It is "D"! Really?

Had an interesting conversation after a test yesterday.

We teach parent functions ... and the current one is the absolute value function.

There were several questions on the test that stumped students but this one I just don't understand.

So we practice ... show me the absolute value parent function with your arms.  Is the absolute value PARENT function ever negative ... no!  What is it's equation ... yes ... always y = |x|.  What if I reflect the graph ... what is the parent function?  The parent function is always positive, it's always y =|x|.

Enter test question:
What is the parent function that represents the data below?

Yes ... a few of our questions are multiple choice.  They are rare but we do it to model other standardized testing.

I haven't actually counted the test papers ... but close to half of the students chose D.

So ... a young man finished his test and was getting ready to leave class.  He said he was sure he did well and he typically does quite well.

I was curious though how this one question went ... so I said ... tell me again about the parent function?  He laughed ... ma'am it is always positive!

Super, I said, and showed him a Desmos graph of the points above.  Tell me then ... what is the parent function for this set of data?  What answer did you choose?

Ummmm ... D!

Really!?!  the parent function is always positive?

The teenage brain ... who can say?

#MTBoSChallenge Week 11 Summary

So this past week was difficult because I was sick.  What I thought would be a simple 24 hour virus, turned into two days of high fever, and a yucky feeling that persisted most of the week!

And so the week did not go as planned.  In my summary today, I want to highlight the one GOOD thing ... and then reflect on the not so good.

The one good thing is that when I realized I was going to miss school, I had a light bulb moment of how to maximize students' time using technology.  We were starting a new unit on absolute value.  The unit is short - just 3 lesson days ... and the concepts fairly straight forward.

Students will know...

• the relationship between linear functions and absolute value functions
• the critical attributes of an absolute value function

Students will be able to...

• determine the domain and range of an absolute value function
• graph an absolute value function from a table or equation
• solve an absolute value equation an/or inequality
• apply transformations to the parent function to graph an absolute value function

So ... I used Regents Prep intro to absolute value and the corresponding practice page to remind students of the basic meaning of absolute value.  Then I sent them to Desmos where I had put in a few equations for them to examine ... to identify the vertex, the axis of symmetry, and to determine the transformation from the parent function.  Last I sent them to a set of videos- two I had made previously, and 2 created by our textbook, to introduce them to solving.  I provided online solving practice using the Regents Prep site, and then additional practice for them to do in their notebook.  I collected all of their responses in a Google Form so I would have a record of their work, and also it provided formative assessment for me to determine where to jump in when I returned to school.  My supervisor told me later that he stopped by my classroom while I was out because he knew the students were working from their computers.  He said when he asked them what they were working on, they could tell him exactly what they were learning!  Kudos to my students :)

I graded a portion of their sub day work - the part about transformations since that information is not new.  We introduce the parameters a, h, and k in our first unit.  I noted that students still have difficulty writing the equation of a vertical line so some did not write the equation for the axis of symmetry correctly.  Many did solve the equations correctly - I was pleased with their work.  A few missed the concept that absolute value equations would have 2 solutions.

Returning to school was difficult simply because I didn't feel good - so enthusiasm, excitement for learning, smiles ... all of those were challenging at best!  And on that day I returned I knew I needed to be sure that students grasped the meaning of absolute value.  I had assigned mini-projects, data collection, guessing game type ... and told students we would use their data to develop absolute value equations.  So that's where we started.  I used Estimation 180, candy corn to illustrate.  From there we spent time composing and decomposing absolute value functions illustrating that they are piecewise functions, made up of two linear functions with restricted domains.  And last we solved equations & inequalities.  It was a lot for one class period ... and I talked too much!

So the not so good thing was my over-explaining on the day of my return.  Students were much too passive, and I did way too much of the work.  It was an over-reaction on my part to be sure that I left no gaps in their learning.

Is it better for students to work through concepts on their own with minimal direct teaching?  Most of the time, YES!  But then how do you summarize the key points, leaving no student behind in the details?  That was my subconscious struggle on the day I returned.

Finally the week came to an end ... and I've spent this weekend resting.  I backed out of all other commitments in order to stay home and be still.

Going into the coming week, students will take a short quiz over the meaning of absolute value, practice solving equations/inequalities in a circuit, and apply the concepts to a few problem situations with partners.  Our test is Tuesday/Wednesday.

Mini-Project Absolute Value

I saw this idea on Growing Exponentially (H Kohn)'s blog.

Students ask 25 people a question that has a numerical answer.  The question should evoke responses above and below the actual answer.

Then they create a graph of the responses, analyze their graph, and illustrate their poster.

My students are putting their work in Google slides.

