APSI Beginning Statistics Day 2

So much information. Landy Godbold, our instructor, is so good at story telling…I get wrapped up in discussion of tasks that I forget to jot down key points and big ideas.

1. One of my favorite tasks todays was when we were asked to sketch box-plot with varying lengths in each interval.  Then we had to create a possible histogram for that same data.  Thinking was going on.  You could see it on our faces.

I believe we don’t ask our students open questions like this enough.  An add on…create another possible histogram for the same box plot.  For some, actually creating a set of data was the approach. 

My question for students…Can 2 different sets of data actually result in the same box-plot?  And let them explore.

Create 2 data sets that match a single boxplot yet have vastly different histograms. 

These are not as simple as I would have expected initially. 

2.  Another task today was with a single set of data.  We created our histogram using zoom:9 feature.  Then we were split into 4 groups and asked to graph using different xmin values.  Great point.  I knew it was possible but did not expect such a big difference in our resulting graphs.

3.  In a group of 4, each person ran 1-var stats for their specific data set, (mckenzie set) then asked to sketch possible graph using our descriptive stats.  Then we were asked to create an actual histogram and compare the 2. 

Please dont judge  my sketches…these are all from memory since I was too absorbed in discussions to write down actual examples!

The thing I appreciate about our class, I am being asked to look at things through a new lense.  I am thinking.  I am learning.  I like it. A lot.  Hoping I can learn enough between this week and TMC to help my students find their own success!

The Lady Not Tasting Tea #apsi Day 1

Yep. Within minutes of walking into our classroom, I spilled my tea.  My super size it tea.  I made a friend for life, Teresa, as she ran down the hall with me to collect paper towels.  A.lot. of paper towels.  Did I say it was super size?  All.of.it. running across the floor.  Bless the people around me for jumping in to be my friends.  Thank you, again for helping me.  Thank goodness I drink unsweet tea, no sticky mess.

Flipping through my INB from Day 1. There.is.so.much.stuff.  oh my.  Class is what I expected but not what I expected.
We are collecting data, somewhat simple things…yet it is the discussions that add to my take-aways.

Landy Godbold from Atlanta is our instructor.  He is good.  Very good.  His tshirt day one read:  Statistics mean never having to say you’re certain.  He says we need to get our students in the mindset: Statistics is about stories.  And he has whiteboards!!!  Love this guy.

Big idea for the day…week…variability.

E.A.C.  -Evidence. Argument. Conclusion.

Hey there’s that word again…ubiquitous…its everywhere.

Tell me the story!  Your students become lawers and must layout their case to the jury.  What do you want me to see, link it to the evidence and make your conclusion.

And the big question of the day… Compared to what?

What is typical?  How do I decide if this is typical or not?
Data set 1: What is the fastest speed you traveled in a car?

Story 1: Driving with cell phone is dangerous.  Given a two-way table and asked if it was typical…compared to what?

Simulation 1: come up with a method to simulate experiment using a deck of cards.  Discussion of ideas.  Ran experiment, combined data and came to a conclusion.
Data set 2: number of drivers, talking on cell phone who missed their exit from the simulation.

Do I really understand what the plot represents?  Where does my statistic of my sample fit?

Case, Sample, Population
Case-subject, variable -information about my case (categorical or numerical)
Sample, statisitc-always numerical
Population-everything that can happen, parameter

How often should I identify these myself to get it down?  I feel these are things that must become second nature for my students.  I suppose I will ask for these quite often.

Case:  driver talking on cell phone or passenger,
Variable: missed exit or didn’t
Sample: # talking on cell phone & missed the exit
Population: 48 who volunteered, bc experimental, really no population…

Data Set 3: measure length of peanuts in the shell
Data set 4: desk widths

When we begin to look at stem-leaf plot, is the detail there? Am I seeing what I want to see?  May need to split depending on size of set and am I seeing what I need to see?  How do we know when to split or not…let my sudents play around with it-let them see it, explore, build in fiddle time for them to experience it.

