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An email I just sent to my dept

22 October, 2014 (08:38) | Personal, Technology | By: Glenn

I just sent this email to my department today. The subject was “If you still assign drill and kill problems”.

I am posting the text of the email without comment. It was spurred by a conversation on Twitter with @DDmeyer and @JStevens009.

Text is below:

Good morning all,

Hate to be the bearer of unwelcome news this morning, but if you are not keeping up with the world of math technology, it is reaching a tipping point of changing what we do. Check out the site: https://photomath.net/ and think about what it means to our profession and our classrooms.

Only around 30% of all kids have iOS devices, but in 2015 when it hits Android and the entire market is open, nearly 100% of our learners will have access to this. For free.

Kuta worksheets? Textbook problems? This type of software will render this type of homework obsolete. Desmos and TI-calculators have nearly done so already.

We have talked about the purpose and need to rethink what homework is for, and the tipping point is rapidly approaching where we really need to make some changes to what and how we handle it.

We need to think deeply about how we can create an environment of learning both in and outside the classroom, because the technology is making outside the classroom a moot point unless we make some changes long term.

New Desmos functions – STATS! Yay!

21 October, 2014 (16:34) | APStats | By: Glenn

My last post was in September and was entitled “I am tired so tired.” That ended up prophetic because with the fall break I ended up not posting for three weeks.  Whew. I needed that break to get back on track and then caught up. I am glad I have my head on right now and am refocused.

So, on to new posts.

Today, Eli Luberof posts on Twitter:

 

Yay! This was amazeballs! You should try it. If you don’t want to try it, I took a screencap of what Stats looks like in Desmos. Desmos 2     

 

This just made my day. Now I can do data entry, just make sure to use the subscripts on the data points and the variables. Notice that you can do different forms of the equations! You can do yhat = a + bx or you can do yhat = mx + b. Either format gives you the r value and the residuals.

Go residual plots! That is awesome in and of itself. I am in love. Right now, the only thing that kind of saddens me is that I can not use “height” and “time” as variables. Desmos needs the x_1 and y_1 format to work. That is sad, because in stats we try to use words as variables. Oh well. At least this gives me a clean, nice, clear way to teach this topic to all classes.

Eli, two thumbs way up for this addition. [And just as an aside to the rest of the #MTBoS to show how responsive Eli is to us. He did a small focus session at #TMC14 with several stats teachers and asked us how we would want to do this. He told us he had not thought about residuals at that time, so to see residuals so easily pop up here was very exciting. Desmos is truly responsive to teachers needs.]  

Edit: Okay, so I kept playing and tried to build a lesson with it on residuals. Found some interesting things that I like and don’t like. I tried to calculate the predicted values, the yhat. Desmos didn’t like merging the algebraic with  the regression. Not at all. This is what I got when I tried: Desmos 3                          

 

 

 

 

 

 

 

I would like to have the ability to show not just the actual value, but also the predicted value. That way I can show where the residual actually comes from. Beggars can’t be choosers though.                      

Edit again: Desmos comes through like a champ. They tweeted this out to me last night.  

 

Which led me to do this:

desmos4Click on it and look at it large. You can see how I used a function per Desmos’ advice to then calculate the residuals instead of just using what is given. This pretty clearly shows where those points at the bottom come from.

I am teaching residuals right now in AP Stats, and I will use this as a demonstration (if it is up long enough) to show what the calculators are doing. Too often the learners don’t think beyond the buttons and just mechanically find the resid plot without thinking about what is going on.

Tired – So tired

30 September, 2014 (17:09) | APStats | By: Glenn

Today wiped me out. I had all 3 sections of AP Stats today, and I heard the same comment from all 3 classes. It went something like this, “I never understood the z score when we did it in Alg 2. My teacher just said, memorize the formula and get find the number.”

Sigh.

That kind of statement just grates on me. We are required to teach it, but some teachers don’t take the time to teach it well, and some just give it a cursory glance and turn learners off.

I am starting from zero with the idea, and building slowly and carefully. It is exhausting though. I never asked who their teachers were (although 3 minutes with the computer will tell me) and I won’t ask. I respect my colleagues too much to think less of them for the destruction of the stats unit.

At least I have learners from my Alg 2 class last year who cheered when I said the phrase “z score”. That made me happy.

