Jun 102015
 

Functions

I begin the class with a “what do you notice?” “what do you wonder?” session. This is probably the 5th or 6th day of class, and sets the stage for the entire rest of year. What do you notice? What do you wonder? I document all the noticings and wonderings, and then we discuss the mathematical questions.

Every year, the question of “I wonder how the 2 and the 1/2,” “I wonder how the 3 and the 1/3,” are related is asked. The best two questions that are always asked are, “Why are they all the same?” and “What changes when we change the exponent from 1 to 6?” I always say that I will answer every question by the end of the year; I will never lie to them and tell them something is impossible when it isn’t, but that some of their questions may need to be addressed in a future math class and not this math class. That honesty goes a long way.

I spend an entire period exploring the different functions with them, showing graphs on Desmos, asking for values to put in for a, h, and k. I ask questions like, “what do you predict the h will do?” and “Did your prediction come true?” The learners who are the typical aggressive type A learners hate it because they want the answers and want it now, but they will come around and start developing ideas on their own.

I start with lines for the (h,k) form because I think this form shows some reasons why to use the form, the benefits of using the (h,k) form over y=mx+b, as well as a simple function to cut our teeth on vocab.

I introduce this form first thing in the year as we get started. Fully Explaining & Understanding functions blank (double sided .docx file). I print off hundreds of this form, and we use it regularly. Some days I have the learners write the functions in their notebooks when I don’t have the forms, but I try to have a stack on hand always.

explaining This is what it looks like. There is A LOT of info asked for, and I start with lines so we can establish the understand of what the different elements are.

It always bugged me that we rarely talk about domain and range of lines. Why not? Why start introducing that idea with absolute value? Just because that is where it changes from all real numbers for both to only one, does not mean we shouldn’t introduce it earlier. Same thing with asymptotes and even/odd functions.

If I can get learners to identify the x and y intercepts on the line, and then connect those points with the standard form, so much the better.

Same thing with intercept and (h,k) form. Cut the teeth on a line, that is familiar and safe, so that as we move forward with quadratics, cubics, cube roots, etc, the learners can see the vocabulary does not change. What changes is the shape of the parent function.

I make sure every learner has one copy of this that is complete, pristine, written clearly and fully in their notes for every single function. When the learner puts them all side by side, they can see there is only one math, one set of ideas through the entire year. What changes is the amount of effort needed to get the intercepts for a cubic vs intercepts for a line? Why?

Another rich focus of questioning is “What makes the line unique?” “What makes the quadratic or cubic unique?” Some answers I have received are, “Only the quadratic always has a vertex form. The cubics can have that form, but usually not,” or “Every point on the line is a critical point, but we can’t always use every point for other graphs.”

Or can we? Hmmm. Leave it at that. Don’t tell them. Plant the seed and let it grow on its own.

This is a big picture post. Philosophy of teaching, approach to the topics, etc. No details yet. Just a pouring out of my thoughts on how I start. I will go more in depth. Notice that there is not enough room to work on the page. Only the results go there. The work is separate.

 

Apr 012015
 

I always tell my speech and debate competitors that a good speech takes multiple drafts, and this speech is no different. After sleeping on it overnight, and re-reading it today I realized that my speech was fighting itself in the wording, so I rewrote some key sections.

I like this version much better.

I really did not expect to spend spring break doing political activity, but here I am anyway. I also was just asked if I would do an interview for another local news story. Wow, say yes to one thing and more activities pile on. At some point I need to put this aside and start reading for my classwork. I need to do that soon!

This is the text of the final version of the speech. It is better than the previous one, I believe.

For the record, my name is Glenn Waddell, Jr., and I am the department chair and teacher of AP Statistics and Algebra 2 Honors at North Valleys High School. Chair Woodbury and members of the committee, thank you for allowing me to address you today and explain why I oppose the sections of AB 303 that delete reference to the common core. I NEED the core standards to be an effective educator. Most importantly, my learners need the common core state standards.

I need the core standards because the prior standards had different “enhancements” in Washoe and Clark counties; which means that I could not collaborate with teachers in the southern part of the state, let alone elsewhere. Today, I work with teachers in other states as much as I collaborate within my building. The internet facilitates connections with math teachers, the sharing of lessons, and pooling of resources with teachers in Oklahoma and New York as easily as teacher across the hall.

