Task analysis in curriculum design: a hierarchically sequenced introductory mathematics curriculum.
Break math into tiny steps, work backward, and keep each list to seven plain steps.
01Research in Context
What this study did
Clark et al. (1973) wrote a how-to guide for building math lessons.
They mapped every tiny skill a child needs before they can count.
The paper shows teachers how to line up skills from simple to hard.
What they found
The paper gives a recipe, not test scores.
It tells teachers to start with the final skill and work backward.
Each step must be a bite-size piece the child can already almost do.
How this fits with other research
Barnard-Brak et al. (2023) kept the same idea but added new rules. They showed that each task list should stop at seven steps and use easy words.
Trimmer et al. (2017) used the same backward chain to teach money skills to kids with intellectual disability. They added hands-on coins before pictures before numbers.
Kellems et al. (2016) swapped the teacher for an iPad. They filmed each math step so adults with disabilities could watch, pause, and copy. All three studies kept the 1973 spine but added new skin for new learners.
Why it matters
You can still use the 1973 map. Just update the vehicle. If you teach early math, first list every micro-skill. Then cut the list to seven steps or fewer. Swap in coins, cubes, or videos to match your learner. The old paper gives the route; the new papers show how to drive it.
Want CEUs on This Topic?
The ABA Clubhouse has 60+ free CEUs — live every Wednesday. Ethics, supervision & clinical topics.
Join Free →List the final math skill your learner needs, then write the last step they can almost do—make that step one.
02At a glance
03Original abstract
A method of systematic task analysis is applied to the problem of designing a sequence of learning objectives that will provide an optimal match for the child's natural sequence of acquisition of mathematical skills and concepts. The authors begin by proposing an operational definition of the number concept in the form of a set of behaviors which, taken together, permit the inference that the child has an abstract concept of "number". These are the "objectives" of the curriculum. Each behavior in the defining set is then subjected to an analysis that identifies hypothesized components of skilled performance and prerequisites for learning these components. On the basis of these analyses, specific sequences of learning objectives are proposed. The proposed sequences are hypothesized to be those that will best facilitate learning, by maximizing transfer from earlier to later objectives. Relevant literature on early learning and cognitive development is considered in conjunction with the analyses and the resulting sequences. The paper concludes with a discussion of the ways in which the curriculum can be implemented and studied in schools. Examples of data on individual children are presented, and the use of such data for improving the curriculum itself, as well as for examining the effects of other treatment variables, is considered.
Journal of applied behavior analysis, 1973 · doi:10.1901/jaba.1973.6-679