Once again I am delighted to say that math camp was a success! We had a productive day exploring learning and the brain, mental math, strategies for all 4 operations (addition, subtraction, multiplication, an division), and equality.
We discussed that both cortisol and adrenalin, when present in the blood stream, tend to “shut down” thinking and memory in the brain. Adrenalin induces the “fight or flight” reaction, while cortisol induces a state of stress when other things are more important than learning. If we want students to learn well in our classrooms, we must take the time to build a safe learning community and do all we can to reduce students’ stress.
The mental math we talked about was similar to what was presented in the Grade 6-8 math camp, so I will direct the readers there for some notes about that topic.
As for the basic operations, it is critical that students do these in ways that are meaningful for them. We shared many strategies for addition and subtraction, some based on numbers only and some based on tools (e.g., 100 dot arrays, blank number lines, base to blocks, etc.). One of the most important things that students should know about the operations of multiplication and division is that they are always, always, always about groups. In representing multiplication, the area model is very effective and can help students understand multiplication beyond basic facts. (Base 10 grid paper is useful for this).
Equality is an important for students to develop in the elementary years. Studies show that when students see the equal sign in an equation, they do not think of equality. Rather, they think it means, ‘put the answer here’ or ‘now do what the sign says to do’. I have had students tell me, when I wrote an equation such as 8 = 2 + 6 on the board, that I wrote it “backwards”. Students expect the single number to be on the left because that is how they always see it! Not only should they see equations written “backwards”, but they should explore equalities with “multiple parts” on both sides, such as 5 + 3 = 2 + 6. Here is a “balance scale” which can be useful in exploring equalities.
I wish you all a wonderful school year!
Mathematically yours,
Carollee
PS: I just remembered that I told all of you at the workshop to write on your 100-dot arrays because there would be clean copies available! So here are the links to the 100-dot arrays: large, 4 small, 6 small, 12 small.
Once again I am delighted to say that math camp was a success! We had a productive day exploring learning and the brain, mental math, strategies for all 4 operations (addition, subtraction, multiplication, an division), and equality.
We discussed that both cortisol and adrenalin, when present in the blood stream, tend to “shut down” thinking and memory in the brain. Adrenalin induces the “fight or flight” reaction, while cortisol induces a state of stress when other things are more important than learning. If we want students to learn well in our classrooms, we must take the time to build a safe learning community and do all we can to reduce students’ stress.
The mental math we talked about was similar to what was presented in the Grade 6-8 math camp, so I will direct the readers there for some notes about that topic.
As for the basic operations, it is critical that students do these in ways that are meaningful for them. We shared many strategies for addition and subtraction, some based on numbers only and some based on tools (e.g., 100 dot arrays, blank number lines, base to blocks, etc.). One of the most important things that students should know about the operations of multiplication and division is that they are always, always, always about groups. In representing multiplication, the area model is very effective and can help students understand multiplication beyond basic facts. (Base 10 grid paper is useful for this).
Equality is an important for students to develop in the elementary years. Studies show that when students see the equal sign in an equation, they do not think of equality. Rather, they think it means, ‘put the answer here’ or ‘now do what the sign says to do’. I have had students tell me, when I wrote an equation such as 8 = 2 + 6 on the board, that I wrote it “backwards”. Students expect the single number to be on the left because that is how they always see it! Not only should they see equations written “backwards”, but they should explore equalities with “multiple parts” on both sides, such as 5 + 3 = 2 + 6. Here is a “balance scale” which can be useful in exploring equalities.
I wish you all a wonderful school year!
Mathematically yours,
Carollee
PS: I just remembered that I told all of you at the workshop to write on your 100-dot arrays because there would be clean copies available! So here are the links to the 100-dot arrays: large, 4 small, 6 small, 12 small. 
Thanks again, Carollee, for a great day. It is good to be reminded of the importance of building a safe environment for our students. As always, you provided some great teaching ideas that we can employ in our classrooms.