Fostering young children’s interest in numeracy through demonstration of its value: the Footsteps Study


Children’s early mathematical abilities are fundamental to their later academic achievement. An interest in mathematics in the early years is likely to establish a positive attitude to later mathematical learning, hopefully sustaining continued interest in mathematics and mathematical learning. Approaches to early mathematics teaching in the early years, however, are typically adult-initiated, which may fail to capture children’s interest. Given the importance of children’s motivation and sustained interest, the study described here strove to spark children’s interests in mathematical problems in everyday life. The study sought to determine if children would incorporate more numeracy-related concepts into their free play if exposed to adult demonstrations of age-appropriate numeracy activities such as patterning. For at least 15 min three times weekly, participating children’s parents and educators demonstrated numeracy problem-solving nearby, while children engaged in other activities. Demonstrations were thought to ascribe social value to the problem-solving activities. If children became interested in participating, adults told them to wait until the demonstrations finished, further indicating social value. Results show these children chose to play with numeracy-related activities in their free play time at preschool significantly more than children in a control group. These results suggest that seeking to foster children’s interest in mathematics through child-initiated play, rather than prescribing adult-initiated mathematics activities, may be an important means of laying the foundation for lifelong mathematics learning. Ascribing social value to numeracy applications is proposed as a new approach to teaching mathematics in the early years.

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Fig. 1
Fig. 2


  1. 1.

    One mother demonstrated using a sock-puppet as her partner when the father was unavailable.


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Correspondence to Yeshe Colliver.


Appendix 1: sample script used in Footsteps Intervention

Adult A and B sit next to each other with coloured blocks

Adult A: [Adding two blocks to an existing tower of four blocks] Okay, so that’s another green and then blue. That gives us … six blocks

Adult B: Cool! Let’s do it with purple and orange! Ok, so can you pass me one of each?

Adult A: I’ll put them together for you.

Adult B: So, if we want to make a tower of six blocks using the purple and orange, how many orange blocks will we need?

Adult A: Hmm… I think we need to divide six by the number of blocks in the unit of repeat. So that’s one purple and one orange. One, two. So, if we want to divide the six blocks in the tower by two, we’d get that two times. Is that right?

Adult B: Ah… let’s see. One, two (once), and one, two (twice) [demonstrating with two units of repeat], then we have one, two, three, four blocks. So NOT six. How many more will be need to make six?

Adult A: I see what you mean. Let me try with another two blocks, one purple, one orange. I’ll put them on top of your four blocks. That’s one, two (once), one, two (twice), and one, two (three times). Can you count to see if that’s six in our tower?

Adult B: Okay: one, two, three, four, five, and six! That’s what you wanted, a tower of six blocks! So how many purple blocks did we use?

Adult A: [Pointing to the purple blocks] One, two, three. So, there’s three! What about the orange blocks? How many are there?

Adult B: [Pointing] One, two, three! So, there are the same number! Shall we add another purple and orange block to our tower? That’s another two blocks…

Appendix 2: an example excerpt from literacy script

Adult A and B sit next to an art easel with crayons and write on a large piece of paper

Adult A: I want to write ‘to Grandma’. I want to start with the word ‘to’ and want a letter that makes the sound /t/ /t/ /t/. Which letter makes the sound /t/?

Adult B: Hmmm, which letter makes the sound /t/ /t/ /t/? I think it’s the letter TEE! Is that right?

Adult A: Letter TEE makes the sound /t/ t/ /t/ … Great! [Writes the letter t in lower case]. Now I want to make the word ‘to’ … and I have the sound /t/ /t/ /t/, … so what letter makes the sound /u:/??

Adult B: Hmmm, which letter makes the sound /u/ /u/ /u/? I think it’s the letter YUUU! Is that right?

Adult A: It usually does, but in the word ‘to’ we use the letter O. So, the word ‘to’ is spelled TEE OH…. Do you know how to write the letter OH?

Appendix 3: Post Study Interview Questions – Parents

Thank you so much for being part of the study. Your participation has led to some interesting preliminary results!

  1. 1.

    The aims of the study were to see if adult behaviour might affect how children decide to play. Do you think the demonstrations had any effect on [child’s name]’s play?

  2. 2.

    How did you find the study?

  3. 3.

    Were you able to do the demonstrations 3 times a week or were you too busy? Did you do more than that?

  4. 4.

    Did you take any notes on changes you noticed in [child’s name]’s behaviour? What were they?

  5. 5.

    Did you notice any other changes in her/his behaviour? (ask for specific examples if they talk generally)

  6. 6.

    Was there anything which you felt got in the way of the effects of the study?

  7. 7.

    Were the materials you received a novel/new thing for the child?

  8. 8.

    Were the activities very different to what you were already doing?

  9. 9.

    Did you find it hard to not tell your child to do things?

  10. a.

    To ignore them when they wanted to join in on the activities?

  11. 10.

    Any siblings? How did they effect the study?

  12. 11.

    How do you think your child’s cultural background impacted on the study?

  13. a.

    The impact of the demonstrations

  14. b.

    The types of play your child was inclined to partake in

  15. c.

    How you interacted with your child?

  16. 12.

    Do you think the study has impacted the way you would like to interact with your children in the future?

  17. 13.

    Do you think you learned anything about your children from doing the activity?

  18. 14.

    Do you think you learned anything about the way that children see their parents?

  19. 15.

    Will this change what you expose your children to?

  20. 16.

    What will you do differently?

  21. 17.

    What were the biggest constraints to doing fifteen minutes of demonstrations three times a week?

  22. 18.

    Do you think the materials you were given will be useful in the future?

  23. 19.

    Do you think you got anything else from the study?

  24. 20.

    Anything else which you would like to add?

Thank you for your time today and for your interest in the study.

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Colliver, Y. Fostering young children’s interest in numeracy through demonstration of its value: the Footsteps Study. Math Ed Res J 30, 407–428 (2018).

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  • Play-based curricula
  • Learning through play
  • Legitimate peripheral participation
  • Child-initiated mathematics