My needs pale when compared to the needs of my learners, however. My learners need the common core for two reasons. First, high standards create engagement. The current standards provide this through the shifts, the practices, and the standards themselves. An example of how much can be accomplished with the standards is two weeks ago, my learners were working on the A.REI group; solving systems of equations algebraically & graphically. My learners had a graph of two functions with solutions that were easy to find one-way and impossible to find other ways. They worked for over 30 minutes individually and in groups before they finally gave up and asked me for help. The understanding we found was; there was no algebraic way to find the solution, and they refused to believe it. The mathematical practices served my learners well. They showed perseverance, appropriate use of tools, making arguments, regularity of structure, and critiquing the reasoning of others. This is the heart and soul of a successful math classroom. My learners need and deserve this high level of rigor.

Secondly, my learners need the standards because they are working. All learners need a solid foundation beginning in elementary school upon which to build future mathematics content, and math teachers in my school agree the learners coming up from middle school are better prepared for high school algebra. The standards are not the maximum, they are the minimum body of knowledge that learners must know. The standards create a foundation that is stronger, substantive, and more demanding than we had in the past. My learners need the core standards so they can build their foundation, and launch themselves to higher mathematics with confidence. My learners do not come into my room to be average, they come into my room to be awesome, and the core standards allow and encourage them to be awesome.

Thank you.

 

Mar 312015
 

Tomorrow I am speaking to the NV Legislature on the Assembly Bill 303 (pdf text) that would eliminate the end of course exams that I don’t like, but would also eliminate the Common Core State Standards from all NV schools.

Can I complain for a second on how difficult it is to give a 3 minute speech? OMG! My first draft was around 8 minutes long, and I finally have it down to 3 minutes on the dot. Below is the text of my speech. If you have any suggestions, I am open to tweaking or rewriting. I leave tomorrow at 2 pm for Carson City!

There may also be an opportunity to be on a local PBS channel show about this bill as well. Who would have guessed that I would have spent this year’s spring break in political advocacy? Not this guy, that is for sure.

For the record, my name is Glenn Waddell, Jr., and I am the department chair and teacher of AP Statistics and Algebra 2 Honors at North Valleys High School. Chair Woodbury and members of the committee, thank you for allowing me to address you today and explain why I oppose the sections of AB 303 that delete reference to the common core. I NEED the core standards to be an effective educator. Most importantly, my learners need the common core state standards.

I need the core standards because the prior standards  had different “enhancements” in Washoe and Clark counties; which means that I could not even collaborate with teachers in the southern part of the state, let alone elsewhere. Today, I work with teachers in other states as much as I collaborate within my building. The internet allows me to connect with math teachers from across the United States and share lessons and pool resources with teachers in Oklahoma and New York as easily as I can with the teacher across the hall.

My needs pale when compared to the needs of my learners, however. My learners need the common core for two reasons. First, my learners need a solid foundation beginning in elementary school upon which to build future mathematics content. The current standards provide this through the shifts, the mathematical practices, and the standards themselves. An example of how much can be accomplished with the standards is two weeks ago, my learners were working on the A.REI group; solving systems of equations algebraically & graphically. My learners had a graph of two functions with solutions that were easy to find one-way and impossible to find other ways. They persevered for over 30 minutes individually and in groups before they finally gave up and asked me for help. The understanding we found was; there was no algebraic way to find the solution, and they refused to believe it. The mathematical practices served my learners well. They showed perseverance, appropriate use of tools as well as making arguments, regularity of structure and critiquing the reasoning of others. This is the heart and soul of a successful math classroom. My learners need and deserve this high level of rigor.

The second reason my learners’ need the standards are because the core standards are not the maximum, they are the minimum body of knowledge that learners must know. The core standards raised the bar tremendously from prior standards, and in so doing created a foundation that is stronger, substantive, and more demanding than we had in the past. My learners need the core standards so they can build their foundation, and upon this foundation launch themselves to higher mathematics with confidence. My learners do not come into my room to be average, they come into my room to be awesome, and the core standards allow and encourage them to be awesome.

Thank you.