With the peanut data, based on our 6 pieces of data, we were asked to predict what we thought graph would look like. 
Everyone showed their white boards.  We got to asked questions….”why the dips/gaps?”  I wondered in a few of others’ sketches…

Unexpected to me to see bimodal behavior. 
The center and spread of bimodal is meaningless…discuss the clusters, and behavior around those. 
Pine needles from 2 types of trees always rssult in bimodal.

Did you know saving list of data in a program on TI84 saves memory?  handy tidbit to know.  Though he recommends Nspire, majority of participants have 84s available.

S.E.C.S
shape-describe patterns, peak, symmetry, skew
exceptions-outliers, gaps
center-what does my eye see?
spread-typical values
Try to create an image with your words.

These are some highlights from my first day at APSI at WKU.  Please feel free to offer corrections, ideas, clarify.  This truly is meant as a reflection to help me begin sorting all that I am learning this week.  I may not have tasted my tea on Monday, but I left with my mind running over…

Oh yeah, if you missed my tweet… @NationWide insurance sent me a giftcard to go purchase a #brandnew iced tea.  Turned my frown upside down!

Strength in Numbers

As mentioned in an earlier post, I started reading Ilana Seidel Horn’s Strength in Numbers just as the last month of school began. But as we all know, the end of the year takes over…EOCs, Finals, Prom, Graduation, closing days, packed up 1/2 of an entire school and stored it in our gymnasium for major renovations this summer.  Yep, my book went to the back burner.

Finally, today, I found time to jump in and start reading again…

…at the pool.  A friend’s mom jokingly asked, “Are you studying over there? Don’t rush it, school will be here soon enough.”  My reply, “Yep, reading a book I’ve been looking forward to for several weeks.  And yes, its mathy, I love me some math.”

Again, proof only my online PLN actually get me and my hunger to learn more.  And that’s okay.

Only 2 chapters completed between snacks, reapplying suncreen, having to leave for a camp meeting…but oh, my, so much to think about.

Some of my highlights…

Positive behavior comes from students’ engagement in the subject matter.

Four Principles for Equitable Mathematics Teaching:
   1. Learning is not the same as achievement. (So.true.  Never thought about it quite like this).
        Every student has something mathematically to contribute.
   2. Achievement gaps often reflect gaps in opportunities to learn.  (This one made me sad).
         “Instead of the blame game that begins when we view our students as low-achieving, we can think about how to re-create our classrooms and departments in ways that will increase the opportunities for students across achievement levels to learn by thinking mathematically.” Yes! Pg 14
    3. All students can be pushed to learn mathematics more deeply . (Sad. Again.  We fail to challenge them and provide interesting, engaging tasks).
        ” opportunity gaps affect all students.  A key characterisitic of an equitqble classroom is that ALL students are supported to substantially participate in each phase of instruction…”
   4. Students need to see themselves in mathematics. ( hmmm.  Ready to read more on this one for sure).
       “Mathematics as a subject , has a reputation for being interesting to a narrow group of people… students often feel mathematics allows no room for questioning… in didactic teaching situations, students feel their job is to receive preexisting knowledge.”

I am excited to continue Strength in Numbers.  Already, its challenged me and given me some things to think about…how I can recognize the difference in learning and achievement, how I can look for ways for every student to engage everyday…

…that I am providing opportunities for my highest achieving to learn and move forward just the same as my middle of the road learners and those who struggle as well.  An email this spring from a parent proved this point, ” in 12 years of school, I have not once had a teacher contact me…”  This is a gifted, creative learner who achieves above their peers.  However, I was not seeing growth for them as I had seen in their peers.  Yes, this student was above proficiency, but that didn’t mean my job was finished.  They needed to grow too.  And I was concerned…was it something in my teaching that I needed to adjust?  In order to help every one of my students, I must constantly reflect on my practices and adjust…

So I will continue reading and thinking on these 4 principles-how they are supported or need to be considered in my own classroom.

Adventures in Geocaching

This week my nephews are in town.  They love playing outdoors, have crazy fun imaginations and are loads of laughter.  My 10 year counts down the days each year until they arrive at gramma’s!  Its more exciting than end of school countdown.

