The author of the book, Christopher Danielson, (on Twitter as @trianglemancsd), does a comprehensive job of summarizing and interpreting the Common Core standards for grades K through 12. As someone who has only taught grades 6 to 8, it was great to see how the standards progressed. I also am now much more able to answer anyone's questions about the standards.
Don't be thrown off by it being for parents, or for dummies for that matter. This book is for teachers, administrators, and of course parents and anyone interested in math education. I actually was obsessed with Macs for Dummies and the author David Pogue as a teenager and love the style of the book and the readability.
I took notes on interesting points from the book and some questions that I have. One topic I liked when he discussed fractions was common numerators. We don't talk about being able to compare fractions with common numerators ever such as what's bigger, 2/3 or 2/4. He also talked about how you can't compare two different units, it's like comparing apples and orange. He also pointed a confusing yet commonly incorrectly solved order of operation problem that is 48 / 2(9+3). I got it wrong the first time too.
An interesting question to ask a 5th or 6th grade class is: why is there no such thing as a LCF or GCM (least common factor or greatest common multiple). This will create a very interesting discussion about vocabulary.
When talking about statistics, a cool way would be comparing heights of 5th and 6th, or 6th and 7th graders at a school. The Common Core does call for mean absolute deviation, though I am still unclear about the applications and what type of context it could be introduced to students in.
I liked the idea of having a discussion of how old your dog is, in dog years and human years, and reason how and why they are different. I honestly can't remember off the top of my head unless I looked at the relationship of two examples.
In 7th and 8th grade classes I have found myself label 2/3 as a decimal, as 0.666... and call 6 the repeating part so you only need a bar over the 6. Well, there is actually a name for that. 6 is the "repetend," the repeating part of a decimal.
One question I had, was in 8th grade he said the standards introduce point slope form. In CPM's Core Connections 3 curriculum there is no mention of this form, only standard form and slope-intercept form. So, I am a bit concerned that I did not cover that last year.
Lastly, I was very pleased in the Pythagorean theorem section he mentioned the distinction between acute and obtuse triangles side lengths. I brainstormed before how to keep students from not remembering which way the inequality sign faced, the two legs squared and added together or the hypotenuse squared. Apparently he thought about this too, because he showed the most common acute triangle you can think of: an equilateral triangle. Which we know has equal sides and is equiangular at 60 degrees each. So, if you have sides of 2. 2 squared plus 2 squared is 8. The last side, 2 squared, is 4. So, clearly, if the hypotenuse squared is smaller than the triangle is an acute triangle. I hope that made sense. It makes sense when you draw a picture.
Oh yes, and the best anecdote of the book was when the author's son got an increase in his bed time on his birthday. So, his son saw a pattern and reasoned he could predict how late is bed time would eventually go. Great example of #tmwyk (talking math with your kids) unprompted.
All in all I enjoyed this book and would recommend it to any math teacher, administrator, or parent at any grade level. It gives you tips on how you can help your student think mathematically and how to help them without doing their homework.
Saturday, August 22, 2015
Wednesday, August 19, 2015
I was already going to write a book recommendation for the one I mention (which will follow shortly after) but I saw this show up on my Facebook feed:
Ok I need to clear this up as a math teacher. The old way is not gone. Kids are encouraged to come up with strategies to add before they are finally taught the old way which we call the standard algorithm.
I couldn't hold back and replied with a long comment because a previous commenter said they had opted their child out of common core testing. Here's what I said:
The example on the right is a terrible example of a common core method and hard to decipher. They are saying decompose 37 into 5+2+10... Without plus signs. Then counting up. Inefficient.
We want kids to know you don't always have to add from right to left. For example 53 plus 37 is the same as 50 + 3 and 30 +7. 7 and 3 makes 10 which represents that little 1 being carried in the standard algorithm. Then add 10 to 50 and 30 and you get 90.
