Tonight we had a discussion of “5 Practices for Orchestrating Productive Mathematics Discussions” (B&N, Amazon) on Twitter, and I wanted to post the Storify here. One caveat, one of the members, MrHodotNet is protected so he didn’t show up in the timeline. I copied and pasted his contributions at the end, but they are not in order.
The link to the Storify.com transcript is here.
The transcript can be read after the break.
The AP exam is over, finals are in two weeks, and my learners have been busy bees constructing knowledge for the community.
That is their goal in this post-AP Exam stage of the class. Their charge and challenge is to do something that constructs, creates, or consolidates knowledge for the school or the community. Below are the projects that have come out of this as examples, in no particular order.
Group 1: This group took last year’s project of finding out which is the cheaper grocery store (Smith’s, Walmart, Raleys and Scolari’s – they found out Smith’s & Walmart were the same) and are extending it. This year they are seeing if last years results are still true, AND then extending the matched pair to a two sample to compare last year’s prices to this year’s prices. The manager of Smith’s is very interested in the outcome of this.
Group 2: Does Walmart change their prices based on the income level of the zip code the store is located in? So far the results show no, but that hasn’t been finalized yet.
Group 3: Are high school students prepared for disasters. This group wanted to do something related to the zombie apocalypse. I used my veto power. Now they are back down to earth doing a multistage cluster & stratified sample of the school.
Group 4: What percent of our seniors go out of state for college and how does this compare to previous years? The trouble is, our counselors have never kept track of this! There is no data base or spreadsheet for previous years. So, this group had to collect the information (census) from all the seniors, build a spreadsheet to house the information and then compare vs. the numbers we were able to get from our local university. When they are done they are giving the results and database to the counselors to maintain.
Group 5: This group of 1 person originally proposed a nationwide survey. I talked them out of it. Then they proposed a city wide survey. Again, talked them out of it. There wasn’t enough time to accomplish such aggressive projects. In the end, the person narrowed the idea down to “what impacts graduation rates the most, income or poverty in Washoe County School District?” This is achievable. The group is collecting information from census bureau data and grad rate data and then doing a regression test on the data. There are some interesting results so far.
Group 6: Are freshmen aware of or comfortable with basic science based on their middle school and freshmen biology class? They took questions from the science standards and talked to science teachers to create a short quiz based on the standards. They did a random sample of freshmen classes and then sampled randomly 5 from those classes using a deck of cards. The sample is VERY small, but the process is good.
Group 7: Do gasoline prices fluctuate together in an area at the gas pump AND do the prices move with the price of light sweet crude on the international market? Whew, big project dealing with daily checking at 7 gas stations and market prices. They have a very interesting topic, and the mechanics of it will require a regression test.
Group 8: Another one person group, but this time the learner is interested if course “difficulty” can be quantified. The learner was upset at being told that certain classes are harder than others and therefore should not be taken because it would hurt the GPA. When the learner asked “how do you know?” to the counselor the learner was not given a straight answer. To help, I received a complete grade distribution of every class in the school, removed the teacher names and replaced with a random word that starts with either “d” or “g” (for no reason, just to make it difficult) and this is what the learner is using. So far, so good. Although I am not sure the question can be achieved, it is worth doing.
Group 9: This group is interested in whether the plans of the senior class changed from when they were freshmen. A cluster sample is being done on the government classes to get senior viewpoints.
and finally,
Group 10: A multistage sample to see if being involved in sports helps or hurts GPA. They are all athletes and they all have different opinions on what the outcome will be.
I am excited to see the results of many of these, and I will be sharing the results with store managers in the area, the local newspaper in several cases, as well as next year’s group of AP learners.
Any suggestions or questions for them (or me)?
Intensive Math Instruction & Double dose of Algebra 1
Success or failure in freshman math has long been thought to have a strong impact on subsequent high school outcomes. We study an intensive math instruction policy in which students scoring below average on an 8th grade exam were assigned in 9th grade to an algebra course that doubled instructional time, altered peer composition and emphasized problem solving skills. Using a regression discontinuity design, we show positive and substantial longrun impacts of double-dose algebra on standardized test scores, high school graduation rates and college enrollment rates. The attainment effects were larger than the test score effects would predict, highlighting the importance of evaluating educational interventions on longerrun outcomes. Perhaps because the intervention focused on verbal exposition of mathematical concepts, the intervention’s impact was generated largely by students with below average reading skills, highlighting the importance of targeting interventions towards appropriately skilled students. This is the first evidence we know of demonstrating the long-run impacts of such intensive math instruction.
Top 3 R resources for beginners
I am not sure “R” is appropriate for AP Stats or not. I need to do some learning about it before I can make that decision. Free is always attractive, but if it is too high a level then it does not help to learn stats.
Advanced Data Analysis from an Elementary Point of View
This is a draft of a new textbook being published in 2013-14. The topics are very interesting and push my knowledge of stats to a higher level.
