Research idea
Learners benefit when reasoning and feedback are made visible.
RESEARCH & EVIDENCE
Design choices should have
reasons you can inspect.
This library connects WHYLO’s design to peer-reviewed research, evidence-informed guidance, and official curriculum frameworks. It also states what each source does not prove.
HOW TO READ THIS PAGE
Peer-reviewed researchA study or scholarly synthesis
Official frameworkCurriculum or international guidance
WHYLO applicationOur design interpretation, not a quoted claim
These sources support individual design principles. They do not by themselves prove that WHYLO improves learning outcomes. Product-specific effectiveness requires transparent evaluation using defined outcomes, appropriate comparison, and enough time.
EVIDENCE-INFORMED METHOD
Explain to understand
HOW WHYLO USES IT
WHYLO uses brief prompts such as “How do you know?” and “Can you show it another way?” so learners explain a method and its reason in their own words.
WHAT THIS DOES NOT PROVE
Self-explanation studies use particular ages, subjects, and tasks. They do not show that the same prompt has an identical effect for every WHYLO learner or mathematics topic.
EVIDENCE-INFORMED METHOD
Move and connect
HOW WHYLO USES IT
WHYLO combines learner choice in AI manipulatives, a clear goal, small prompts when needed, and a gradual move from objects to diagrams, speech, and equations.
WHAT THIS DOES NOT PROVE
Manipulatives or additional representations do not improve learning automatically. Goals, interface constraints, sequence, and guidance matter, and guided play has not shown a universal advantage over direct instruction.
EVIDENCE-INFORMED METHOD
Revisit the principle
HOW WHYLO USES IT
WHYLO revisits a principle in the same lesson, the next lesson, around one week, and two to three weeks later while changing numbers, context, or representation and mixing related strategies.
WHAT THIS DOES NOT PROVE
Useful spacing depends on the goal, retention period, and learner response. Verbal and pictorial memory studies are not direct evidence for young children's mathematical concept learning.
EVIDENCE-INFORMED METHOD
Adjust the next question
HOW WHYLO USES IT
WHYLO uses one question at a time, a small hint, a representation change, and observable evidence that informs the next prompt and lesson.
WHAT THIS DOES NOT PROVE
Broad classroom evidence does not guarantee that every AI tutor is effective. WHYLO must not diagnose ability, attention, or intention that was not observed.
EVIDENCE-INFORMED METHOD
Apply in a new context
HOW WHYLO USES IT
WHYLO first asks for a prediction without the manipulative, changes one condition, applies the idea in a practical context, and asks for another representation.
WHAT THIS DOES NOT PROVE
Mathematical-proficiency frameworks, curricula, and international assessments guide design; they do not evaluate WHYLO's own effect on transfer.
SOURCE LIBRARY
Read each source once, with its use and limit.
Every full source record appears once. Method sections link here instead of duplicating a claim.
01Research synthesis · 2001Adding It Up: Helping Children Learn MathematicsNational Research Council · National Academies Press+
WHAT IT SAYS
Mathematical proficiency is described as five interwoven strands: conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition.
HOW WHYLO USES IT
WHYLO keeps understanding, strategy, reasoning, and disposition visible rather than collapsing them into one accuracy or speed score.
LIMIT
Open the original source ↗The five strands are a design framework; the report does not evaluate WHYLO itself.
02Peer-reviewed paper · 1998Assessment and Classroom LearningPaul Black & Dylan Wiliam · Assessment in Education+
WHAT IT SAYS
This influential review brought together classroom formative-assessment evidence and described how strengthening feedback during learning can support improvement.
HOW WHYLO USES IT
WHYLO uses evidence from the current response to shape the next prompt instead of waiting until the end to return only a score.
LIMIT
Open the original source ↗It synthesises varied classroom studies and does not guarantee an identical effect in every digital setting.
