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| Didax "Class Ideas" Newsletter Archive |
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April is Math Awareness Month, and to help you celebrate, we're taking a fresh look at place value, a concept that math educators acknowledge isn't always easy for students to grasp. Fortunately, manipulatives such as Base Ten blocks are a great way for children to learn place value.
This issue features a new article by Paul Swan and Geoff White, authors of "Developing Mathematics with Base Ten," as well as downloadable activity pages from this great book and some fun Internet links on place value to share with your students. And, last but not least, a subscriber-only special on some of Didax's best place value products. Enjoy!
Cindy O'Neill, Editor |
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| Developing an Understanding of Place Value |
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 By Dr. Paul Swan and Geoff White
Place value is a recurring theme in the new series of books: Developing Mathematics with Unifix, Developing Mathematics with Pattern Blocks, and Developing Mathematics with Base Ten.
Over twenty years ago a famous British mathematics educator, Hilary Shuard, wrote, ?The ability to make full use of the place-value system for writing whole numbers and decimals is one of the most important insights into number that children need to acquire.? And the eight-year lad in my class demonstrated he had acquired the insight when he commented that ?place value is where the numbers sit.?
Understanding the Concept of Place Value
Too often, it is assumed that the concept of place value can be easily understood after a few directed lessons. Not necessarily so! It took civilization eons to ?invent? the notion of place value, and, likewise, with individuals this invention needs to be developed systematically over time, as a person gains an understanding of the number system. In some cases, it may be well into adulthood that a person masters the concept of place value. In the Place Value workshops for teachers conducted by Dr. Paul Swan and Geoff White, the authors of the series of books mentioned above, the exclamation of ?Oh! Now I see how it works,? is heard frequently. That is to say that many teachers are not too sure of the concept of place value and the important role it plays in being able to master the number system. Too often for children, the idea of place value is muddied by rules and procedures that attempt to tell them what to do rather than develop an understanding of what needs to be done.
The authors of the Developing Mathematics series (Unifix, Pattern Blocks, and Base Ten) have had extensive experience in introducing young children to mathematics and are convinced of the two most important characteristics of successful mathematics education:
1. A constant awareness of the developmental needs of children is essential, for it is obvious that if this facet of teaching in not considered in the classroom, students soon become lost.
2. To become confident and able to master a mathematical concept, a student needs a variety of experiences relating to the same idea.
Professor Zoltan Dienes, who popularized the use of M.A.B. (Multibase Arithmetic Blocks) in the 1960s (later changed to Base Ten blocks, it seems, because only that base is readily available), termed this process multiple embodiment. In other words, a single-lesson approach or short focus seems to be insufficient experience for students to successfully come to grips with a specific concept.
Learning Place Value with Trading Games
Consequently, in each book in the Developing Mathematics series, attention has been focused on the practice of trading games. As stated by the authors, ?One of the best reasons for using Trading Games is that the students are taking control of their own learning: they are not waiting to be told or trying to interpret the presentation of the teacher. Many teachers note that the students find the games easy and enthralling because the rules are simple and rewards come by rapidly. Played with a sense of fun and adventure, the students do not realize the depth of mathematical understanding in which they are involved. In no time, it seems, the students are demonstrating these understandings in oral and written manifestations with confident facility.?
The notes and ideas in the books serve as a guide for the teacher while, at the same time, they are user-friendly because they have come about after years of experience of teaching mathematics to young children.
In early childhood, the use of Unifix cubes has tended to revolve around counting. However, the authors have used the Unifix cubes as the material by which the trading games may be learned. In Developing Mathematics with Unifix, a full script for developing the understanding of the procedures is provided, and it is advised that this is adopted when using both pattern blocks and Base Ten materials. Experience has shown that it is essential to ?learn the script? because an ?honest short cut,? usually fostered by a teacher?s understanding of the concept, may mean a child misses a vital step in the building of a sound comprehension of an idea. These missing links can hinder further sound mathematical learning.
Using Base Ten Materials
It is forgotten that the original Multibase Arithmetic Blocks were designed as a developmental material. Originally, the materials were available in bases 3 to 6 (at one time, bases 2, 7,8, and 9 were manufactured) but their use declined, mainly because teachers failed to understand the developmental use of the material. Sadly, today the material is most commonly used?when used at all?as a demonstration material controlled by the teacher; that is, the children are forced to follow the instructions of the teacher or the blackline master. Both Paul and Geoff advocate that the children have the opportunity to master the material, an experience that, in turn, will help them to master both the arithmetical concepts inherent in the blocks and the subsequent written work. They believe the systematic use of trading games, along with a variety of manipulative materials, has contributed to successful results in the schools with which they have been associated.
Of course, there are other advantages to using Base Ten materials, and a number of these are featured throughout Developing Mathematics with Base Ten. If students have a sound understanding of place value, the Base Ten materials serve as one of the best materials for the introduction and development of understanding of the decimal system. For example, if the "long" has a value of 1, what is the value of the "mini" (short)? Likewise, if the "flat" is worth 1, what is the value of the mini? These ideas can be developed orally before any written work is carried out. ?Trading with Decimal Fractions? (pages 51?55) develops these ideas very clearly.
Finally, the authors advise that Base Ten materials are not introduced until the students have experienced number work with other manipulative materials such as Unifix and pattern blocks. It is advised that activities with Popsicle sticks precede the introduction of Base Ten materials (see pages 12?17). In this sense, Base Ten material is most definitely developmental and forms an integral part of a child?s mathematics learning experience. |
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| Downloadable Place Value Activity Pages |
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 Need some great ideas for teaching place value? Developing Mathematics with Base Ten is a comprehensive resource you'll want to have. Authors Paul Swan and Geoff White believe that young children acquire math ideas developmentally through all their senses?and this book is designed to help your students do just that. |
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| Place Value Internet Links |
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 Lots of teachers out there have come up with their own original ways of teaching place value. Check out these Internet resources for an article and activities from Education World, an interactive Base Ten game for the elementary grades, and a look at the origins of place value back in ancient Babylonia! |
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| May Newsletter Theme: Probability |
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 Join us next month as we focus on another challenging math concept: probability. The authors of Dice Activities for Math, just published by Didax in February, will weigh in with some wonderful new ideas for teaching probability using dice. And we'll have some downloadable pages from this fun book to get you started. See you in May! |
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