Accelerating Learning in Exploratory Study

Target Group: Students who are at year 6 to 8 andcan not recall their basic facts.

Focus: To move Basic Facts (Add, Sub, Mult, and Div) knowledge from the ‘working’ memory to long term memory.

Suggested Approach:

Alongside effective numeracy approaches the focus of this study will be on enhancing the students’ recall of the basic facts through using a variety of strategies and memory activities.

Support Readings:

Memory may have a significant impact on thinking with numbers. As Dr. Mel Levine points out, "Almost every kind of memory you can think of finds its way into math." Factual memory in math is the ability to recall math facts. These facts must be recalled accurately, with little mental effort. Procedural memory is used to recall how to do things -- such as the steps to reduce a fraction or perform long division.

Active working memory is the ability to remember what you're doing while you are doing it, so that once you've completed a step, you can use this information to move on to the next step. In a way, active working memory allows children to hold together the parts of math problems in their heads. For example, to perform the mental computation 11 x 25, a child could say, "10 times 25 is 250 and 1 times 25 is 25, so adding 250 with 25 gives me 275." The child solves the problem by holding parts in his or her mind, then combining those parts for a final answer.

Pupils struggle because of poor memory not low intelligence, research finds.

Teaching unknown basic facts through strategies.

Alex Neill Set 3, 2008 Basic Facts: Start with Strategies, move on to Memorisation

Diagnostic assessment:

Ask the students the following Basic Facts questions:

  1. 3 + 4
  2. 7 + ? = 10
  3. 8 + 8
  4. 14 – 6
  5. What two numbers did you add in question one?
  6. 20 - ? = 14
  7. 4 x 5
  8. 6 x 7
  9. 70 ÷ ? = 7
  10. Show the student a card with 5 numbers written on it. The numbers are from 1 – 20. Give the student 4 seconds to memorise the numbers. Then turn the card over and ask the student the following questions.

i)What was the largest number?

ii)What numbers were less than ten?

Analyse the data todetermine the students’ area of strengths and weaknesses.

Ongoing Information Collection

Collect student voice at the beginning and the end of the intervention.

Samples of student work.

NumPA data – initial and final

Data from the memory activities e.g. what level has the student reached on a particular game.

What to do:

Programme Structure.

Personnel and role:

Either The classroom teacher will take the targeted group every day for a minimum of twenty minutes in addition to the daily mathematics programme or the specialist teacher will take the targeted group every day for a minimum of twenty minutes in addition to the daily mathematics programme.

Note: If the classroom teacher takes the targeted group then the specialist teacher will support the teacher in their classroom.

Location: If the targeted group is taken by the specialist teacher then the group can be taken either in the classroom or a withdrawal space.

Time: Twenty minutes at least. (max 30 minutes) every day for four weeks.

Size of group: Four to six students.

Lesson Structure.

This session will be divided into two parts:

Part A: Strategy teaching

Focus on the unknown basic facts, teach strategies to help students to be able to solve the basic facts questions.

Teaching format:

  1. Start with teaching the students strategies to solve basic facts.
  2. Have plenty of practice using the strategies
  3. Memorisation occurs when students have practiced and used the strategies repeatedly.

For example;

  • 6 + 8, students can solve using doubles (Bk 4, p32) or make ten. ( Bk 5, p26, 28, Bk 4, p32, 33, 34)
  • For basic facts less than 10 such as 5 + 2 focus on patterns and subitising.

Note: Students will need to practice the strategy independently (can be independent work during maths time) (refer to article by Alex Neill Set 3, 2008 Basic Facts: Start with Strategies, move on to Memorisation)

Part B: Memory

Students will participate in a variety of quick activitiesthat target their working memory.

For example;

  • Remembera new telephone number, PIN number, web address or vehicle registration number.
  • Follow spoken directions such as go straight over at the roundabout, take the second left and the building is on the right opposite the church.
  • Show images or numbers on a PowerPoint and students then record the numbers.

Note:Students should be encouraged tosharestrategies that they use to remember numbers, shapes etc. Strategies that students have found support them to remember mathematical facts could be recorded in the modeling book.

Issues/misconceptions:

  • Which basic facts do they know from the Number Framework? Where are the gaps?
  • Do they understand the relationship between addition and subtraction?
  • Do they understand the relationship between multiplication and division?
  • Do they understand what the commutative property looks like?
  • Can they model any given multiplication fact?
  • Equipment needs to be used at all stages to reinforce understanding
  • Development of student understanding by the teacher varying the vocabulary used e.g groups of, sets of, lots of etc.

Home Links.

Share the Parent information pamphlet that is appropriate to the year level that you have targeted.

Create a maths back pack to go home. Inside the maths back pack is a game for the student to play and a notebook that the parent and the student can write in reflective comments.

See support material: Basic Facts for some activities.

Students could be given the web sites from the Memory support material to use at home. They could be asked to evaluate and rate them.

Support Material

See the support material for Memory

See the support material for Basic Facts.

NZMaths units

Using Tens Frames for the Strategy of Bridging to Ten

Number Cards

Smart Doubling

Digital Learning Objects

The Part Adder

The Take – away Bar

The Array

The Difference Bar

Developers.

Deborah Gibbs

Jill Peterson