Theme 4: Worthwhile mathematical tasks

Effective teachers understand that the tasks and examples they select influence how the students come to view, develop, use, and make sense of mathematics.

Requiring students to think deeply about mathematical ideas will ensure that conceptual understanding is developed and that higher ordering maths thinking is achieved. Teachers therefore need to be able to design, select and sequence mathematical tasks, both for teaching and for practice, that support the development of big ideas of mathematics rather than isolated strategies and skills. Tasks should challenge students to explore concepts (not simply ‘get the right answer’), to be able to generalise and to develop ideas about the nature of mathematics. Independent tasks should be well chosen to achieve this and not simply be time fillers.

Many of the short term interventions that teachers have implemented to accelerate learning in mathematics have focused on developing aspects number knowledge and related skills because these have been identified as foundations upon which to build. Some of these interventions are in addition to and complement the regular classroom programme in which the development of mathematical concepts and processes is a priority.
 

Exemplars:

See, say, do
A powerful teaching model is based on recognising that there are six things that students need to understand before they can be said to understand the meaning of 2 digit numbers.
Process to See, Say, Do (Example)
See
  • They see a numeral, “64” as “sixty – four”.
  • They read sixty four as sixty four
Say
  • They say “sixty - four” as 64 or “sixty-four”
  • They say “64” as 6 tens and 4 ones
Do
  • They show 64 or sixty-four, by counting objects from one to 64
  • They show 64 or sixty-four as six bags of lollies and 4 loose ones

 

The COSDBRRICS programme as a tool is a well organised and sequenced resource to aid in accelerating learning in maths.
  • Counting forwards and backwards
  • Counting in 10’s, 5’s and 2’s
  • Ordering numbers 1-1000
  • Saying numbers up to quadrillions (as students requested it – challenged themselves!!)
  • Dictation
  • Basic facts – doubles, instant recall to 20 add/sub
  • Revision
  • Place value/fractions as needed (strategy)
  • Game
  • Students independent activities (games, worksheets, puzzles etc)
  • Homework
I was very keen to use the Targeted Learning Group programme working on number knowledge and place value. The programme is very structured and requires the teacher to closely follow a consistent format. Each day the students' session would involve counting forwards and backwards, ordering numbers, saying (reading) numbers out loud, dictation, basic facts practice or place value teaching, strategy revision, number games, self evaluating progress and a homework check. The predictability of the session was a key ingredient for my six students. I added a number of clapping/ counting games to our format and this was quite an eye opener. All the students struggled to put an action and a number together and we were only working from 1-6 initially. This lead me to reflect on the changing nature of children’s play and how the common games of hopscotch, skipping and clapping to rhymes (games where actions, words and movement are all interlinked) were fast disappearing from our schools. Another implication is, if some students find it difficult to link action with information, how disadvantaged they might be in our busy, moving learning spaces.
The children enjoyed keeping the journals but it was tricky trying to fill them up with things we had learned as we kept the pace fairly slow at times when things weren’t being retained. However, a benefit of the journals was that the children were encouraged to care for the development of their own mathematical proficiency. Although these were not used as much as they could be the journals were a real hit. A spin off was the positive attitude raised ‘comfort levels and gave them greater confidence in their capacity to learn and to make sense of mathematics.’ (Anthony,G. and Walshaw,M. 2009 p.8)