I'm back with some thoughts about Building Mathematical Comprehension chapters 3 (Making Mathematical Connections) and 4(Increasing Comprehension by Asking Questions). I'm going to just do this wrap-up really quick for each chapter.
3 Types of Mathematical Connections:
- Math-to-Self- connections between own life experiences and mathematics
- Math-to-Math- connections between past and present studies of math
- Math-to-World- connections between math and our world
2 Math Stretches to Encourage Making Connections:
- How Did My Family Use Math Last Night?-making connections is explicitly taught and immediately applied by students.
- _________ Makes Me Think of...- students practice making relevant math-to-self, math-to-math, and math-to-world connections.
One Major Take-Away/Point Summing It All Up:
This quote from the beginning of the chapter really sums up the importance of this strategy in mathematics:
"People are wired to search for ways to connect the new with the familiar...In the same way, learning is intimately linked to the connections we make between our prior knowledge and our new experiences. Prior knowledge or experiences help learners interpret and construct meaning from newly introduced ideas or concepts" (p. 85)
3 Ways to Classify Questions:
- Right There: These are literal, easy-to-answer questions, that can usually be answered from one line of text.
- Think and Search: These are found within the text, but with a bit more work than the right there questions. Requires thinking, searching, and more than one line of text to answer.
- On My Own: These questions are not easily answered from the text and instead require the reader/mathematician to make an inference.
2 Things to Incorporate into Math Journals:
I currently use my math journals for daily problem solving or whole-group problem practice outside of our math workbooks. Here are 2 things that I want to incorporate in my journals this year (along with vocabulary work, as described in chapter 2):
1) Question Journals- these provide a way for students to keep track of their questions. Rather than devoting an entire journal to them, I want to incorporate them into one math journal. Question Journals include this information:
Before, During, or After?
(did the question arise before, during, or after the math task)
Record possible answers/make predictions
2) Question Webs- For those of you that use Thinking Maps, this is essentially a detailed bubble map, with the question recorded in a center circle (ex. in the book, they ask Why do we have standard units of measure?, p. 137). Branching out from the circle are various potential answers to the question. Finally, the student's definitive answer to the question is recorded at the bottom of the page.
1 Major Take-Away/Point Summing it All Up:
Per Sammons (p. 119), "As students read about mathematical concepts or problems, the generation of authentic questions about the subject matter leads to deeper understanding and retention."
As I'm getting into this book, I'm really beginning to see how a few small adjustments can help me marshal my reading comprehension toolbox of strategies to maximize math achievement and transform math instruction in my classroom this year. I can't wait to get started!
I'll be back soon with more about GoNoodle and Building Mathematical Comprehension.
Until next time!