Informal mental strategies are the strategies we are familiar with using AVMR. Students develop an understanding of place value because they understand numbers and not just a procedure of what number is in what place. They can count by 10 from any number; they can count in steps of 2, 5 or 10. They use the empty number line to show their addition or subtraction strategy. Their strategies gradually become more efficient. Whereas formal place value instruction splits numbers into ones, tens, hundreds, etc. This instruction often causes students to work with numbers that have no real meaning to them. Because again, they are learning procedures (algorithms too early).
The fact that Common Core is structured to teach mental strategies before algorithms should show its importance. Offering support, teaching ideas (AVMR) and materials for teaching mental strategies to support the Common Core requirements of the teachers, might encourage them to try teaching their students to develop a true understanding of number and not just a procedural understanding of number. Frankly, there are some teachers who do not add or subtract mentally using jump or skip strategies. Helping them understand them could lead to some epiphanies and excitement on their part.
***What I learned...On page 6 paragraph 2 it said to introduce the ENL using first the bead string and then a number line with only decadal numbers (the "back" of the number line). I have not thought about doing that! I would love some discussion as to how to go about doing that (as the green book does not have this in its sequence of lessons).
Nick, I agree with your comment about helping teachers understand strategies could lead to epiphanies and excitement! I felt like I had that when I started seeing strategies for the first time, and teachers who are excited, have students who are excited about learning.
The difference between informal mental strategies and formal place value procedures is that dealing with numbers in a wholistic way makes number operations more meaningful than the algorithm. When students are taught to carry the one, they don't completely understand that it is a ten or a hundred. When they are jumping 10 or splitting 50 into 48 and 2, they are developing their own understanding that makes sense to them; not just an algorithm.
I would challenge a teacher to try to teach without paper. Start small and only use numbers under 30 to begin. Then as students progress you can use numbers to 100. Offer the suggestion of the empty number line. Let students come up with their own way to solve a problem.
I really liked the phrase, "dealing with numbers in a wholistic way makes number operations more meaningful than algorithm", p. 3. Before becoming a math teacher, I taught the algorithm because that is the way I was taught. I now see the benefits of allowing students to create math their own way, so they have a deeper understanding, and also ownership of their learning.
Yes! Students need to develop number sense, something teaching only algorithms does not develop. What a simple, but effective challenge for teachers to try to teach without paper. Writing student's responses on the whiteboard for them using the ENL would be a way to track and show their thinking.
Informal mental strategies are the strategies we are familiar with using AVMR. Students develop an understanding of place value because they understand numbers and not just a procedure of what number is in what place. They can count by 10 from any number; they can count in steps of 2, 5 or 10. They use the empty number line to show their addition or subtraction strategy. Their strategies gradually become more efficient. Whereas formal place value instruction splits numbers into ones, tens, hundreds, etc. This instruction often causes students to work with numbers that have no real meaning to them. Because again, they are learning procedures (algorithms too early).
ReplyDeleteThe fact that Common Core is structured to teach mental strategies before algorithms should show its importance. Offering support, teaching ideas (AVMR) and materials for teaching mental strategies to support the Common Core requirements of the teachers, might encourage them to try teaching their students to develop a true understanding of number and not just a procedural understanding of number. Frankly, there are some teachers who do not add or subtract mentally using jump or skip strategies. Helping them understand them could lead to some epiphanies and excitement on their part.
***What I learned...On page 6 paragraph 2 it said to introduce the ENL using first the bead string and then a number line with only decadal numbers (the "back" of the number line). I have not thought about doing that! I would love some discussion as to how to go about doing that (as the green book does not have this in its sequence of lessons).
Nick, I agree with your comment about helping teachers understand strategies could lead to epiphanies and excitement! I felt like I had that when I started seeing strategies for the first time, and teachers who are excited, have students who are excited about learning.
DeleteThe difference between informal mental strategies and formal place value procedures is that dealing with numbers in a wholistic way makes number operations more meaningful than the algorithm. When students are taught to carry the one, they don't completely understand that it is a ten or a hundred. When they are jumping 10 or splitting 50 into 48 and 2, they are developing their own understanding that makes sense to them; not just an algorithm.
ReplyDeleteI would challenge a teacher to try to teach without paper. Start small and only use numbers under 30 to begin. Then as students progress you can use numbers to 100. Offer the suggestion of the empty number line. Let students come up with their own way to solve a problem.
I really liked the phrase, "dealing with numbers in a wholistic way makes number operations more meaningful than algorithm", p. 3. Before becoming a math teacher, I taught the algorithm because that is the way I was taught. I now see the benefits of allowing students to create math their own way, so they have a deeper understanding, and also ownership of their learning.
Yes! Students need to develop number sense, something teaching only algorithms does not develop. What a simple, but effective challenge for teachers to try to teach without paper. Writing student's responses on the whiteboard for them using the ENL would be a way to track and show their thinking.
Delete