The one problem with having a summer list is that I always want to add to it. I try not to, but things come up that I cannot say no to.
This is one of those things. It is a course taught by Stanford University professor Jo Boaler. If you don’t know about her, she has gone to bat for math teachers and taken some professional licks for it, and she is the author of the fantastic book “What’s math go to do with it.” (Amazon, B&N). I can not say how much I liked this book, and then to have the opportunity to take a class from her for free; well, that is too good to pass up.
The class is: EDUC115N: How to Learn Math.
Many of my Twitter PLC has already signed up for it, and I just sent the link out to my department and hopefully many of them will sign up too.
I hope many people will sign up for it so we can have some great conversations in the class.
Here are the topics the course will cover, which makes it even more inviting and exciting! See you there!
CONCEPTS
1. Knocking down the myths about math.
Math is not about speed, memorization or learning lots of rules. There is no such thing as “math people” and non-math people. Girls are equally capable of the highest achievement. This session will include interviews with students.2. Math and Mindset.
Participants will be encouraged to develop a growth mindset, they will see evidence of how mindset changes students’ learning trajectories, and learn how it can be developed.3. Teaching Math for a Growth Mindset.
This session will give strategies to teachers and parents for helping students develop a growth mindset and will include an interview with Carol Dweck.4. Mistakes, Challenges & Persistence.
What is math persistence? Why are mistakes so important? How is math linked to creativity? This session will focus on the importance of mistakes, struggles and persistence.5. Conceptual Learning. Part I. Number Sense.
Math is a conceptual subject– we will see evidence of the importance of conceptual thinking and participants will be given number problems that can be solved in many ways and represented visually.6. Conceptual Learning. Part II. Connections, Representations, Questions.
In this session we will look at and solve math problems at many different grade levels and see the difference in approaching them procedurally and conceptually. Interviews with successful users of math in different, interesting jobs (film maker, inventor of self-driving cars etc) will show the importance of conceptual math.7. Appreciating Algebra.
Participants will be asked to engage in problems illustrating the beautiful simplicity of a subject with which they may have had terrible experiences.8. Going From This Course to a New Mathematical Future.
This session will review where you are, what you can do and the strategies you can use to be really successful.
Look! Something Shiny! How Some Textbook Visuals can Hurt Learning
A summary of a research article about how bad graphs make learning harder. Makes total sense to this AP teacher, actually.
Mathics – A free, light-weight alternative to Mathematica
A free, opensource version of mathematica. Very interesting but requires a learning curve to get the format and commands correct.
25 Personal Finance Resources Every College Grad Should Read
Great article listing some free and some paid resources on personal finance. This info will fit well into the personal finance section of my Advanced Alg course.
I am trying to put some order to my to-do list this summer, as well as create some structure for all the work. I want to avoid creating a broken, fragmented summer where I accomplish nothing but spend a lot of time spinning my wheels.
First off: Trainings, conferences and travel I am planning.
1. A training given by my district on CCSS changes to Algebra 2, 10-12 June. Kind of important since I signed up to teach the new CCSS Algebra II STEM changes at our August Mandatory PD session. It will be a great three days in June, and a great way to start the summer.
2. The Silver State AP Institute in Las Vegas 24 to 27 June: Really looking forward to this institute given by Josh Tabor to the experience AP Stat teachers. It says he is going to work with Fathom a lot, which is good, I have no experience with Fathom. I am interested in seeing what the new additions to GeoGebra can do as far as stats teaching, so I will work with both programs and see what I can do to crossover.
3. A fun trip to Chicago for some family time around the 4th of July, and then a week later a motorcycle trip to Portland and Montana. That will be a blast! It is always good to see mom, sister & family in Portland as well as family in Montana.
4. TwitterMathCamp 2013 from 25 to 28 July! Yay. Last year it was amazing and hands down the best PD I have ever done for myself. I am very happy to be going again. Looking forward to developing relationships with more teachers and building stronger relationships with the ones from last year!
5. In addition to all that, I signed up for a MOOC on Coursera on the Philosophy of Mathematics starting in July and going through August.
Whew, that is a lot of traveling, and it will definitely keep me hopping. But in addition to traveling and learning, I want to really dive deep into a some books and synthesize some ideas.
My reading list, in no particular order is:
The Art of Problem Posing by Stephen Brown and Marion Walter
Common Core Mathematics in a PLC at Work: high school by Gwendolyn Zimmerman et al.
I have some other sitting on my bookshelf that I want to revisit, but those are the 4 that I absolutely want to get through this summer.
The thread I am working on is connecting classroom practice to better questioning, learning how to ask and guide better questions, and then teach other teachers in my department how to ask better questions.
This is a big chunk, but I think it is important to developing a better math program and math classroom.
I will post here on the books and conferences.
“We’re Number Umpteenth!”: The myth of lagging U.S. schools
An article by Alfie Kohn with research and links to reports that show the US system is not meeting the expectations of a “failed system”. Actually the reverse is true for the most part.
