As a fifth grade teacher whose primary mission this year is to teach math well, I decided to join Keith Devlin's Stanford University MOOC, Mathematical Thinking. The quote on the top of the page is a big take-away from the first week of the course--we're not born knowing math, math is an acquired disposition and ability, one that everyone is capable of learning, and that learning takes time and attention.
This leads to the second reason why I'm taking the course which is that I find that when I take a challenging course of study during the learning/teaching year, I am more attuned to my learners--I remember what it's like to be a learner.
I just finished week one's assignments and I made a LOT of mistakes, mistakes that will better prepare me for week two. I also learned a lot which will impact my math teaching. Overall, I recognize that if we're going to teach the Standards of Mathematical Practice well, we have to be mathematical thinkers. I've listed my mistakes and learning below. And in the meantime, if there's any 4th or 5th grade math teachers that want to join me in taking this course I welcome your collaboration. We can cross-check our assignments online via Skype or Google.
First, the mistakes:
- Typical for me, I rushed, and therefore, completed and submitted the assignment before watching the second video which was a direct match to the assignment. Thus I anticipate a poor score for the first assessment.
- Next, I didn't prepare well for the time the course takes. I kept putting it off until today when I have little time left. I know I procrastinated because I felt a bit nervous about the skill level of the course, and I worried that I couldn't do it. But now, after finishing week one, I realize that if I give the course about 30-60 minutes a day for four days, I'll probably manage the learning well.
- Lastly, I haven't found a peer group yet, and that's mainly to do with my very busy schedule. I hope to do this, but it may be a requirement I won't meet at this time.
Now, the application to grade 5 learning.
- Much of this week's course work dealt with the use of precise mathematical language. This is a great emphasis for grade 5 teaching, and I'll continue to look for ways to introduce, practice, and apply precise language as we learn and study each math standard.
- Another focus was identifying true and false mathematical statements. By asking children to choose which statements are true and which are false, you're prompting them to think deeply about the material as they evaluate and compare expressions, equations, inequalities, and problems.
- Devlin focused on the importance of the words "and," "or," and "not." Words that can be used as we discuss, evaluate, interpret, and compare mathematical statements.
- Devlin provided important sentence frames which I altered a bit for the younger children:
- A property of ____ is ________.
- Ex: A property of prime #s is that those numbers are odd except 2.
- A property of every _______ that _______ is ___________.
- Ex: A property of every even number that ends in 0 (except 0) is that those numbers are multiples of 2,5,10.
- A property of __________ in this set is__________.
- A property of all even numbers that end in 5 is that those numbers are multiples of 5.
- If ____________, then ________________.
- Ex: If a number ends in 0,2,4,6,8, then the number is even.
- Before we can determine if a statement is true or false, we have to understand what the statement is saying. Mathematical language is precise and does not rely on context in the same ways our typical language does. Mathematical language relies on literal meaning.
- Learning to think in new ways is hard work. We tend to rely on what we know and what we're used to, and to develop mathematical thinking we have to consciously work towards new ways to think.
- Frequent check-in mini-assessments during a learning period fosters optimal learning. If the check-ins are troubling for you, then it's likely you're not giving the work enough reflection, concentration, or time.
- Numbers were first developed with regard to money, topology is the patterns of closeness. Numbers were developed about 10,000 years ago.
- Today's world needs innovative mathematical thinkers who can work well in teams and cross disciplines.
- "Education is the preparation for life, and only part of that is mastery of specific work skills."
- As mathematicians "we identify key features of a problem mathematically, use math description to analyze the problem in a precise fashion."
- Mathematicians discuss the "behavior" of a function--we can use that term to discuss the "behavior" or operations and other standards.
- It's important in the early years to focus on both the "doing of math' which are the procedures and the concepts. In my opinion, this is an area of focus so that we balance the approach in a way that builds engagement, confidence, good habits of mind, skill, knowledge, and concept.
- "Mathematics makes the invisible visible" for example we can't see what holds a plane up, but you can demonstrate that with mathematics. "Physics is the universe seen through the lens of mathematics."
- "The language of the universe is the language of math."
- "Symbols on the page are representations of math like notes on the page represent the music."
- The Commutative Law for Addition: "When two numbers are added, their order is not important."
- Mathematics is "The Science of Patterns"
- Arithmetic/Number Theory: Patterns counting
- Geometry: Patterns of Shapes
- Calculus: Pattern of Motion
- Logic: Pattern of Reasoning
- Probability: Pattern of Chance
- Topology: Patterns of Closeness and Position
- Fractal Geometry: Patterns of Self-Similarity Found in the Natural World.
- Mathematicians have to learn to "trust in math above intuition."
