In nearly all of my parent meetings, I hear about Common Core. My response attempts to educate parents between the difference between the standards themselves and the curricula various publishing companies create that align to those standards. The methods of each curriculum may vary. Today, I will not be speaking about the standards themselves – that debate is only solved if you have the solution to poverty. Instead, I am going to address some methods the new curricula are teaching.
One of the standards for 2nd grade simply states, “Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers.” I assume no one has any qualms with this. Other 2nd grade math standards simply state that the students should be able to use place value while adding/subtracting as well. So, if Sally knows that 2 + 3 = 5, she should be able to extrapolate that 20 + 3 = 23, 20 + 30 = 50, and so on. However, it is the funky problems like the above image that leave parents frustrated. We have seen these examples floating around the Internet. Don’t blame the standard. Blame the curriculum.
New curricula are aimed more at the discovery process. This shift stems from studies in developmental psychology where children interact with novel toys (e.g., Bonawitz, Shafto, Gweon, Goodman, Spelke, & Schultz, 2011). Those children who were not directly taught how to play with the toy used the toy in more creative ways than those children who were given a rule. However, math is not a toy – there is a clear end result. For example, 32-12 will always equal 20. The process by which individuals reach that answer may be different; however, the answer is always 20. This is unlike the toy study where the end result (i.e., function of the toy) could vary. These curricula, focused on creativity and discovery, encourage students to find different ways to seek out the answer. The above example is just one method. Others may use the traditional algorithm 99% of us learned how to use. Others, may subtract 10 two times to reach 12.
The problem with this format is that many kids lack number sense. They lack the mathematical equivalent to phonics where they can pictures smaller numbers making up larger numbers and the relationship between them all. Further, these kids will create unique but erroneous rules to reach the answer. I had one student work on a problem like 31-9. She said she found the answer (which is 22), by subtracting the 1 from the 3 and then writing it twice. Yup – that method will give you 22. However, that rule does not extend to 32-9 and other problems.
I have also witnessed teachers and trainers say that student no longer need to quickly know their math facts since everyone is walking around with smart phones with calculators on their hips. Do I need to even address why this is a silly statement? I can’t tell you how many middle and high school students I have worked with who either don’t understand how to solve a simple equation or consistently solve it incorrectly because of the lack of simple math fact fluency.
A recently published neurological study shows that math fluency creates new connections to the hippocampus, the memory region of the brain (Qin, Chao, Chen, Rosenberg-Lee, Geary, & Menon, 2014). Therefore, as students gain math fact proficiency, new pathways are created allowing for ease in retrieval. The authors of the study state that “If your brain doesn't have to work as hard on simple maths, it has more working memory free to process the teacher's brand-new lesson on more complex math,” which is a observation my colleagues and I have been stating for years.
Therefore, if we truly focus on building math fact fluency, it can make permanent changes to how students think. Further, it will allow them, given their established foundation, to see how they can extrapolate these numbers and use other methods (like image above) to reach the same conclusion. Start with the rule; then, focus on deriving more creative methods using place value and number sense.
To help do this at home, Rocket Math came out with a free app a few months ago to build math fact fluency. It is pretty good. For the younger kiddos, Endless Numbers incorporate not only number recognition but also counting, skip counting, place value, and addition to start a foundation for number sense. These are just two examples in a sea of education apps. For those students who struggle with number sense and math facts using apps, call us. We would love to help!