Polish Math

High-quality math education has historically been a pathway to socioeconomic mobility for individuals from disadvantaged populations and for poorer nations. However, especially in less affluent settings, schools are often not able to help children reach a level which allows for that sort of mobility. The gap is key in the critical ages of 3-7. I would like to provide parents with effective, guided resources, grounded in the science of learning, designed to allow them to support their children's math development at home. These would consist of materials to read with their children, math games to play, manipulatives, worksheets, etc., designed to help children develop advanced concepts in mathematics at a young age. Virtually all parents want their kids to succeed but there are three key gaps: (1) Time (2) Knowing what to do (3) Availability of resources. This solution targets two of those three gaps.

I would like children from less affluent households have the resources such that, with drive and focus, they can learn mathematics to a level where they may be competitive in STEM fields on an international scale. STEM is relatively resilient to cultural differences, looks, communication styles, and as such has been a key driver to mobility for historically disadvantaged populations. By applying the learning sciences, we should be able to leapfrog math curricula in developed nations. Developing mathematical reasoning is key during the early years, while the brain still has high plasticity. At present, such resources unavailable in the early years, and are exceptionally expensive in later grades. A complete AoPS math curriculum runs nearly $2000, while enrollment at centers like RSM costs around $2000/year. Expanding access to such resources to a broader population could eventually positively impact billions of lives; very few people who know calculus, statistics, or programming end up in deep poverty. The curriculum I have been working on may be cheaply deployed and is designed to be used by motivated (but potentially less educated) parents. It integrates research from a broad range of domains of education research and has done well in very small-scale pilots. 

My target audience is families with children ages 3-7, primarily from communities operating at levels 2 and 3 on the Gapminder wealth scale. It is constrained to families where caretakers have enough time to work with their kids regularly to help them develop math skills, and to caretakers who have sufficient motivation to invest enough effort to do so. A likely target for a pilot deployment would be a setting like Azraq camp in Jordan. In this camp, there are around 10,000 kids in the target age range. The culture is education-focused. By the structure of the camp, parents, and especially mothers, have time to work with their children. However, if a pilot is successful, there are millions of families worldwide who meet the target criteria.

The solution consists of a set of mathematics activities and guidance for parents which they may work through with their children at their own pace. The activities are motivating for kids and integrate a broad range of techniques from the learning sciences. They include books for parents to read with children to guide conversations about mathematics, math games, puzzles, and manipulatives. These expose kids to advanced concepts in mathematics, including fractions, concepts from algebra, and concepts from calculus. They make many, successive passes over the concepts, gradually transitioning kids from exposure, to zone of proximal development, to surface learning, eventually through deep learning. This process takes a few years for each concept, but many concepts move through this process in parallel. Children develop subitizing, counting, addition, subtraction, and multiplication at the same time. Concepts like algebraic variables, functions, area, perimeter, place value, and fractions begin to come in once kids know math facts up to roughly 3+4 and 3*4 (12% of the addition and multiplication tables).

A complete set could be printed for roughly the cost of a Sunday newspaper and assembled by families together with their kids. These have been piloted with small numbers of kids and preliminary evidence suggests they work as well as research predicts. Kids at age six are capable of manipulating basic algebraic equations, understanding functions, and intuitively (graphically, not symbolically) understanding operations on functions (including ones traditionally considered advanced e.g. derivatives as changes in functions and definite integrals as the area under a curve).

There are several pieces of innovation:

• The solution fuses multiple areas of research which, as far as I know, have never come together in one curriculum. Those range from research in how memory works dating back to the late 19th century through the latest research in motivation, psychology, and the learning sciences. It borrows from math curricula both present and historical to create something which appears quite effective.
• Just-in-time manufacturing processes allow us to be agile in how we develop and test resources with young kids. We can print a book or game virtually overnight, test it on children, and rapidly iterate. We’ve been going through this design process for three years.
• Clever use of printing technology allows us to deliver a broad range of learning materials economically -- for about the cost of a newspaper -- which families can assemble themselves into books, games, and manipulatives at home, reducing costs.
• Many of the activities themselves are novel.
• Many of the activities are borrowed too. One additional – and slightly odd -- piece of innovation is avoiding not-invented-here syndrome. Many pieces come from looking at curricula and learning designs both historic and contemporary and bringing together best pieces.
• We rely on diversity over standardization and consistency. Children are exposed to a broad way of thinking about math.

