by Lara Francisco
Earlier this week I had a brilliant idea for a blog post that I couldn't wait to share with you! By the time I was finally able to sit down and write it ... I had completely forgotten what it was. I'm the "old".
The "new", are all of those wonderful students that I get to see every day at QAE. They are the reason that we do what we do. And quite often they teach us just as much, if not more, as we teach them. Last night I went through some recently turned in Math Challenges and was reminded of how special the minds of the "new" are. When your mind is uncluttered, there is a freedom to how you express your thoughts or go about solving problems. You aren't bound by previous knowledge or past experiences or "old" expectations. One of my favorite things about being a teacher is seeing the way children respond to questions and show their thinking. Last night I was laughing, smiling, sharing with my boys, and felt happy!
Question: What do you think is "wrong" with this family tree?
(The expected answer is that I would not have been 10 years old in 2001.)
The "new", are all of those wonderful students that I get to see every day at QAE. They are the reason that we do what we do. And quite often they teach us just as much, if not more, as we teach them. Last night I went through some recently turned in Math Challenges and was reminded of how special the minds of the "new" are. When your mind is uncluttered, there is a freedom to how you express your thoughts or go about solving problems. You aren't bound by previous knowledge or past experiences or "old" expectations. One of my favorite things about being a teacher is seeing the way children respond to questions and show their thinking. Last night I was laughing, smiling, sharing with my boys, and felt happy!
Question: What do you think is "wrong" with this family tree?
(The expected answer is that I would not have been 10 years old in 2001.)
Answers:
* The newest generation part isn't centered.
* Although she does look very young. Mrs. Francisco could not have been ten in 2001,
or twenty-four today.
* Why is her name Ms. Francisco instead of Ms. Shorb or Ms. Darnell?
* Ms. Francisco wouldn't be Ms. Francisco at the time.
* You don't have the title Ms. when you are 10 years old.
See what I mean? Their "new" uncluttered minds took them to the structure of the family tree itself, as well as the social norms of adult titles.
Question: How do you know?
Answers:
* I just did.
* Because I counted.
* I knew it in my head.
* I used my eyes.
Plain and simple. Nothing fancy. No explanation needed...
Then there are the declarations of honesty. "My mom helped me." " I had help." "PS my dad helped me and did some of the writing." "I don't know!!" "My dad wrote all of the problems but I answered them."
I love it!
Another thing our "new" little minds are doing, and pay attention here adults, is Algebra, multiplication before 3rd grade, and math diagraming. Starting at Kindergarten ... no lie! It's beautiful! They have no idea that they are doing it, or that this type of math is for "older" kids. That's the beauty of it! By the time the "new" are enrolled in Algebra and upper grade math, they'll be saying - "Man I learned that in 1st grade!" Seeing the complexity of how the kids solve my Math Challenge problems is both amazing and inspiring - at all grade levels. I look at what they've written and I can see how that same process, formula, drawing will be used many years down the road as they get older. Here are a few examples:
* The newest generation part isn't centered.
* Although she does look very young. Mrs. Francisco could not have been ten in 2001,
or twenty-four today.
* Why is her name Ms. Francisco instead of Ms. Shorb or Ms. Darnell?
* Ms. Francisco wouldn't be Ms. Francisco at the time.
* You don't have the title Ms. when you are 10 years old.
See what I mean? Their "new" uncluttered minds took them to the structure of the family tree itself, as well as the social norms of adult titles.
Question: How do you know?
Answers:
* I just did.
* Because I counted.
* I knew it in my head.
* I used my eyes.
Plain and simple. Nothing fancy. No explanation needed...
Then there are the declarations of honesty. "My mom helped me." " I had help." "PS my dad helped me and did some of the writing." "I don't know!!" "My dad wrote all of the problems but I answered them."
I love it!
Another thing our "new" little minds are doing, and pay attention here adults, is Algebra, multiplication before 3rd grade, and math diagraming. Starting at Kindergarten ... no lie! It's beautiful! They have no idea that they are doing it, or that this type of math is for "older" kids. That's the beauty of it! By the time the "new" are enrolled in Algebra and upper grade math, they'll be saying - "Man I learned that in 1st grade!" Seeing the complexity of how the kids solve my Math Challenge problems is both amazing and inspiring - at all grade levels. I look at what they've written and I can see how that same process, formula, drawing will be used many years down the road as they get older. Here are a few examples:
And check out this student's answers! Sometimes "new" minds put more energy and information into their answers than "old" minds. I can't remember when I was that thorough! (My husband is nodding his head right now...)
This past week I started working with my small math groups. There are actually quite a few students that I don't know very well, so I thought we would do a "get to know you activity". I called it My Life in Numbers. To give the kids an idea of how you can represent your life in numbers, I made one for me:
While my "old" numbers consisted of how many kids I have, how many years I've been married, or perhaps the year I was born ... The "new" numbers were how many pets I used to have but are now dead, how many teeth I've lost so far, and my personal favorite ... assigning a number to a favorite color ... No one was sure what year they were born, so that was out!
I started this post last Thursday. Today is Sunday. As frustrating as it is to me that it has taken me so long to finish this, I am glad because I have one more lovely example of how the "new" look at, and think about, math. I found it on Twitter this morning (a link to the original tweet is embedded in the picture). The student who wrote the answers clearly understood the concept, he or she just didn't understand the convention. This is something that weighs heavily on my mind in regards to the current state of education in this country. If a student does not conform to the expected conventions (the old) but understands the concept (the new) is that OK? Is there room in this system for them to be successful and to feel good about their learning? And if there isn't room for this kind of thinking or learner, what then?
Thank you for reading this far - I appreciate you sticking with me! I also hope that no one took offense to my use of the word "old". I could have used a more creative, age positive, term ... but personally I'm OK with "old". My goal wasn't to remind you of age ... but to inspire you to embrace your children's "new", uncluttered, honest, and free thinking. And to encourage it as often as possible!