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Understanding Multiplication and Division in Early Numeracy Education

The Multiplication and Division aspect of the learning framework emphasizes early strategies in numeracy, focusing on forming equal groups and understanding composite units. Students progress through levels, starting from perceptual counting and advancing to using multiples without visible items. This framework highlights the importance of recognizing and coordinating groups for effective problem-solving. Observations indicate varying confidence in multiplication and division, with students benefiting from visual aids like arrays. Emphasizing modeling strategies can enhance learning outcomes in these foundational skills.

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Understanding Multiplication and Division in Early Numeracy Education

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  1. The Learning Framework In Number:Multiplication & Division Chris Francis

  2. The Multiplication and division aspect of the learning framework underpins: Count Me In Too Counting On Taking Off With Numeracy

  3. Structure • Early multiplication and division strategies focus on the structure and use of groups of things. • A composite unit is formed when a student takes a group of items and treats it as a unit. • Recognising units is not sufficient. It is necessary to develop ways of coordinating the groups that are formed.

  4. Typical progression Not intended to be aligned

  5. Level 1: Forming equal groups The student: • uses perceptual counting and sharing to form equal groups • finds the total of the groups, counting by ones • does not take notice of the structure of the groups when finding the total. NES1.3 PAES1.1

  6. Level 2: Perceptual multiples The student : • uses items to form equal groups • finds the total of the groups through rhythmic, skip or double counting, only when the items are visible • cannot deal with concealed items. NS1.3 PAS1.1

  7. Level 3: Figurative units The student: • does not rely on items being visible • counts forwards or backwards using multiples (or a combination of multiples and rhythmic counting ) • uses perceptual markers (e.g. fingers) to keep track of the groups • reconstructs the groups before counting. NS1.3 PAS1.1

  8. Level 4: Repeated abstract composite unit The student: • uses repeated addition or subtraction to find the total • does not need perceptual markers to represent the groups • might use fingers to keep track as they count • might use skip counting or a double count. NS1.3, NS2.3 PAS1.1, PAS2.1

  9. Level 5: Multiplication & division as operations The student: • recalls a wide range of multiplication and division facts • uses multiplication and division as inverse operations to solve problems • explains the composite structure in a range of contexts; not simply recalling facts. PAS2.1 NS2.3

  10. Observations • Students are usually confident with some multiples over others. • Strategy use is strongly dependent on knowledge of multiples. • Students may use a combination of strategies. • Students typically appear more confident with multiplication than division. • Modeling of strategies is needed. • The use of arrays is useful in developing visualisation.

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