Okay, repeat after me: The z score is the number of standard deviations from the mean.

Why over complicate such a simple idea?

Okay, back to grading hell.

Pictionary in Stats

29 September, 2014 (14:59) | APStats, Lesson idea | By: Glenn

I tortured my learners with a game, a game that was awesome and they all agreed was worth while. We played a Stats Pictionary!

I used this document.  Ch 5 – various distributions- Pictionary   I created these distributions using the Illuminations Applet called plopit.   http://www.shodor.org/interactivate/activities/PlopIt/

Here are my rules:

1. Each pair gets one distribution.

2. You have to write your SOCS (Shape, Outlier, Center and Spread) so clearly, using values and descriptive words so that the other learner can duplicate the distribution without asking any questions.

3. Once the SOCS are written, trade papers, and then try to re-create the distributions from the descriptions only. DO NOT SHOW the original.

4. Once the distributions have been done, show the distributions and compare.

5. Repeat.

 

That’s it. Very simple. I did model one for one class. They were struggling with the idea. Once I modeled one, they were fine.

Big takeaways: They realized their SOCS sucked. The figured out what they needed to do to make them not suck, however. Also, the first round went poorly, but they quickly modified their SOCS statements to be clearer.  Finally, Spread was the one thing they still struggle with. They are getting better, but trying to estimate from a graph is hard.

We ended up doing around 4 to 5 graphs in the 35 minutes I allowed for it. It was a great experience I think.

 

I was asked to show my notes. This is the ppt I am using for all of 1 variable quantitative stats. I don’t think it is anything special, but I AM trying to be more creative and thoughtful with it.

I can’t get away from all the notes. I don’t know if it is me, or the material. I do know this is about 14 days worth of notes. I have not done a whole day. A few slides. Stop. Do activities. More notes tomorrow. More activities.  Check out slide 64. :)

Categorical & 1 variable Quantitative

 

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Sorry to be silent last week. It was crazy and I was in a spiral of grading hell. I am not out of the grading hell, but I am out of the depression that results from the spiral. Now I am focused and getting caught up.

Greedy Greedy learners – a good thing

23 September, 2014 (19:15) | Alg 2, APStats, Lesson idea | By: Glenn

gottoogreedy

That’s right, they got greedy, and lost. Well, everyone gained, knowledge and skills that is.  Today (and tomorrow in one period) in AP Stats we are playing The game of Greed. This is a great game, that challenges the learners in the end to make box plots and comparison statements about the created data.

You end up with some great data to use in class.

2014-09-23 10.46.52     2014-09-23 14.10.14

 

What is especially great is the right picture, period 5. Notice the big, fat zero? Yes, a female in the class purposefully took zero points. This was a VERY high scoring game as well, the die was very generous to them, and that zero affected everything. I just laughed when she said she was going to purposefully take a zero. It is well within the rules.

This achieved one goal of getting learners talking about the math, at least. 1 thing accomplished today for sure. They also learned more about comparing distributions and using boxplots. 2 and more things accomplished.

 

Algebra 2

This class was awesome today. I gave them a quiz. They had 1 quadratic function in vertex form, 1 in intercept form, and 1 in standard form. They had to turn the one they chose into the other two forms, and then answer all the questions about the function.

Oh, did I mention that if you choose the vertex form, the max points you can earn is 80% of the points? Intercept was worth 90% and standard form worth 100% of the points. They could choose 2 to do, but I would only grade the ONE they told me to.

As I walked around, I saw lots and lots of little mistakes. Silly mistakes. They would be losing, as a class, a ton of points because of not checking signs, and other silly things. I didn’t want that to happen, they knew better, but they were being inattentive to details. So, with 15 minutes of class I told them they could ask anyone in the room any question they wanted to, but they could not ask me.

They figured out pretty quickly they were being silly. Tomorrow’s quiz for real will go differently. Same set-up. Different equations.

Mixed bag today

22 September, 2014 (21:11) | APStats | By: Glenn

Today was a mixed bag of, well, weirdness and frustration with some awesomeness.

I will start with the awesomeness. This morning at 7:15am, a learner from last year walked in and asked for help with his college math class. Loved it. I worked with him for about an hour (into the first class of the day) and he left feeling much better about his class and caught up. I felt really good about being able to continue to help my learners even after they have graduated and moved on.