Any suggestions? Comments?

Mar 072014
 

My goals:

  1. Construct a consistent vocabulary of problems that can begin in Algebra 1 and extend through to Calculus, Statistics, and all courses in between.
  2. The problems must have the potential to be engaging to learners.
  3. The problems must hit at least 4 of the eight Mathematical Practices & high school math standards (CCSS).

My idea started with this idea for Algebra 2: Model the escape velocity of a rocket on the Moon and the Earth. ( PDF and Word DOCX) This ended up being a far more difficult task than I expected, mainly because the learners did not connect the idea of writing the equation of a line with the fact we had a function in front of us.

I Desmosed the project for a visual display, and we spent another day discussing it and achieved the goal. [Is it okay to use the name as a verb? I don’t care, I am doing it anyway.]  It turned out great in the end, but it made me start thinking hard about how to connect Algebra 1 through Calc and Stats and make the ideas more real, more understandable, and more connected.

From there came the idea of using an “off the shelf” structure in a new or different manner to extend the lessons. Enter http://graphingstories.com . Dan Meyer started the Graphing Stories with a long time ago, and they are awesome. But they also fit the idea of using the video / graph combination to write the equations of lines and finding area under the curves.

With that in mind, I offer the following Desmos files:

File 1:

  1. This uses the Graphing Story of water being poured into a graduated cylinder to create the graph. I took some points from the graph on screen, and wrote a function that goes through the point (0, 0) because we know it was empty at time 0.
  2. Notice that the line does not go through exactly all 4 points! That allows for discussion of variability and observation skills.
  3. I also used the (h, k) form to write the function f(x) because it is the easiest way to show the line.
  4. What does the slope MEAN?  A standard AP Statistics interpretation is: As the time increases by 1 second, the water increases by 40.67ml.
  5. Next, find the area under the curve. Move the slider for “b” to the right and you see the area highlighted.  Okay, standard triangle, ½ b*h, and you get 5205.33 ml*sec. ??? What does that even mean?
    1. It is called “absement” and it is the time-integral of displacement. Yes, we don’t need to discuss that for Algebra 1, but as teachers we should know it.
    2. The area is the sum of all the instantaneous moments of water before. With the Desmosed file, you can see and clearly communicate what it means. It means that you are adding up the area of the little triangle when b=1 with the larger triangle when b=1.5, and then with b=2, etc. Except the area is the sum of the instantaneous areas, not the discrete areas.

Notice that this one lesson required the learner to interpret a real life action, pouring water, into a graph, and then find the slope and write the equation of a line, and then interpret the slope, and then find the area under the curve.

These are all essential skills of the Calculus learner, done at the Algebra 1 level!

A second one.

  1. Now we are removing cups from a scale.  There are actually several questions that the video brought to my mind, like is this really a continuous line, or should it be more discrete? Time is continuous, but the weights really are stepped.  But, I left it as is though because I wanted to not change it from what the video shows. That is a larger conversation in class.
  2. We now have a negative slope to calculate, which does not really make a huge difference for interpreting the slope: As the time increases by 1 second, the weight of the cups decreases by 3 grams.
  3. The fact the line only hits 1 point absolutely creates some conversation about which point to pick, variability, ect.
  4. The area gets fun, however.
  5. Notice that the FULL area is still a triangle. However, if you move the “b” slider across, you notice the partial areas, the area at 5 seconds, 8 seconds, etc, are trapezoids! Now the learner can be challenged and pushed to incorporate some extra questions of find the area of trapezoids.
  6. We still are doing and absement calculation and not a displacement calculation.

Finally, the Desmosed Lunar Modeling I started with:

It is far more complex and involved, but that is why it is an Algebra 2 lesson and not an Algebra 1 lesson.

Jan 172014
 

I am soon to be embarking on a new direction / undertaking in my professional career, and in doing so will need to seriously delve into the realm of research and resources. Starting this summer, I am beginning a Ph.D. in Mathematics Education at the University of Reno, NV in the Math, Science, Technology and Society area of emphasis.

As a high school math teacher I need to be an expert in CCSSM. As a Ph.D. student I MUST, without question be an expert in CCSSM. To that end and because I have always been interested in research, I am going to compile lots of CCSSM resources and create a page here to house the ongoing collection.