On Tuesday I was brainstorming with mom and looked into geocaching.  I had never been, only heard it mentioned a few times and needed to learn how it worked.  So I went to geocaching.com registered an account, downloaded the app and yesterday, we set off on our first adventure.

Though most were the grab and go – the kids enjoyed it and were super excited when we found a cache filled with kids party favor swag.  Only problem, we had to scavenger the car to find some trade items…a creative venture in itself. 

Each find has a log where you date and sign to prove you were there.  There are hints, clues on the app if you have trouble locating it.  For example, one clue was Australia.  We looked around trying to connect something with that and finally “down-under.”  Sure enough, the cache was underneath the landmark.

We found 10 on our first day and learned some great tips.  We even saw a robin’s egg that had fallen from the nest, a double rainbow as we drove from place to place, played on a playground and visited the gravesite of their great grandparents as one cache was near the cemetary.

Some very clever hiding techniques!  One cache was so tiny, we thought it was only a magnet that had lost its container somehow!  It took a while to roll the log back small enough to place in it again!

Some where along the way, someone asked if I could spell supercalifragilisticexpealidocious (sp?).  My oldest nephew said, well, it shouldn’t be that difficult if you just break it apart.  True.  My response, most words are the same way.  For example, geocache.  Geo is earth, cache, a hiding place.  Which led me to geometry…geo, earth; metry, to measure.  I went on to explain how people wanted to measure distances, areas of land, patterns they noticed in the earth, so they created geometry. 

I explained how people noticed patterns with their shadows at different times of day.  I asked, when is your shadow longest, when is it shortest?  Without a hesitation, someone popped up, when the sun is on the horizon, your shadow is longest, when the sun is above you, your shadow is shortest.  I asked how do you know?  One said well, we learned that in science, but if you think about it, it just makes sense.

Again, I am convinced we force too many ideas on our students rather than just letting them think about it and develop their own sense of reasoning.

On our earlier finds, I allowed the kids to look at the GPS readings on the app.  They had to decide which direction to go -are we too close or too far north, and how far to walk.  We needed to moved west once and they could use the compass corectly, but I asked, what if we didnt have it pointing out the directions for us?  I explained how the sun sat to the west and each time after that, they immediately gauged direction based on the sun.

When I returned home after dark, I tweeted of our adventures.  In a convo,

So, now I am curious…how can/are teachers using geocaching as a context for learning?

#made4math Monday: Learning Target Quiz Cards

Last year I wanted a file for each course, with sample questions addressing the learning targets to use as either an intervention or for retake quizzes.

Different suggestions were made in a discussion on Twitter regarding organization, offering different levels of questions.  This morning, I am trying to plan out my format.

Here is what I have come up with so far:

Supplies:

Standards/Learning Targets
Index Cards
Index Card Dividers (Tina suggested coupon organizers for built in dividers)
Markers/Pens

I chose a standard.  Labeled my divider and thought it might be handy to write out the actual standard.  (Yes, this could be done with printed labels).

I am using level colors that coordinate with our Discovery Ed. Benchmarking system.

  L1-red, is the very minimal; L2-yellow, shows more understanding;

L3-green, is where I want to get everyone (this set came from Illustrative Mathematics Project); L4-blue, are open questions for this example anyway…may need to change this later.

I am including answers on the back for guick-check.

These are a quick, rough sketch…trying to iron out my goal, how I want to use them.

My idea is to have a coupon/photo organizer for each unit I teach.  Use actual learning targets from our unit organizer in order to move Algebra 2 closer to SBG.

Suggestions for improvments or your own experiences are welcomed!

First Day of Summer Break #MTBoS30 Post 23 non math

One of my favorite down times is a bit of sewing.  So the first day of summer break, I put off doing laundry (gasp) and got to work on some quick projects.

My 10 yo will be attending camp in just a few weeks.  Since the beloved pet cannot travel along, she chose some kitty fabric for a pillowcase.

For all that dirty laundry, I wanted to help her keep it all together.   With some green chevron she picked out, a laundry bag, complete with shoulder strap.

