him.

An example from a textbook is shown and then reworded so that the children see maths as a language system to describe aspects of creation.

Ideas are then provided. These usually contain some real-life example and historical aspects to look at.

Two key points pervade this approach: mathematics is dependent upon God and that we can do mathematics only because God has created a consistent universe. As she states:

Counting, written numbers, comparing and grouping numbers, addition, subtraction, multiplication, division, fractions, decimals, percents, ratios, proportions, number sets, exponents, roots—all the concepts we refer to as “arithmetic” are useful methods to help us count and work with quantities! These methods only work because a faithful, all-powerful God holds all things together predictably.

The book is aimed at Christian home schoolers and so these points need no justification. She rightly states that:
Teaching math from a biblical worldview means so much more that saying over and again "God created and sustains a consistent universe and math records it". 
And yet at times, there is a tendency for Loop to do exactly that.

Occasionally she overstates the point; for example: "Most modern math books present fractions exclusively as ways of representing partial quantity, without letting students know they also represent division." This is certainly not the case in the UK. Here the emphasis has been on a connectionist approach to maths that stresses the connections between different areas of maths (see for example Mike Askew et al.  Effective Teachers of Numeracy in Primary Schools: Teachers' Beliefs, Practices and Pupils' Learning).

The use of manipulatives are continually encouraged here, particularly the abacus and Napier's bones. Worksheets on using and making an abacus are included as well as on using and constructing Napier's bones.

I was particulalry pleased to see that a number of different approaches to the four rules were discussed and advocated. For example, eight different methods for multiplication were examined. This book provides a great starting point for all those who want to think Christianly about mathematics education. It is explicitly Christian and is aimed at Christian homeschoolers and for those working in Christian schools. The ideas will take some adapting and modifying to make it applicable for Christian teachers in schools that are not explicitly Christian.

Reflecting on the book it did make me wonder how much of this approach is distinctively Christian -  would a Jews or Muslim happily concur with the approaches here (and does that matter)? What difference does Jesus make to mathematics? As G. K. Chesterton so brilliantly put it:
You cannot evade the issue of God, whether you talk about pigs or the binomial theory, you are still talking about Him. Now if Christianity be. . . a fragment of metaphysical nonsense invented by a few people, then, of course, defending it will simply mean talking that metaphysical nonsense over and over. But if Christianity should happen to be true - then defending it may mean talking about anything or everything. Things can be irrelevant to the proposition that Christianity is false, but nothing can be irrelevant to the proposition that Christianity is true.
Mathematics is relevant because in Jesus everything matters.

Math Concepts from a Biblical Worldview?    
Written Numbers         
Place Value               
Comparing Numbers           
Addition: Foundational Concept       
Subtraction: Foundational Concept      
Addition & Subtraction: Multi-Digit Operations         
Multiplication: Foundational Concept   
Division: Foundational Concept   
Multiplication: Multi-Digit Operations   
Division: Multi-Digit Operations    
Fractions: Foundational Concept      
Fractions: Operations          
Ratios & Proportions  
Types of Numbers (Number Sets)
Exponents & Roots     
Math & the Gospel 
Answer Key  
Appendix A: Mathematicians
Appendix B: Different Number Systems 
Appendix C: Abacuses
Appendix D: Math Methods
Appendix E: Resources for Further Study  

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