Here are the first few submitted ... love to show off my students' work!

Student Blogging - have to share

Just have to share two student blogs I read this morning - polar opposites - one creative, one logical - both awesome!

In Depth: Matrix Multiplication ~ Tips and Tricks #1

A Terrible Matrix Tragedy

Obviously students are just finishing up their unit on matrices.  We test on Thursday and Friday this week.  Their blogging challenge is open-ended.  There are no specific prompts.  I provided students with a grading checklist that includes these key items:

Content related to math

Connections to our course content or other school content

Critical or creative point

Substantive

Enhanced with pictures, video, or links

Loving what my students can do when given just a small push in writing.

#MTBoSChallenge Week 9 Summary

#MTBoS Challenge

My Summary of Week 9

3 Engaging Activities

1. I wrote about our math oases, islands of study, in this post.  Students were highly engaged and the practice was worthwhile!
2. We also worked through 8 stations in class this week.  I love station work because students again are talking the math, working together to solve problems, checking their work with my key, and when necessary hunting down their errors.  My only concern this time around was that our time was short, so I didn't grade the stations.  A few students took advantage of that.  I need a way to hold students accountable that doesn't end in a grade.  I should have continued the hole-punches that I used the day before on the study islands.
3. The third engaging activity is happening on Tuesday.  It's a review game, ZAP (I wrote about it last year).  I'm excited about the process of working problems out in small teams, calling on a random team member, and then using the surprise of the ZAP cards to add fun to the game.

2 Fun Activities this week ... Balancing Act

1. My husband and I don't get to the movies very often, but we did this weekend.  We saw The Judge.  I usually check Rotten Tomatoes for ratings ... and disagree wholeheartedly with the critics.  Both Robert Downey Jr and Robert Duvall give award winning performances!
2. I shopped briefly at Lakeshore Learning and Half Price Bookstores this weekend.  I found a construction set half-price at Lakeshore ... a new set to stimulate my grandsons' imaginations.  I didn't buy anything at the bookstore this time ... but I always enjoy browsing there.  It's very relaxing!

1 BIG WISH

I wish our district had a fall break.  Yes, I don't have students tomorrow, but I do have school, meetings, training.  I would gladly start school a few days earlier in August to have a 4 day weekend in October!

Island Study

So today's activity went very well.  The noise level was high ... but all due to constant math talk!  The very talk you want in your classrooms!  (I didn't post a picture with students - no faces allowed but here is a picture of our empty space ... waiting for students to arrive on the islands!)

This idea comes from Cheesemonkey's post ... read it here!  Thank you for sharing.

I am drowning in grading.  Giving feedback is a must!  This process is great for simplifying peer to peer feedback as well as teacher feedback.

To break up the monotony of working in desks, I brought in beach towels - 10 of them ... to create "islands" ... oases of math learning!  On each island there is a group whiteboard, 3 markers, 3 calculators, and necessary handouts (could be done without any but I'll explain why they were helpful).

As students entered they set their bags aside, brought only their math notebooks with them, selected an island and had a seat.  I required no more than 3 people to an island.  I had a few islands with just 2 people.

I gave each team an index card ... students put their names on it.

Then I gave instructions ... our topic of the day is solving systems using matrices.  The first half of class was practicing solving 2 x 2 matrices by hand, the second half of the day was practicing solving 3 x 3 matrices by calculator.  (We have 90 minutes ... every other day ... rotating schedule).

I projected 3 systems on the board.  In groups students solved each system using matrices ... clearly outlining the determinant, inverse matrix, and matrix multiplication.  As groups finished a problem I checked it and hole-punched their index card.  When punched, students immediately moved on to the next problem.  Groups had to rotate who did the writing and who coached.

As students finished the 3 systems that were projected, they moved to a handout with word problems - practicing the same skill but first finding the equations.  So having the handout served as a differentiation tool ... students who worked quickly through the projected problems could move forward.

Students clamored for their hole punches!  Amazing. Free.  Simple!

About half way through we switched gears so that students could learn how to solve systems of equations using their calculators.  To get a hole punch every member of the team had to have the answer on his/her calculator.

Teams earned about 12 - 16 hole punches in the class period.  BUT much more than that ... every student was coached in how to solve the problems of the day.  Every student got feedback.  Every student had support for the parts they found difficult.

And the energy was high.  The conversations totally about math.  And they clamored for their hole punches!  Amazing. Free. Simple!

#MTBoSChallenge Week 8 Summary

A summary ... the truth be told ... this last week was difficult.

Each day someone had something critical to say ... true or untrue ... didn't matter, still the criticism was offered, heard, absorbed.  The criticism threw me off kilter ... stymied the creative flow ... made work feel too much like work instead of the joy that teaching generally brings.

