Geometry Problems

When I was assigned to teach geometry last year I thought I would love it.   It seemed so simple.  It's just shapes!  There aren't many numbers! It's pretty!  Being at an arts school I felt like I got the easy assignment.  Connecting Algebra 2 to art was a bit of a stretch at times, but geometry?  That stuff is art.

Oh how naive I was.  For sure some parts were easy, but the class ended up being really haphazard.   I had some interesting projects (I'll upload them when I remember) that I will modify and reuse, but I didn't love the way I structured the class.

I also had a hard time getting the course to be at the right difficulty level.  And a lot of the stuff was review.  Gee, a square has four sides of the same length?  Most know that.  But it's supposed to be new and fancy because I'm throwing in the term "congruent" and some x's here and there.  A square has 4 congruent sides.  Much more high school level.  Label one side of the square "x+7" and the other side "3x+1" and somehow the problem is extra hard.

Then there was stuff that was crazy hard for my students.  Let me introduce you to: Angles of Elevation and Depression . My students had limited algebra ability so problems that had two variables instantly upped the ante.  Add in word problems requiring the students to draw pictures, and multiple set ups of trigonometric rations and we have a recipe for disaster.  Here is an example from IrrationalCube's Blog

And during particular units (cough, cough, quadrilaterals, cough cough, circles) there was so much to cover that I just rocketed through everything. I felt like I was just throwing theorems at the students.  On a good day they "discovered" the theorem themselves.  But most of the stuff seemed so disconnected and not necessary.  When was the last time you needed to solve a problem like these:

If your answer was...high school geometry or ....the GRE....then I think you fall in with the majority of Americans.

I haven't quite come up with solutions yet, but this is the first year I'm reteaching a class, so I'm excited for the opportunity to figure it out.  I'll be splitting the class with another teacher (she has 2 sections, I have 2 sections) so I'm really grateful to have someone next door to bounce ideas off of.   While I still don't think I'm in love with geometry I'm ready to give it a go.

Stat Class- Standards Part 2

After diving into the MN standards I broke them down into 68 little nuggets of understanding.  Small, manageable, bite-sized pieces. 

 

These standards become:

These are the first two standards.  As the standards progress (and honestly as I got lazy/tired/bored of actually doing work) I got less specific.    I still need to do some refining to actually get my concept list finalized, but I feel pretty confident that we can accomplish this in a year.

Moreover, while Minnesota seems to really not want math common core...the standards are VERY VERY similar.

For example: 

S-ID.4. Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.

Perfectly matches:  

9.4.1.4 Use the mean and standard deviation of a data set to fit it to a normal distribution (bell-shaped curve) and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets and tables to estimate areas under the normal curve. 

On the whole, MN standards are pretty closely aligned with the common core.  Common Core included expected outcomes and occasionally went a bit more in depth into a topic, but overall, very similar.

Stats Class- Standards

I started out by looking up the state standards in Data & Probability.  Minnesota has not yet adopted the Common Core Standards.   We just adopted new math standards in 2007 in which all 8th grade students must take Algebra 1.  High school students cannot receive credit for Algebra 1.  Many people in the Minnesota Department of Education and many Minnesota teachers feel that the state standards are more rigorous than the common core standards.  Additionally, the math standards are not scheduled to be revised until 2015, and making changes before hand would require legislative action.  I thought I saw something in an article about the end of the shutdown that the legislature approved changing the standards sooner, but now I can't find the article.  In case Minnesota ends up adopting those standards and so I can know what is relevant to teachers outside of Minnesota, I looked up the Common Core Data & Probability standards.  Then for good measure, I took a gander at the AP Statistics Standards.

In summary, I don't see how high schools can just squeeze those things into other classes.  My geometry textbook had a chapter of probability lessons tacked on at the end.  Yeah, like I have spare time in a geometry class.

AP Statistics Standards: (found here)
Common Core Statistics & Probability Standards: (found here)
MN Statistics & Probability Standards: (found here)

Ignoring the fact that the AP test only briefly covers probability, at least it is easy to read and decipher what the heck IS covered. I've been using the MN 2007 standards since I have started teaching so I really like the boxed layout and the occasional insertion of samples, but man, those standards are packed.  There are only 15 standards, but they each cover like 5 things.  For example,

"Describe a data set using data displays, including box-and-whisker plots; describe and compare data sets using summary statistics, including measures of center, location and spread. Measures of center and location include mean, median, quartile and percentile. Measures of spread include standard deviation, range and inter-quartile range. Know how to use calculators, spreadsheets or other technology to display data and calculate summary statistics." 

First you have to know all these ways to describe data, and compare them, and measures of spread, and center, and oh ps, all that technology stuff.  At least it is specific and tells you exactly which measures of spread and center students/teachers are responsible for.

Then, there is the common core. The standards are a bit more broken down than MN, but some are still biggies.   Like this one.  You know it's big because it comes with parts a-c

S-ID.6. Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
a. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.
b. Informally assess the fit of a function by plotting and analyzing residuals.
c. Fit a linear function for a scatter plot that suggests a linear association.

