Instead of, “Is he passing?”
Let’s try, “Is he learning?”
Our conversation will never move on from the pass-fail construct, until our questions move on.
Let’s move on.
We can do better.
#Project180
@melbrethour We can explicitly guide discovery toward the conclusions needed. Discovery need not be reinvention nor glacial-paced reevolution of ideas.
A fun problem from openmiddle: Using the digits 1-9 each exactly once, create three 3-digit numbers where their sum is as close to 1,000 as possible. Here's why it's impossible to get exactly 1,000.
"[Students] believe that the equal sign means the answer comes next. They've been trained that way throughout school." @BuildMathMinds#BuildMathMinds24 Untraining this later is VERY difficult. We have to be aware of what we're incidentally teaching.
Avoid "mathematical run-on sentences" (thanks for this phrase!). If you write 3+4=7+5=12, your work says that 3+4 is the same as 7+5 is the same as 12.
Make sure you write 9=4+5, not only 4+5=9. Also make sure students see things like 7=7 to disentangle the equal sign from reliance on operations or "doing something" for its inherent meaning.
"Relational Thinking is using the structure of math & connections between numbers to solve problems." Algebra IS structure and relationships/connections. @BuildMathMinds#BuildMathMinds24
Yaaas! "Algebra is _soooo_ much easier if you have built relational thinking so that when you look at things you can see relationships and not just always have to compute." Christina Tondevold at #BuildMathMinds24