03Cognitive science paper · 1989Self-Explanations: How Students Study and Use Examples in Learning to Solve ProblemsChi, Bassok, Lewis, Reimann & Glaser · Cognitive Science+
WHAT IT SAYS
This classic study found that learners who generated more self-explanations while studying worked examples built stronger problem-solving knowledge.
HOW WHYLO USES IT
WHYLO uses prompts such as ‘How do you know?’ and ‘Can you show it another way?’ to make reasoning explicit.
LIMIT
Open the original source ↗The study used a specific worked-example setting and should not be treated as direct proof across every age and maths topic.
04Official curriculum · 2025 / 2026The New Zealand Curriculum — Mathematics and Statistics Years 0–10New Zealand Ministry of Education+
WHAT IT SAYS
The curriculum effective from 2026 combines conceptual and procedural knowledge and highlights abstraction, visualisation, and symbolic representation across quantity, space, data, and uncertainty.
HOW WHYLO USES IT
WHYLO lessons move between objects, drawings, tables, equations, and graphs while connecting concepts and procedures to real situations.
LIMIT
Open the original source ↗WHYLO does not replace the school curriculum or an educator’s responsibility for sequence and assessment.
05International framework · 2022PISA 2022 Mathematics FrameworkOECD+
WHAT IT SAYS
Mathematical literacy is framed as reasoning mathematically and formulating, employing, and interpreting mathematics across real-world contexts.
HOW WHYLO USES IT
WHYLO stages 3–5 use recipes, mobile plans, café revenue, and statistical claims to practise modelling and interpretation.
LIMIT
Open the original source ↗PISA is an international population-level assessment of 15-year-olds, not a complete curriculum or individual diagnosis.
06Evidence-informed guidance · 2017Improving Mathematics in Key Stages 2 and 3Education Endowment Foundation+
WHAT IT SAYS
The guidance emphasises understanding how pupils learn mathematics and where difficulties arise, with purposeful support for representation, problem solving, and metacognition.
HOW WHYLO USES IT
WHYLO hints make a task smaller, shift representation, and prompt checking instead of supplying the final answer.
LIMIT
Open the original source ↗The guidance was written for UK school stages and must be adapted thoughtfully for New Zealand and individual learners.
07Representation research · 2006DeFT: A Conceptual Framework for Learning with Multiple RepresentationsShaaron Ainsworth · Learning and Instruction+
WHAT IT SAYS
Multiple representations can complement information, constrain misinterpretation, and support deeper understanding, while also creating cognitive work when learners translate between them.
HOW WHYLO USES IT
WHYLO asks learners to connect representations—for example, what stays the same between a diagram and an equation—rather than merely displaying more formats.
LIMIT
Open the original source ↗More representations do not automatically improve learning; their sequence and guidance matter.
08International AI guidance · 2023Guidance for Generative AI in Education and ResearchUNESCO+
WHAT IT SAYS
UNESCO calls for human-centred, age-appropriate use of generative AI with privacy protection and ethical and pedagogical validation.
HOW WHYLO USES IT
WHYLO bounds the AI away from diagnosis and permanent ranking, focusing it on one brief follow-up and observable learning evidence.
LIMIT
Open the original source ↗The guidance sets a direction; real operation still requires privacy policy, security review, and age-appropriate safeguards.
09Research synthesis · 2013Effects of Virtual Manipulatives on Student Achievement and Mathematics LearningMoyer-Packenham & Westenskow+
WHAT IT SAYS
A synthesis of 66 reports found a moderate average effect across available comparisons and identified affordances such as focused constraints, varied solutions, and linked representations.
HOW WHYLO USES IT
WHYLO uses open manipulation with purposeful constraints and connects actions to diagrams and equations.
LIMIT
Open the original source ↗Effects varied by age, domain, and comparison condition; this review did not evaluate WHYLO or its AI tools.
10Peer-reviewed paper · 2015Benefits of “concreteness fading” for children's mathematics understandingFyfe, McNeil, Son & Goldstone · Learning and Instruction+
WHAT IT SAYS
In a mathematical-equivalence study, moving from concrete materials towards abstract symbols supported transfer better than the reverse order.