At first glance that doesn't sound too bad, its just scatter plots and fitting linear functions to a scatter plot.  But then there is the line about "Emphasize linear, quadratic, and exponential models."  Knowing my students they will remember what linear is, but not how to write an equation and will flop what the slope is an the y-intercept is.  They will recall that quadratics was that really, really long and difficult unit.  And we just scraped the surface on exponential. 

Then there are others that are super vague. "S-IC.6. Evaluate reports based on data." Ooookkkk.  Evaulate how?  What kinds of reports?  What kinds of data? Awesome.  I get the general idea and I think that yes, students should be able to evaluate reports based on data, but some clarification would be nice.  I think I heard that specifications and examples were coming out soonish.

So where does this leave me, the first year stats teacher?  A little lost.  I'm going to build my skills set around the MN standards because that's what my students will be tested on. 

Now to actually do that.

Summer's Almost Over

I had envisioned writing a series of blog posts reflecting on my classroom practices.  I made it through my posts on goal setting and started working on one on classroom management.  However, I'm really excited about the statistics class I will be teaching and I'd much rather think about that.  (I will keep calling it statistics, but it really is a data/stats/probability course).

My school has never had a statistics class before,  we do not own textbooks for it, and will not be purchasing textbooks for it.  I have been given carte blanche by administrators.  I can do anything I want.  I have never really felt constrained by curriculum before and tended to do my own thing, but not having a textbook to default to when I haven't planned a killer lesson or to look to for guidance is both empowering and frightening.

What am I going to do with them for a full year?

Well, the students in the class will be juniors and seniors.  The seniors have already taken their state math graduate exam, but many did not pass.  The juniors will take the semi-high stakes test in April (if you don't pass you can keep trying, but you need to pass to graduate).  I had many of the juniors last year, in Algebra II, and know that many students are far behind where the state wants them to be.  The majority of students have computational difficulties (heavy reliance on calculators for anything calculation with positives and negatives), low math self esteem ( "I have no idea how I passed geometry.  I should have failed."  "I don't know how to do anything"), and difficulty connecting concepts.  To their credit, the majority of the students are technologically savy (they picked up excel in a flash and made awesome videos for our review archives).  Moreover, they are willing experimenters and went along with just about everything I asked them to do.  Problems written on the windows?  OK Miss...sounds like "fun".  Taking a test through google docs?  Sure no problem.  They are very flexible, they trust that I am helping them to learn math, and a result will try earnestly.

I'm fairly certain I will be testing their ability to be flexible and try new things with this statistics course.

Rough ideas:

Review of all concepts on the state exam

• Post a video/smart-board display of me working through a sample problem
• Have a "pre-test" on Fridays to assess where individual students are with the concept
• Examine pre-tests over weekend to inform creation of classwork/grouping
• Use Tuesdays to refresh/relearn the concept

Lingering questions:

• What order?  Should I post the video before the pre-test so students can jog their memory?  Should I post it after to get a real picture 
• If the students didn't understand or store the information for recall the first time, what am I going to do differently? 
• How can I feasibly do this without over-burdening myself with work and grading?  
• Am I overemphasizing the state test? 

Be Organized, Help Students to Organize

• Students have two notebooks- 1 for classwork, 1 for the test review.  Last year I let students do work anywhere, looseleaf, computers, anything, and stuff got lost.  The few students that had been using notebooks could flip back to past work easily, find late work, and turn in multiple assignments at once.  On the rare occasion that I mark something as "missing" that really was turned in, it is very easy for the student to find it and show it to me. 
• Students will create a Stats Class Folder on their desktop and I will tell them how to name notes, handouts, etc. 
• My prep hour is at the end of the day.  That time needs to be used to grade work and update the online gradebook.  At the LATEST I want to be giving work back the following Monday. 

Lingering Questions

• How/what am I going to be grading?
• Am I keeping with my school's paper-free vision by reverting back to notebooks/paper tests?  I really tried to go all digital last year, but it is a hassle to open up 70+ versions of the same assignment, grade it on the computer, switch screens to enter the grade online, and if there is feedback on the document, manually return it to the student's desktop.  Until the return feature is improved, I think I need to stick to paper. 

Standards Based Grading

• I've always wanted to use SBG.  I have a great tracker and always start off the year using it.  My tests were broken down by concept and I'm comfortable grading in chunks like that.  I allowed for reassessment. 
• Be more open with the students about SBG.  I was tempted to have a shared google doc between me and each student where we could each update progress on individual concepts.  However that would be management nightmare.  I think I will start off the school year by listing each of the statistics concepts in the online gradebook.  In the front of their notebook they will staple a folded copy of the statistics concepts followed by all of the concepts we will be covering in Tuesday's review day.  
• Have a firm set of reassessment guidelines.  Students must correct work on quizzes/tests/HW before reassessment.  In one day, I can either work with them to learn the concept,  or give the test, not both.  They can only reassess once per day.  They need to make corrections to the reassessment and pass my verbal pre-test before attempting again.   With some exceptions, reassessment window ends two weeks after the original test was given.