The frustration was that classes can be so very very different. My one period is chatty. And by chatty I mean so talkative they actually miss out on some of the lesson because they just won’t learn to listen. They are great learners, but the social aspect is killing them. Meanwhile my other two classes have exactly the opposite problem. They are so un-chatty that they sit there in silence waiting for someone to speak up.

The classes were so polar opposite today, and I was completely flummoxed by it. I need to get the one class to talk about the math, and the other classes I need to get to talk about the math! Well, at least it is a common problem.

 

Finally, the weirdness. I gave my AP Stats class this lesson. Ch 4 – Tomato plant experiment But today we were learning how to calculate the fences for outliers and we applied the calculation to data set E.

The NSpire says the data point 20.2 is an outlier, as does the TI-84. But using the 5 number summary and doing 1.5(IQR) + Q3 and Q1-1.5(IQR) we get a fence of 19.95.

The value o 20.2 is not an outlier, but the graphing calculators call it an outlier. That is weird.  I used JMP hoping it would give me different values for the 5 number summary. Nope. Same as the graphing calculators.

This is some weirdness I can’t easily explain, but it did hammer home the idea we should not trust the calculator.

Torturing, er, teaching today

18 September, 2014 (17:07) | Alg 2, APStats | By: Glenn

All models are wrong, but some are useful. George E.P. Box

AP Statistics

I was able to use this quote today in class. I was happy.

My learners were happy too, well, mostly happy. Well, okay, not happy at all at first. At first they hated me. They were struggling with learning how to do 1-variable stats, boxplots and histograms on their calculators in AP Stats. To force the issue of “you must do this, quickly and accurately” I gave them the following handout.

Ch 4 Box Plot Histogram 5 number summary INB 2013

5 data sets, all real, all crazy, none of them particularly easy. The golf data set is just weird.  These are clearly not data sets made up to look like something legit. They are data sets chosen to make them question whether or not their window is set right, whether they entered the data correctly. It forces discussion.

Then, they had this as homework.

Ch 4 – Tomato plant experiment

Yea, I am a demanding. They have until Monday, so I am not worried about the time it takes. But if they can’t make a graph, this is an impossible handout. If they try to get summary statistics by hand, they are in trouble.

I am interested to see what happens on Monday.

 

Algebra 2

Whew. This class started out brutal, but by the end of class they were ripping quadratic equations in standard form into (h, k) form in seconds. y=2x^2, or 3x^2, no problem. They were able to factor out the coefficient and jam on it. I was really happy about it. They struggled at first, but they were helping each other and they all had it by the end of class.

The assignment was to take 3 functions and put them all in the other two forms. Yes, the form for the second one requires the intercepts be written with complex  numbers. Are all functions factorable? Yes. Are all functions easily factorable? No.  Graphing will get them the intercepts? No. Graphing will get them the vertices at least? Yes, but (1,18) and (-3,-22) are two of the vertices. Not easy at all.

Sneaky Waddell, sneaky.

3 functions

Notes, Pacing & lesson idea

17 September, 2014 (13:40) | APStats, Lesson idea | By: Glenn

brickwall

One thing I am really working on in AP Stats is the amount of notes, the lack of notes, and the engagement of my learners. AP Stats is one of those courses where the amount of vocab to assimilate is so huge, that it cannot all be done by activities. I have found that a mixture of activities and notes, and assignments and cycling back again helps tremendously.

I have the one slide from my notes today above. The literal, not figurative, brick wall between the two ideas of mean & standard deviation and median & IQR was very well communicated this year. The learners told me they understood. The formative checks I did supported that.

I still am not confident. Too many learners mess up this idea every year for me to take the face value word on it. I will be giving some questions over the next couple of days to make sure.

The re-writing of my slides to be word minimal, picture heavy, and discussion focused has changed how the class goes when I am doing notes, at least. I am happy with that aspect, and the learners I have asked directly about the notes have told me they are very useful and not boring.

That is something at least!

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PhD spillover

As an aside, the class on non-parametric statistics has taught me one thing that has impacted my AP Class. The structure I used last year as far as how I teach the content is right on the money.

2014-09-16 16.08.00

In the PhD level class, we look at every problem first from the perspective of “is it categorical or quantitative” and then “how many variables”. So far, we have limited the decision to just categorical, non-normal problems (hence the non-parametric! label of the course.)