On top of that we gave a Unit test ... 2 part test ... so instead of 160 papers to grade, there were 320 papers to grade.  I did the math with my students.  If I spent just five minutes per paper - not much time to read through the work - it would take about 25 hours to grade them.  I needed a quick turn around because the marking period ended Friday.  Students needed the opportunity to see their tests, what errors they made, and to correct them if possible.  That made for long nights of grading.

And then this morning I opened my email.  I saw this note ...

Thanks for being [my son's] teacher. He really loves math.

And that reminded me that I had had similar notes this week ...

Thank you so much for the detailed analysis of [my son's] work.

[The videos] are very detailed and your pace has just the right balance…fast enough to keep their interest…and slow enough that they can grasp the material. Thank you for all you do!

It's good to hear [xxxxx] is doing so well. We all got a kick out of your comments in his ARD :)

I appreciate you contacting me to let me know. We will begin checking his grades weekly.

That sounds wonderful, thank you. We will support you and [xxxxx] in any way possible.

I can't tell you how relieved we were to get your reply tonight. Thank you so much for understanding and for the opportunity to place [xxxxxx] on the path for success.

You are wonderful! I was just bragging to friends that there are High School teachers who interact with parents. Thank you so much for the emails, my son doesn’t tell me anything.

Don't you wonder why even one criticism can block out all positive thoughts?

This weekend I've had time to regroup, step back, gain some perspective.

Looks like my classes are ending with 75% making As and Bs, almost 10% making Cs, almost 10% making Ds and 6% not successful YET!  I'm feeling good about those results knowing the kind of expectations we had this first marking period!

In the coming week students and I will be exploring matrices ... how to solve by hand and how to solve by calculator.  The lessons are very skill driven ... somewhat different than our usual focus.  The pace will be a bit slower, the instruction more direct.  My plan for Thursday/Friday are stations of sorts - thinking about using cheesemonkey's idea for group whiteboards and quick formative assessment.

I'm ready ... to see what the next week brings!

Front-Loading Instruction

Last year I used videos to provide an extension of tutoring - short videos that I created or found online that illustrated lessons already taught in the classroom.  Students used those videos to review concepts they found difficult.  And they seemed to appreciate them.

This year I decided to extend the use of video to front load instruction.  I ask students to watch 1 - 2 short videos (usually not more than 10 - 12 minutes) to preteach vocabulary or illustrate a skill.  Students take notes on the video ... but the notes are not checked ... just recommended.  Many students report that watching the video to know what's coming in the next lesson has already been helpful!

Here are examples of videos I've used for frontloading ... 

1. Before teaching parent functions and basic transformation, students watched this song.  The song introduces the linear, quadratic, and absolute functions with a few key characteristics of each ... all under 4 minutes.
2. Not every pre-teach activity has been a video.  I used Desmos to give students an opportunity to explore transformations before class.
3. Before teaching how to solve wind and current problems in our systems unit, I asked students to view this video.  I loved the graphics and thought it would help make the next class go more smoothly.  Most of my students this year did well on the wind/current problem on the test!  Hooray!
4. The other problems in the unit on systems of equations that give students fits are the mixture problems.  And although some students still struggled with these on the day of the test, I thought this video did a great job introducing the concept.

Finding really good videos that illustrate vocabulary or a skill is the challenge!  I wish I were more skilled (or had more time) to create some of my own!  

There are obviously times were pre-teaching would not be appropriate ... for example, a discovery lesson planned in class.  But most times, front-loading is not only appropriate but primes students to be ready for the lesson planned.

Note, the video front-loading does not replace teaching in the classroom.  This is not a "flipped" model ... not really even partially flipped since I don't ask students to work out any problems based on the video itself.  That is an area worth thinking about ... but right now, it is enough for me to use the video just as a preview of what is to come!

Currently October with a Treat!

It's October already ...

In beautiful central Texas, our morning was cool and our midday is mild!  Loving the open windows and fresh breezes!

Most of the Currently entries are self explanatory.  Notice the "trick or treat" ... I have a real treat for you!  I'm loving my students' blog posts!  So far the requirement has been to write just one post ... about any topic that is related to math in some way.  I invite you to check out all of our blogs - use this link as a jumping off place.

I'm also highlighting a few specific posts today ... check these out ...
Is a Member Card Really Worth It
Math News
Cantor's Diagonal Proof
Bohemian Mathsody
Math in Gaming
Euler's Sonnet
Shhh….Seven Super Secret Study Tips

There are many more ... such talented young men and women!  Love my students!!