MeTA musings: SBG is more than teach, test, reassess [A fable]
A really, really good tear down of what assessment means in the SBG world. I especially like the flowchart and discussion of actual classrooms it is being implemented in.
I have had this long term struggle going on in my head this year that we really don’t do a good job making connections between material in our classes, and that lack of connection is one reason why “transfer” (ala. Grant Wiggins and Understanding by Design) doesn’t occur as frequently as I would like.
Well, I am not going to talk about it any more. I have the beginnings of a plan to enact. There will be many steps to this plan, but I think the starting point needs to be simple to enact and creates some opportunity for connections to be made.
Every test in my department from Algebra 1 through Trig/Precalc must have a couple of different kinds of problems on it. This is step 1 I am implementing next year.
The first type is a literal equation. Of course, as a stats teacher my first thought was M=z*root(pq/n). Perhaps at the algebra 1 level we won’t start there, but we can select most of the formulas needed in geometry and use them as literal equations and every quiz and test solve for a different variable of one of the formulas. And, here is the kicker, EVERY time, the learner must explain why they are doing the operation. Justification is mandatory. If we look at the Margin of Error formula above, there are 4 different questions to be asked. That is 4 quizzes or tests that one question can be used.
The goal is get learners to think of literal equations a part of algebra and the justifications as the same thing as every other problem. By the time they reach AP stats, they will have seen this equation repeatedly and know how to manipulate it as a literal, not just with numbers in it. We need to connect AP Stats to Algebra 1.
Next, every test at algebra 1 level must have some form of the following question:
Evaluate (x – (x+h))/x with x = 2 and h = 3. Yes, I know it reduces to h/x, but as we move forward with notation, it becomes:
Evaluate [f(x) - f(x+h)]/f(x) with f(x) = 2x+5, x = 2 and h = 3. As the years progress the function can be moved from linear to quadratics to absolute value to cubics or rationals.
Finally, truly stress and monitor that verbage “rate of change of” every time the word “slope” is used. The learners need to hear and write over and over the “rate of change of” the line in algebra 1, geometry, and algebra 2.
The goal is to create a common language / strands through all math courses and chapters that lead to AP calculus and AP statistics. All learners need to be exposed to the language of statistics and calculus repeatedly throughout their education so it is not different at the upper levels.
So those are the three things I can and will implement next year, without fail.
What am I missing?
Any other language to implement? Any other formulas / concepts that can be used at the lower levels of math that lead directly to the upper levels?
Assessments: The Collateral Damage of SBG | Mathy McMatherson
Absolutely terrific post on SBG and the impact SBG has on assessments and gradebooks. This post should be mandatory reading for anyone thinking about SBG.
Mathy Ladies to Follow on Twitter | Roots of Unity, Scientific American Blog Network
Some great math teachers and mathematicians here.
Cheating to Learn: How a UCLA professor gamed a game theory midterm | Which Way L.A.?
How can I use this in class? I see some good possibilities here.
Drawing On Math: Global Math: Understanding by Design
An UbD project presented at the Global Math Department. There is a lot here in a surprisingly small amount of words. The ideas branch out into huge areas, however.
for the love of learning: A short history of grading
Another article on the history of grading, including a person I have never heard of, “William Farish” who is credited with creating the grading scale to increase his pay as a tutor.
A brief history of grades | Quantum Progress
Conversation at school has created some thoughts about the arbitrariness of grading scales. Some additional information to make you go hmmm, including a great infographic.
Waffle Bytes: Performing a Mail Merge with Google Spreadsheets & Gmail
Using google mail and drive to do a mail merge? Impossible you say. Not so and this little tip is priceless for sending emails after using, say, drive forms to collect information.
Math ‘Publishers’ Criteria’ Aim to Guide Common-Core Materials – Curriculum Matters – Education Week
Did you know there are revisions to the CCSS already? I didn’t until I read this. This article demands further reading, especially the links embedded.
Leinwand gave a fantastic presentation at the NCTM13 conference. The slide deck is out there, and this is a recording of the presentation. Great listening and reading. Highly Recommended.
One teachers curriculum materials for Geometry and Alg 2 used in standards based grading situation. A HUGE amount of materials shared here.
25 Cool Android Sensor Apps that give your phone some unusual super powers [Freeware] |
First off, there is some seriously cool software here. The real question is how to leverage some of these for classroom use? Not sure yet, but I am working on it.
ACT National Curriculum Survey | ACT
Some interesting results, such as 60%+ HS teachers think their learners are college ready, but college profs disagree.
4 presentations from the NCTM Denver Annual Meeting. The presentation by Philip Treisman is especially good and is on equity in the classroom.
A teachers dropbox folder where they have stored and SHARED projects from elementary through high school. Lots of good items here to look and think about.
Assessing approximate distribution of data based on histogram – Cross Validated
This is a great example of kind of a “reverse Anscome” effect where the exact same data gives you radically different results as histograms. Very odd, and shows you have to do due diligence when working with your data.