For Inference section, the course will be divided up into a. quantitative 1 sample, a1. confidence interval, a2 hypothesis testing; b. quantitative 2 sample b1. confidence interval, b2. hypothesis testing, etc. I think this structure leads better to the advanced level stats if they take a next class.

It is also the exact opposite of what our textbook does. Oh well. I didn’t use the textbook structure for 2nd semester anyway for the last 3 years. This just reinforces that decision as a good one.

——————————

Finally, some lesson ideas I am working on.

2014-09-16 16.09.51 2014-09-16 16.09.01

That’s right. Funky dice!

On the left we have odd shaped, non-standard dice. Awesome. Are they fair? Not sure. On the right we have, yes, for reals, 5 sided, 7 sided and up dice. No joke. I once argued that a 5 sided fair die could not exist. Is it fair? Not sure. I am writing some lessons for expected value to take advantage of both of these.

I also received word from Robert at http://thedicelab.com/ that my order of weighted dice is coming soon.

Heh heh heh. That’s right. Real, honest to goodness (well, dishonest to goodness) weighted dice.

Expected value here we come! More later on this idea.

Relaying in Stats, Melting down in Alg

16 September, 2014 (16:35) | Alg 2, APStats, Lesson idea | By: Glenn

2014-09-16 16.08.00

You are here! That is my AP Stats objectives board for the next few weeks. Today and yesterday we finished up Categorical data analysis with Relay Cards. It was very successful. I had many learners telling me they understood what they were doing, and they were saying this even though they were making mistakes in the reading of the problems.

I like the fact they were happy with the content and realize that making mistakes in reading did not mean they were not understanding. I need to figure out a way to make sure they realize that.  This is an issue I need to think on tonight and figure out a way to pull it together for them to think on as well.

I wish I had a magic phrase that everyone would hear and just go, “Aha.  I understand that making mistakes does not mean I don’t understand, it just means I made a mistake.”

I have RADICALLY revamped the notes I am doing as well.

This is the old PPT from the book. I am ashamed to say I used this for several years.

bookppt1

Here is my notes for this year, same topic. Yes, the quote is from Dr. Who. I will see how many learners pick that up.

notesme

 

Yes, there is still text on the slide, but less. And more of a story instead of regurgitating stupid words.

histogram  I am trying to do more of this type of thing with my notes instead of the “The definition of a relative frequency histogram is” blah blah blah. So far, the learners are telling me my notes are not horrible. They read less, they write less, and they are learning more and being much more quick in doing problems and asking better questions.

So far, success on that front.

Ch 3 – Relay Cards (made by Shelli Temple)

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Algebra 2

Whew, but Alg 2 is brutal.

We are working our way through a series of Quadratics. Today I introduced completing the square and justified it by needing the vertex form. All of the quadratics we have done are found here:

 

I started them off in vertex form, they had to provide intercept and  standard form. Now I am giving them standard form, and they provide vertex and intercept form (among all the other information found on the exploration sheet.)

They are hating me right now, but it is getting easier. The idea that ALL quadratics are factorable, is stressing them out. Some are easily factorable, some require the quadratic formula, but ALL are factorable.

Ouch.

Miss a day, miss a lot

15 September, 2014 (20:49) | APStats | By: Glenn

I can’t believe I did it, but I missed a day. I did not post on Friday. I don’t have a real excuse, other than tiredness. I took a nap after school on Friday because I was running chains for the varsity football game. After doing it two games on Thursday I was beat by the end of school on Friday. That I took the nap in my classroom with the lights off just shows how tired I really was! Thankfully the custodian didn’t come in. That would have given him  a heart attack.

A quick recap from Friday to get caught up, and then today in a different post.

On Friday in AP Stats I did “bad graphs”. This is always a fun day, because we look at graphs and they learn what NOT to do. I tell them that if I ever see a graph that is 3D, or violates the Area Principle, or bad axis labels I will stop reading and return ungraded. We looked at lots of pics. Here are some examples:

road sign graph-01-01 voting_methods 3-D graph Bush-cuts-625x461 changing scale changing scale2 courses CUSD growth daily oil production genetest29 infoweek11-24 japan-world no scale quakeroats

 

And this is the assignment we did: Ch 3 – Analyzing Bad Graphs

This was fun day, but still informative and useful.