One reason we will not teach the standard algorithm for example for subtraction first is for example doing 100 - 3. It makes no sense to cross out numbers and regroup. Why not break up 100 into 95+5 then minus 3. Now I got 95 + 5 - 3 which is 95 + 2 or 97.
Final point. When kids are taught a procedure they regurgitate it then forget it. If you learn it conceptually, struggle, learn strategies cooperatively with your peers, the odds go way up for retaining the information.
I read a book this summer. Common core math for parents for dummies. It's great and talks k-12. Hope this helps or gives you a different point of view. I obviously support common core."
And the person thereafter replied with:
Everyone should read the book. Teachers, parents, administrators. I already did.
Monday, August 10, 2015
I was one of the lucky 32 teachers from around the nation to enjoy five full days at Seattle Pacific University for the CPM Academy of Best Practices presented by Mark Cote, Karen Wooton and Sharon Rendon. Not only was a stipend provided, but three CEU’s from the college, a year membership to NCTM, flight, board, food, and plenty of lasting ideas, discussions, and relationships.
On day one we considered a ratio problem in NCTM’s Principles of Action, our nightly reading assignment. It was about creating a bigger jar of jawbreakers and jollyranchers with the same ratio. We worked it ourselves and came up with alternative solutions, and looked at how a teacher anticipated all of the possible solutions, wrote down the names of students in groups that had different strategies, and sequenced those students to present their work in order of sophistication and allow students to ask questions. It is important for the teacher to relate the different vocabulary and methods in each strategy and relate them back to the original learning goals you set.
For homework we also read a passage from “Success from the Start” and the “Talking about Math” article (authors of Intentional Talk). I learned that myself and many other teachers use the IRE method of discourse. I is the teacher INITIATING the question, R is a student RESPONDING by raising their hand, and E is the teacher EVALUATING what the student said. This limits students opportunities to learn and tells the teacher little about what the students know and can do.
Some of the alternatives to IRE are turn and talk (think pair share), write your answer first on paper or whiteboard, and/or cold call (randomly pick a student after a turn and talk). We talked about elevating the status of students that don’t usually raise their hand in class by selecting them to share their group's work.
There are four productive talk moves: Revoicing a student’s response for others to hear with possible academic language added, repeating is asking the class if anyone can repeat what a person said, applying one's reasoning to another (do you agree with that person’s explanation?), and finally adding on (prompting students to add on or share additional insights). Get students to practice these moves. Have a student lead the class discussion. Ask the class, “what do others think?”
An example in the text and in my own practice of a teacher move is when a student is stuck on solving a linear equation. You want to offer hints. Unfortunately, you start funneling the student towards the answer, peppering them with questions towards the correct solution. I/we need to stop funneling a student towards the correct answer. This results in little learning. Instead, focus the student so you can ask them what they know and observe so they can use their intuition to learn a strategy from the conversation.
On Day 2 a conversation I had with Traci about subtracting integers from something she called “Integer Soup.” She shared that positive is hot and negative is cold. So, if you add cold (ice), your drink gets colder. If you take away cold (ice), it gets warmer. If you take ice cubes out of a warm drink, it gets warmer. In class we also used the Study Team Strategy “Pairs Check” when working with tiles. Basically, you can build an equation and have student A writing while student B is telling them what to write, coaching the person. When finished, Student B will write the next problem and student A will tell them what to write. Then they will check those two problems with another pair of students. During the session we analyzed the probability game Color-Rama and discussed how it told a story. We can connect with our students if the lesson is sequenced properly and evokes emotions from our students.
For homework we read from NCTM Principles of Action again. I learned that students learn through doing mathematics that have a high cognitive demand and have multiple entry points that are usually non-routine problems. Low-level procedural problems do not help extend a student’s thinking. Some questions I had about the text: Can they provide more evidence of how a high cognitive demand task can be lowered by a teacher, and what actions lower the demand? What can I do to scaffold without lowering the demand?
