Part 3: When is not helping my son the right thing to do?
In the first post of this series, I explained how my five-year-old son was having difficulty with DreamBox “Quick Images” lessons. In the second post, I explained how those lessons are designed and then briefly shared why I was choosing not to help him through his difficulties. In this final post, I’ll elaborate more about why I shouldn’t help him despite how much I want to.
As I shared in the second post, the Quick Images lessons aren’t simply teaching mathematical content related to counting; they are also helping students learn Common Core Mathematical Practice Standard 7: “Look for and make use of structure.” Because of these dual learning goals, DreamBox lessons do not explicitly tell students about the structures in these Quick Images. And as parents, we should avoid this explicit telling as well. Because the instant we do, we are actively preventing children from the important mathematical practice of “looking for structure.”
If I directly explained the 5- and 10-structures in these tools to my son, he would definitely be able to use them. And he would likely be grateful for the hint I gave him. Unfortunately, I’d be the only one thinking of it as a small hint. If I step in, my son would think I’m showing him a trick or shortcut. These are very different than “hints” in the mind of the learner. If he thinks there’s a trick involved, then he won’t learn, understand or appreciate the underlying mathematics. It’s risky enough that he will have lost an opportunity to look for structure on his own. But what makes matters worse is that he’ll begin to believe that I am the “fountain” of mathematical knowledge. If this impression takes hold, he’ll always ask for a “drink” from others first and won’t initiate his own mathematical thinking skills when he encounters an unfamiliar problem. This impression becomes a huge problem in the long run.
I taught mathematics to high school students, and there were amazing structures, patterns and relationships for them to find and appreciate in all of the courses I taught. But few students were interested in looking for them; even fewer felt confident enough to look for them. Many students didn’t even think it was their responsibility to look for useful structures in mathematics because their teachers, parents or classmates too often told them what structures were useful and important. Without question, every person who showed students a structure had the best intentions and was genuinely trying to help. And it’s certainly not a foregone conclusion that a little bit of assistance along the way translates into a lifetime of mathematical dependence on others. But if a child is never expected to independently look for mathematical structures from a very young age, it becomes extremely difficult to internalize this habit later in life. We have to plan backwards from the long-term goals of the Common Core Practice Standards.
Thankfully, my son’s habit of looking for structure has already begun. And he’s using DreamBox because most early math programs focus on the skill of counting but fail to use mathematically structured models and representations. For example, if a five-year-old is counting objects that are placed randomly and sporadically on a page or screen, then she has no structures to look for, let alone ones she can use. In this situation, counting by ones is the only option she has. And even though she may be able to successfully count large groups of objects, she can’t actively look for relevant structures that will help her count these larger numbers in groups (which is necessary for developing number sense). DreamBox lessons require students to engage in “looking” while developing an early understanding of place value, additive structures, and multiplicative structures.
I want all students to be curious and creative learners who confidently explore ideas and independently look for relationships. And while I hate to see my 5-year-old struggle with DreamBox Quick Images, I know that stepping in to show him the relevant structures may advance his content knowledge in the short-term; but it will hinder his ability to develop the long-term mathematical thinking habits I want him to have – many of which are outlined in the Common Core Standards of Practice.
Not coincidentally, the Common Core Practice Standards help me live comfortably and patiently with my son’s frustration and my deliberate inaction. CCSS Practice Standard 1 is “Make sense of problems and persevere in solving them.” Since I started this blog series, my son actually came to realize the structures in the Ten Frame on his own, and he’s been using it to complete those Quick Images lessons. He still hasn’t made sense of the Math Rack structures, but all he needs is more time to think independently. While he looks for this and other mathematical structures in DreamBox, my son will persevere, learn from his mistakes, and embrace worthy challenges. When he’s 30 years old, those habits will be just as important as the skill of counting. So they should be just as important now, too.
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