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When is not helping my son the right thing to do? Part 2

Part 2 of a 3-Part Series

Back by popular demand, we have dug up a three-part blog series from 2012 where our very own Dr. Tim Hudson explains that at times, helping your students through a tough problem may not be the best approach. Read on and let us know what you think in the comments below!

In part 1, I explained that my son is having difficulty with DreamBox Quick Images lessons.  I’d like to share a bit more background and context for why I’m choosing not to help him.  So I’ll start with a brief overview of curriculum standards, as we should always plan with the end in mind when making instructional choices.
The Common Core State Standards have two components: (1) Standards for Mathematical Practice and (2) Standards for Mathematical Content.  The act of counting falls in the ‘Content’ category, as do most familiar math skills such as adding and multiplying.  The DreamBox Quick Images lessons aredesigned to also meet the Practice Standards.
The Practice Standards describe certain habits of mind used in thediscipline of mathematics, and every student needs to develop these Practices in order to be a great mathematical thinker.  Though there are only eight Practice Standards, they apply to all grade levels from Kindergarten (where my son is) on up to high school and beyond.  DreamBox Quick Images lessons are most closely aligned with Practice Standard 7: “Look for and make use of structure.”  My son isn’t struggling with Quick Images because he can’t count; he’s having difficulty because he isn’t looking for mathematical structure in the visuals used in the Quick Images.  And therefore he can’t make use of those structures to determine the number of counters that are shown so briefly on the screen.
Two visuals used in our Quick Images are the Ten Frame and the Math Rack (also known as a rekenrek).  Students using DreamBox have significant learning interactions with both of these virtual manipulatives before encountering the Quick Images lessons.  The Ten Frame and Math Rack have been strategically used for decades to help students use the 5- and 10-structures to develop early understandings of place value, additive structures and multiplicative structures.  And though the 5- and 10-structures themselves are relatively minor structures in the grand scheme of mathematics and the CCSS, they are critical for young children to learn.  Here’s how they are designed.
With a 20-bead Math Rack, there are two rows of 10 beads each.  Each row has 5 red and 5 white beads.  The number 17 could therefore be represented in multiple ways.  One way would be to use all of the beads on the top row (5 red, 5 white), and then 7 beads on the bottom row (5 red, 2 white).  The Ten Frame is similar, but with only two rows of 5 blue counters.  When a student looks for structure in these manipulatives, she finds she can use both the rows and the colors to instantly recognize groups of fives and tens.  Once she realizes the structure, she makes use of it to quickly recognize the values represented.  She stops counting by ones and progresses through the Quick Images lessons with ease, enjoyment, confidence and success.
Unfortunately, I can’t do the work for my son to help him get to enjoyment and success more quickly.  I can’t step in to show him the structures inherent in the manipulatives.  These structures are so obvious to adults; and we think, “I’ll just show him what to look for in the images, and then he’ll be successful.”  Despite these good intentions, parents and teachers who intervene at this point are accepting a short-term gain in exchange for a negative impact on long-term learning and independent thinking in mathematics.  I’ll share more about why in the third and final post on this topic.

Tim Hudson