It may just be me but I find this study on 4-6 year olds (pre-k to first grade age-wise) pretty stupid - unless it is at least fifteen years old and therefore prior to the shift in elementary math education, which added elementary algebra and elementary geometry and elementary data analysis (graphs, tables, probabilities). As far back as a dozen years ago, my oldest DS had problems like 10 - ? = 3 in first grade (6 year olds), which progressed to 3p = 24 by 3rd grade. At that time, I refer to these problems as kiddie algebra because the term elementary algebra wasn't common in the lexicon yet.
Of course, the title itself is meant to spark interest but rather misleading. As another poster pointed out, it does come down to how you define "Algebra". Being able to differentiate between a much large quantity (12) and a much smaller quantity (4) to conclude 12 or 4 is a far cry from solving systems of linear equations and quadratic equations requried in "real" first-year Algebra curriculum. While the concept of solving for an unknown is part and parcel of Algebra, so are arithmetic concepts and both are routinely covered in first-grade curriculum aimed at 6 year-olds. I suppose this is no different from the number of lay people who equal a math degreed person with facility with arithmetic skills.