On day three we spent a lot of time with Baylor PHD student Aaron Brakoniecki talking about cognitive demand and rating tasks on a level between 1 and 4. I learned that not all talks must be rated a 4, and the lower demand tasks can be used to assess the level of a student’s basic knowledge of a skill. I also learned that a delivery of a task must have the qualities of a story evoking emotions like joy and suspense. We also talked about the sequencing of a task can scaffold for students or frustrate them so they want to learn how to do it. We also learned some math brain breaks like points of contact. How many people in the room? How many points of contact How do you get one and a half times that many points of contact? We also played math shoot. It’s similar to rock paper scissors except on the 1, 2, shoot, you put out a number between 0 and 5 and the first person to add the two numbers wins. Then you play a round where you multiply instead of add. Finally, a group of 4 can add to get 11. You can extend it. Another cool brain break that Mark Cote did, besides telling his math jokes at the end of each day, was getting general and unique information from each person in the cohort. He would say, “Sit down if you were not born on the west coast.” He would continue saying this until he got down to the story the person shared that makes them unique and that other people don’t know about them. It’s a great team building activity for a positive culture that can get students to know each other much better.
For homework, we continued reading and learned from an example of two fifth grade teachers teaching a fraction problem. After the students struggle and give up, the first teacher sets up the problem for them resulting in no learning. The second teacher responds instead by asking her class for strategies to start and gets a student's idea to guess and check with $50 and the other suggests to set up a tape diagram marked off in 1/5 increments. She tells them to consider these ideas and continue their work. The first teacher’s students know that if the students say they can’t get it, their teacher will set up the problem for them, doing all the work. The second teacher won’t give the solution, but will facilitate the ideas of students moving the students in the right direction. Once again, an example of funneling opposed to focusing, respectively. We also read about how tracking students in homogenous groups puts low students in low classes with low expectations creating a vicious cycle. Page 68 of the reading offered a structured Math intervention model for high school freshman that can be used for middle school.
On Day 4 we worked with former president of the NCSM Valerie Mills. In the morning we discussed growth versus fixed mindset with videos and situations that we responded to with post-its on the back in the Carousel study team strategy. We need to praise students on their process and effort. Listen for our fixed mindset voice and reply with our growth mindset voice. Add the word, yet. “I can’t do it...yet.” We also watched the Teaching Channel’s “My Favorite No” where student responses are sorted into yes or no piles and the teacher selects their favorite no and asks the students what’s right about it first. Then they discuss what’s wrong and how they can improve their original answer.
An important concept I learned from Val was the difference between equality and equity. She presented a diagram with equality being students with different heights on the same sized box trying to reach their goal, the apples in the tree. Some can’t reach. Equity is all students reaching their goal with different sized boxes and amounts of support. Equality is qualitatively unfair and quantitatively fair. Equity is fair and is coincidentally the name of my equity sticks used to randomly pick a student to share their ideas. We also read the five equity based practices from the article “Impact of Identity in K-8 Mathematics.”
We also discussed descriptive effective feedback. Avoid writing great job. Instead, point out where the student clearly showed their understanding on a method and how they can extend their thinking to another strategy. All of this leads to a bigger idea, that we didn’t fully discuss, which is wanting social justice for all students. To end the week we learned a ton about Desmos from the creator, Eli Luberoff. We got a crash course, used Polygraph: Hexagons, the new Activity Builder, and heard about the new 6th grade activity called Pile of Tiles. The main principle is to be successful at describing hexagons and differentiating them, a need for vocabulary arises. This is what would motivate students to understand the difference between convex and concave. We also stood in a circle for an Elevator Talk and gave a 30 second reflection on what we took away from the week. Every teacher left with an Action Plan with one or two goals of how and when we will implement what we learned from this week at math camp.
Elevator talk panoramaUpdate: CPM posted the video overview, I've linked it below:
CPM Educational Program held their first new teacher institute, the Academy of Best Practices. The ABP is... http://t.co/vyETPf1v1l— CPM Director (@CPMmath) September 25, 2015