The key technology we rely on allows for mass-manufacturing of printed materials (Gutenberg 1455). We also fuse:

• Recent progress in gamification and the psychology of motivation to make activities engaging,
• Methods from a broad range of learning scientists, both from key replicated results from history (e.g. Vygotsky, Bruner, Ebbinghaus, etc.) and major modern metastudies (e.g. Hattie, Chi, Bransford)
• Specific techniques from a broad range of educators, also both historical and modern (e.g. AoPS, Brizuela's early algebra, Cohen's calculus for 7-year-olds, Montessori, etc.)

To create a curriculum which seems to work really well both for engaging kids and rapidly developing mathematical ability. 

I have an excellent track record of improving learning outcomes across a broad range of settings based on learning science. I believe that this curriculum works well. However, I don't have data to prove that; the curriculum is at a prototype stage. I've used the full curriculum with only one child end-to-end (my own, so a very biased sample too), and pieces with others (a limited sample – a dozen children, with good results).

A key risk is whether others will be able to replicate this success (that's where most similar projects failed). In the early days, most of my focus has been on developing activities, and I am only now working on packaging them up for use by others. I have only had two parents try scripted resources with their kids, with one a spectacular success, and the other less so. I’m trying to apply similar levels of intellectual design rigor to looking at how to engineer how parents learn and how parents are motivated as to how children learn and how children are motivated (which, I think, is pretty unique). 

Logistically, deployment is straightforward. We need to print out a few thousand copies and ship off to a refugee camp (if that’s our pilot setting). I have colleagues who can probably manage that. I have enough experience scaling that if a pilot is successful, we can grow -- global manufacturing, open licensing, and digital distribution have made scaling much simpler. 

Currently: between one and a dozen, depending on how you count. 

In two years: Either a few dozen or a few thousand, depending on pilot demographic

In five years: I believe I’m supposed to say 100 million. :)

I think, in practice, education projects tend to be a little more longitudinal. Targeting ages 3-7 means there is a four-year window before the first children finish working through the curriculum, let alone before we’ve understood even medium-term impact, let alone validated long-term outcomes. Although I think we can reach millions of children, it will take time to get there (or at least to get there well). The pendulum starts to swing quickly once there is a validated pilot, with a reasonable sample of children who have passed through this curriculum and are building from this base in higher grades. 

Right now, quality math education costs $500-$2000 for books (AoPS), or around $2000/year for instruction (RSM). The former option -- self-serve books -- is only practical for educated families. It is also only available in major languages. My goal is to make access to this sort of education possible within the budget of most of the families in the world, including in low- and middle-income countries. I think that's achievable in a ten-year timeframe.

Within a one-year timeframe, I would like to see a curriculum usable in the sorts of settings I've described, and ideally start a small- or medium-scale pilot. Within a five-year timeframe, I would like to see learning outcomes from that pilot validated, and to see the model begin to scale.

I will mention that while the scale discussed is achievable, I'm not sure it's achievable within the timelines proposed by projects like Solve. Education projects fundamentally have long timescales for high-quality evaluation, and the fail-fast models have done more harm than good in this space. Elevator pitches and five-year timelines favor projects which do a good job of appearing to work over those which work well work. 

• Whether people will choose to adopt this. Historically, major educational interventions sold on marketing (to a naive audience), rather than genuine efficacy.  
• Whether people will be able to use these. Many interventions have failed to scale because parents, teachers, and learners could not replicate initial pilots.
• My own time, especially for packaging these in a format which may be useful to parents. An upside of a spare-time / self-funded project is fewer constraints, but a downside is less time. Thus far, I've been making rapid progress working nights and weekends. 