The page can be found here:  http://blog.mrwaddell.net/ccssm-resources or at the top of the page.

 Posted by at 12:03 pm  Tagged with:
Nov 092013
 

Peg had a very busy Friday at NCTM Las Vegas, giving 3 different presentations in 1 day. The first was for newbies to the NCTM conference, the second was the resource presentation I already posted about, and then there was this presentation entitled: Pedagogical Judgment & Instructional Choices for Building Mathematics Classrooms.

I thought this presentation was the best one of the two I attended, mainly because it allowed the audience to get inside of her head and see what she thinks about. Short answer, she thinks about helping kids succeed. A lot.

That also means she is not thinking about BS like micromanaging homework, parents, etc. She thinks about how to support learners, how to know what they know, and how to demonstrate what they know.

This is going to turn into another “link fest” post because she cited some resources that I need to link to as I go. With good reason. She also could have used another 4 or 5 hours instead of the 1 she had. I would love to sit down with her and spend some time one on one just talking and learning from her.

Point 1: Management of Homework.

She started with a simple question, “Why are you assigning the homework?”

Are you assigning it for practice? Why? Are you assigning it as pre-learning? Why? Are you assigning it for some other reason? Why?

Are you THINKING about the homework you assign? Do you care more about the homework then your learners do? If so, you really need to stop and think about what you are doing.

This conversation immediately put me in the “Rethinking Homework” by Cathy Vatterott discussion that has occurred in my school and department. Other people mentioned Alfie Kohn’s “Rethinking Homework” article and discussion. I am embarrassed to admit I had not read that article, but I have rectified that deficiency.

Here are some quotes / statements on homework by Peg that I captured because they really struck home:

Distributed Practice not focused practice & one topic practice.  Focused practice does not show the long term results in research. [I would love to see and read the research, I am a research junkie.]

Assigning something the learners have never seen before is a way to get them to persevere.

Instead of reviewing, have the learners write the test questions. You will be surprised at how difficult they make the questions.

Turn homework into a way to take possession of their own learning. 1. Teach someone else how to do it. 2. Exeter type presentations

Teach parents to Ask, Don’t Tell. Teach the parents to ask questions instead of trying to help do the math and tell the learners answers.

Point 2: Putting work on your walls

Are you putting the perfect work on your walls? If so, think about what message that says to the rest of the class who are not there yet. If you only celebrate the perfect work, you are devaluing the work of the F, D and C learners. Their work is not important, so it does not count. Is that really the message you want to send?

Public displays of work should create an “Institutional Memory for the reminders of what happened in class.” That is a very different use of displays of work than most teachers do.

Point 3: Assessment

How do the learners inform what you do in the classroom?

At this point, Peg was running out of time and she listed off some resources that are impactful on this discussion.

Dylan Wiliam and Paul Black wrote an important article entitled, “Inside the Black Box”. (another source is http://weaeducation.typepad.co.uk/files/blackbox-1.pdf). Peg strongly recommends reading the thinking about the impacts of the article. A follow up article that should be read as well I think. “Working Inside the Black Box”

Peg also recommended Dylan Wiliam’s “Embedded Formative Assessment”. This is a book I have not read (shocking) and I know is very well regarded in the #MTBoS community.

And then Peg slipped in some gems on assessment, grades and feedback that where pure gold. Seriously, pure 24 caret gold. These are things she has done in her classroom to encourage learners to take ownership of their learning.

Give the homework back to a group, with comments only, no grades, and the comments written for the group on a separate page. The learners have to then go through everyone’s homework and correctly matchup the comments to the correct problem on each person’s homework.

On EVERY CHAPTER Test, Peg required (as in not optional) a correction and reflection. The grade was such, that if a perfect test taker failed to turned the reflection (because there was nothing to correct) they ended up with a 89% on the test.

Yes, that is correct. The reflection & correction was worth 10% of the test grade, and not doing it took you down an entire letter grade.

Again, no grades on the actual test handed back, only comments. They can look online for the grade or speak to you one on one if they want to know the score.

These are ideas I will be implementing.