HOW WHYLO USES IT
WHYLO moves from objects to dots, groups, and equations while asking what stays the same.
LIMIT
Open the original source ↗The study used a specific equivalence task and does not establish one universal sequence for every concept or age.
11Research synthesis · 2022Can guidance during play enhance children’s learning and development in educational contexts?Skene et al. · Child Development+
WHAT IT SAYS
A review of studies with children aged one to eight found some advantages over free play, while comparisons with direct instruction did not show a clear overall advantage.
HOW WHYLO USES IT
WHYLO combines learner choice, a clear learning goal, and small prompts when needed.
LIMIT
Open the original source ↗Results were heterogeneous and mixed; guided exploration should not be claimed as universally superior to direct instruction.
12Research synthesis · 2006Distributed practice in verbal recall tasksCepeda et al. · Psychological Bulletin+
WHAT IT SAYS
A synthesis of 317 experiments found an advantage for distributed over massed practice and showed that useful spacing depends on the desired retention interval.
HOW WHYLO USES IT
WHYLO adjusts the next principle revisit using independent success, explanation, and support used rather than a universal calendar.
LIMIT
Open the original source ↗The synthesis focused largely on verbal memory tasks and is not direct evidence for young children's mathematical concept learning.
13Peer-reviewed paper · 2007The shuffling of mathematics problems improves learningRohrer & Taylor · Instructional Science+
WHAT IT SAYS
Experiments found better delayed performance when mathematics practice was spaced and mixed rather than completed in one block.
HOW WHYLO USES IT
WHYLO changes surface conditions and asks learners to retrieve the same principle instead of cloning an item.
LIMIT
Open the original source ↗The experiments used university students and limited topics, so they are not direct evidence for WHYLO lessons with five- to seven-year-olds.
14Peer-reviewed paper · 2014The benefit of interleaved mathematics practice is not limited to superficially similar kinds of problemsRohrer, Dedrick & Burgess · Psychonomic Bulletin & Review+
WHAT IT SAYS
In a Grade 7 classroom study, interleaved practice produced higher scores than blocked practice on an unannounced test two weeks later.
HOW WHYLO USES IT
WHYLO mixes related principles so learners must select a strategy from the problem rather than the worksheet heading.
LIMIT
Open the original source ↗The study covered one grade and selected problem types and should not be generalised to every age or mathematics domain.
15Cognitive science paper · 2020Retrieval Practice Promotes Pictorial Learning in Children Aged Six to Seven YearsMa et al. · Perceptual and Motor Skills+
WHAT IT SAYS
A study of 104 six- and seven-year-olds tested picture memory after five minutes, one week, and one month and found longer-term benefits in some retrieval conditions.
HOW WHYLO USES IT
WHYLO uses short, age-appropriate retrieval through speech, pictures, and objects with feedback when needed.
LIMIT
Open the original source ↗This was a picture-recognition study; it did not test mathematical principles or WHYLO's scheduling rules.
FROM EVIDENCE TO PRODUCT
Research is translated into testable product rules.
Product rule
Ask for one explanation; record observable evidence; adapt only the next step.
Interface behaviour
Offer speech, drawing, objects, equations, and a small hint without ranking the learner.
Evaluation question
Do learners explain more independently and transfer the idea to a new context over time?
HOW WHYLO WILL TEST IT
External evidence is not WHYLO-specific effectiveness.
WHYLO is currently at the stage of connecting design rules to external evidence. Product-specific claims require separate evaluation.
Outcomes
Baseline-to-change evidence for independent explanation, recorded support used, linked representations, delayed unaided recall after time without help, and transfer in a new context.
Method
A starting check, immediate check, delayed check, an appropriate comparison, and enough time.
Disclosure
Report unclear, neutral, and unexpected findings as well as positive ones.
SEE IT IN PRACTICE