• Start with populations interested in education, but with few other options. Refugee camps are a good environment for a pilot. My own reputation in this space also helps establish credibility. 
• Provide clear scripts and guidance for activities and target how parents learn and how to keep parents motivated with the same level of rigor as how children learn.
• Continue to work very hard. Ideally, form partnerships around co-development.

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One.

• I have extensive experience engineering learning experiences which have dramatically improved student learning outcomes.
• I have experience working on educational projects internationally, including in refugee camps in Jordan, schools in Sub-Saharan Africa, and schools in China.
• I have read countless books on how people learn, from across many research disciplines in education, and interacted with experts in most of those disciplines. I have read many books, primary sources, and curricula specifically focused on math education.
• I have experience with scaling and high-growth: I have been involved in three organizations which broke $200 million, either as an early employee or as a founder.
• I have a working curriculum that worked well with the kids I've tried it with, with six-year-old kids understanding some concepts from calculus, algebra, decimal numbers, and fractions.
• Ironically, given the low-tech nature of the project, but aligned with the focus areas of Solve, I have extensive experience with educational technology, AI/ML, big data in education, and educational measurement.

At this stage, I have no public partnerships.

The solution is beautifully free of a traditional business model! I am developing this as a volunteer in my spare time. I've helped launch three organizations which all broke the $200 million mark, and this is my first major project intentionally launched without a traditional business model. That allows me to align everything I create to research, effective learning practice, and impact (as opposed to aligning to the constraints of keeping VCs and donors happy). For this project, I think that’s more effective than the resources provided for by formal funding. I think this space benefits from the opportunity to engage in an in-depth, long-term design process of a type which would be difficult with traditional funding.

An example of the sort of setting I am considering for a pilot is Azraq in Jordan, home to 40,000 Syrian refugees, around 10,000 of whom are in the target age range. Assuming 20% market penetration, I could afford to run a pilot for around $10,000, which I could support from Solve (or even my own pocket). In other words, this is something which, at this stage, does not require a business model. In future stages, I think a community model may work. Once validated, with open licensing, free markets could handle bringing these resources into the hands of people who need it at the lowest possible costs as essentially commodity goods. 

My path to financial sustainability is to hold a job and to continue to build this on nights and weekends. For this sort of project, that’s sustainable in a way in which many traditional sustainability models are not. Projects like Linux have demonstrated how serious, well-structured, unfunded projects can have a broad impact. In the longer term, I can see several places this project might go:

1. As a community-supported project licensed under free and open licenses. With appropriate community development, a community of researchers, students, and practitioners could continue to improve resources, while free markets handle internationalization, translation, and distribution.

2. As a for-profit / not-for-profit hybrid of some sort. The curriculum I have is significantly better than anything else I have found for this age range. At slightly older ages, parents pay around $500 for similar products (e.g. Beast Academy), and comparable companies are valued at tens of millions of dollars, so there are clear and proven business models. 

3. Some model combining #1 with some kind of significant donation (an endowment or fellowship of some sort). 

The $10,000 prize just about covers the cost of the initial pilot. The networking opportunities would be valuable, especially with Dubai Cares, since they work in the area. The enhanced visibility would help as well.

Potentially, co-development, assuming ownership and similar issues can be managed. It's more fun to work as a team!

I am looking for partners who are patient and thoughtful, who could eventually help deploy and test solutions in small (10-60 families) or medium (<5000 families) scale settings. Although I use agile, rapid iteration approaches, this is not a fail-fast project. This is a project where I'd like to really get things right. It's also, by time constraints, not a speedboat.

I'm also looking for partners who aren't afraid to "boil the ocean." There have been many projects to teach very young kids concepts from algebra and calculus. I've had success combining, integrating, and building from such approaches as well. I expect it will take several rounds before we bring this to a point where ordinary parents will be able to do my activities with kids, though.

The goal is to leapfrog the current math curriculum, not incremental progress or having kids do almost as well as ones in developed settings. I believe I can describe with scientific rigor why this is possible, but not in 250 words or less.

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