Finally, something I saw last spring at a swim shop.  Jammer/Capris made from a beach towel.  Great cover up for those late evening meets.

#readthree Summer Challenge #MTBoS30 Post 22

Last summer I wrote a post after a tweet from @burgess_shelley (she’s married to that Pirate guy)…but I enjoy reading her journey and experiences as an educational learner and leader!

Time to read the blogosphere is sometimes put on the back burner during the school year.  I hate this because interacting with #MTBoS challenges me to be a better teacher.  But it happens.

So today, I offer this challenge (again) to myself, but feel free to join in.  Read posts from 3 people you follow on twitter.  If you cannot do it daily, set a goal for yourself. I am challenging myself to 4 days a week and one day to reflect and share my take-a-ways by compiling my to-do list for next year. 

My intentions for next year are to incorporate more hands-on labs/data collection, focus on vocabulary and literacy strategies to empower student reasoning (writing and summarizing, @druinok!), providing more purposeful interactions/discussions (Strength in Numbers, @tchmathculture!) and planning more engaging tasks/activities.  Hopefully these goals will guide my focus in this challenge.

I am looking forward to reading from some new bloggers as well as catching up with those tried & true!

Summer Kick-Off with Colleagues #MTBoS30 Post 21

Following our final teacher workday, several colleagues gathered at Nail Spa in town for a late afternoon of pampering, yummy treats and girl time.

Its important to develop and nurture healthy relationships with colleagues…they’re your support system on a daily basis, your soundboard when seeking a new challenge and your accountability when you begin to vere.  In my opinion, a healthy school culture begins with the heart of the teachers.

I have some amazing and passionate colleagues.  It was a great afternoon.  We missed those who were not able to join us.

A recipe from our gathering…

Wondering if you added crushed pineapple to the cake mix…

A family member has made something similar using chocolate cake with toasted almonds and coconut as topping. Delicious.

Inverse Functions #MTBoS30 Post 20

This week we wrapped up our school year with 2 final teacher work days.  One day our department had some time to reflect onmour year.  One of our big issue is the immense amount Kentucky requires in Algebra 2.  Its nearly impossible to ‘cover’ it all, much less allow struggling math students time to process and develop a slight understanding.

I, personally, don’t worry with getting it all in.  I attempt to make the students’ time worthwhile and hopefully they leave with some deeper understanding about concepts rather than a list of procedures only 30% may be able to recall at any given time.

Anyway, we attempted to pick out 10 Big Rocks for our focus next year..the non-negotiables in a sense and that is where we will begin.  Sure we will have the “extras” ready should we achieve at a faster pace than expected.  But the goal is to truly develop reasoning and conceptual understanding of our Big Rocks.

While looking over the outline, there were a couple of things I remember thinking we needed to ensure we focused on during our functions unit.  1) composition of functions, not just in equation form, but to make sure we look at them numerically in a table of values and graphically as well. 2) a different approach to finding inverse functions.

It was Sam’s post that made me wonder if this way would make more sense for our students.
Looking at “x” think about and list order of operations.  Then, in reverse, list inverse operations and apply to x to get the inverse function.

Inverse operations and inverse order.
Is this a strategy others use as well?  A couple of colleagues seemed to really like this.
Wondering what situations it may not work…or at least reasons I shouldn’t use this approach.  Is there anything that follows this would cause issues for my students?

One good thing… #MTBoS30 Post 19

Our county fair is in full swing this week.  Our Jaycees arranged a free day for special needs children in our community and their families to enjoy.

Loved this post by a colleague who adores her family, is passionate about teaching English and capturing life-moments through photography.

“The Russell County Jaycees arranged for the carnival at the fair to be open and free to special needs children and their families today.  As the mother of an autistic child, I know I can never put into words how grateful I am for the people who made that happen and treated us with such kindness today.  Finley had a blast riding rides with his big brother (and his daddy), and we enjoyed a stress-free family outing, which rarely happens for us.”

Thankful to live in a community of people who care…

Thanks Lindsay for letting me share this one good thing!