Finally, somewhere along in the conversation, Peg plugged the PCMI, the Park City Math Institute as one of the absolutely best Professional Development she has ever done.

http://pcmi.ias.edu/ I may have to look into it in a serious way. Especially since it is on my end of the country.

Jul 032013
 

This is a two part lesson, an experiment and simulation that together meets the CCSSM S.IC.B.4-6 and explains AP Stats concepts as well:

clip_image001

This exercise is one we did at the SilverState AP Institute with Josh Tabor, but the nice this is that if you do the first part it fits in Alg 2 nicely, but you can extend it to AP Stats as well.

It is LONG, with lots of pictures to explain how to use the applet so I will put the post after a break:

Continue reading »

Mar 212013
 

Nevada is one of the SBAC (Smarter Balanced Assessment Consortium) states, and the SBAC has released some questions on their website in a way that shows us how the test will look and work when it is fully released.

Guess what, I can’t get it to work at school. Why? The district is standardized on IE7, which is too “old” of a browser for the SBAC, and Chrome is too new. I had it working in Chrome one day, and then Chrome updates and it is broken again.

So, I go home and using Firefox I can get it to run. Great, how do I now get this info to my department? I know, I will use Snagit and make captures of the screens. …. Not so much. One question is actually animated. Great, I will use Snagit and make a video! Yay.

Here it is. The 11 released questions for the High School level proficiency CCSS exam. Please don’t judge the voice over. I sound like an idiot.

Jan 032013
 

I started out to write a post about my frustrations and fears last week, and deleted it over and over again. I just couldn’t get what I wanted to say correctly on the screen, nor could I collect the facts and links that led me to the conclusions I was making.

I had previously said, “as public school math teachers … we are screwed” in my first Exeter article, and I still feel that way. The alignment of major money against teachers is overwhelming, and I definitely see signs of attacks on public schools and public school teachers. Just look at the research about education right now, it is about merit pay, charter schools, and how to abuse teachers more, not about how to benefit learners more. Look at what the publishers are doing with Common Core.

Example 1

Example 2

You can’t look at these examples and not get a sense of dread in the pit of your stomach. If this is common core, then we are just doubling down on mediocrity. And as I struggle with the CCSS and my Exeter project, I am finding out just how difficult it is to work with the CCSS in a substantive way.

Then I read Kris Nielsen’s post, This is How Democracy Ends – An Apology, and it struck a vibe with me.

Here is my takeaway question though. Given that this is occurring, and I believe it is, then what can I do in my classroom to have a positive effect?

After all, I believe I can and do have a positive impact on my learners, and I have faith and confidence in them that they are not all “common”. I need to keep Kris’ article on my desk and re-read it weekly, to remind myself that just because this is the trend, I don’t have to accept it. I can fight against it and give my learners skills and abilities to reach beyond it.

Which brings me to my reason for posting, my resolution for the new year: To reach beyond and push my learners above common place standard thinking, and to give them skills to do the same. In short, my resolution is to fight, every day, to do my small part in not allowing the worst case to occur.

I am re-blogging Kris’ article in its entirety below the fold. It is worth reading, and even has an interesting Venn diagram to explain his arguments. I don’t think I agree with everything he says, but it resonates strongly none-the-less.

Read it. My thoughts above will make much more sense afterwards. I just found myself quoting most of his piece in sections the first time, and realized it would have a better flow this way.

Continue reading »

Dec 312012
 

Made4math

My friend Anthony created a blog post the other day saying he was looking for the CCSS in Excel format instead of PDF format. He did all the work to create the file he needed, which made me feel a little bit bad.

You see, I have had exactly what he needed for the last 6 months, easily. I too, prefer to search and work in Excel. It is just an easier and faster platform to search and copy/paste from.

So, with that in mind, here are my files.

 

The main difference between my file and Anthony’s is the way the standard are presented. Anthony’s files are all in one tab, so searching / filtering for a complete strand is easier, while mine are broken up into different tabs for each grade level. Depends on what you need.  I have also indicated STEM standards with a “+”.

The one thing I have not done is changed all the standards to include the Cluster designation. That is something I need to do still. Besides that, the formatting is slightly different, but they are the same. I just felt bad he had to do all that work when I had what he needed all along.

I wonder how much other stuff is on my hard drive that other people can use?