## Todays Discoveries Aid Tomorrow’s Understandings!

According to eSchools News, a study released by the University of Missouri suggests that students beginning first grade with a good understanding of number lines and basic math facts were more successful in math skills over the next five years. This should be no surprise – just as building a house on a strong foundation makes for a stronger home, building new math skills on a strong foundation of math knowledge makes for a more robust understanding.  These recent findings also suggest that teaching ‘a mile wide and an inch deep’ may not fully develop a conceptual understanding of key math concepts. Young students need a lot of modeling, time, and a variety of experiences to practice math skills for true understanding.

One way to help develop these skills at an early age is to incorporate the Quantile Framework for Mathematics in specific math lessons. Utilizing the Framework allows teachers to determine which prerequisite skills are necessary for success with a particular math skill or concept, allowing educators to target struggling math students with the appropriate prerequisite skill.  For example, if a third grade student is working on estimation for sums and differences with whole numbers he/she must first be able to:

• Make reasonable estimates of the number of objects.
• Subtract 2- and 3-digit numbers with regrouping.
• Round whole numbers to a given place value.

These prerequisite skills are necessary for students to understand before they are able to extend to estimation skills when they add and subtract whole numbers.

And the Quantile Framework allows teachers to go even lower: if a student is having trouble making reasonable estimates of the number of objects the knowledge cluster for this skill may indicate that he or she is having trouble with:

• Use counting strategies for totals to 100 that include counting forward, counting backwards, grouping, ten frames, and hundred charts.

The Quantile Framework allows for the possibility of identifying areas where students are deficient.  Furthermore, for educators looking to differentiate math instruction, the Quantile Framework can serve as a valuable classroom resource by helping teachers target lessons to the needs of the students. Additionally, the Quantile Framework is linked to a variety of free tools and resources that – in addition to providing tools for task analysis – provide access to a host of free targeted resources, including worksheets, online tutorials, videos, websites, literature guides, and classroom activities.

As we enter the new school year (and as many students are suffering the effects of summer slide), be sure to check out the Quantile Framework as a way to help struggling math students.

## Rethinking Math Education: An Experiment with Video

We’ve written before on how organizations like Virtual Nerds or individuals like Salman Khan are capitalizing on easy access to video and then harnessing the Internets capability to rapidly disseminate short chunks of information through multiple channels.  The ability to access specific, targeted material – and repeatedly view on-demand content – means that many students are able to engage with the content in a setting of their choice, a setting hopefully free of other distractions.  Plus, accessing information on-demand means that students are able to free up valuable mental real estate; students don’t have to be distracted by monitoring social cues or focusing on facial expressions, or even worrying about the speaker’s perception.  Instead, the student is free to focus almost exclusively on the actual content.

Here’s Khan at a recent TED talk explaining what he thinks may account for the appeal of his math videos.

Khan is not alone.  Vi Hart has garnered recent acclaim for her ability to take high-level, abstract, mathematical concepts and render them both accessible and fun.  Hart offers her visual work and explanations through both YouTube and her own site.

Video formats – like the Khan Academy YouTube videos and those created by Virtual Nerds – offer math students a valuable way to reinforce their current lesson or access more in-depth explanations in a setting of their choice.  That sort of accessibility and ease of use were a part of our thinking in making both Virtual Nerds and Khan Academy videos available through our own Math at Home utility.   Math at Home allows parents and educators to link students to resources at a targeted level based on the Quantile Framework for Mathematics.

If you haven’t already checked out this valuable new resource, be sure to take a look.

MetaMetrics is an educational measurement organization. Our renowned psychometric team develops scientific measures of student achievement that link assessment with targeted instruction to improve learning.