Math = Love: Reflecting on Concept Maps in Algebra

Wednesday, May 7, 2014

Reflecting on Concept Maps in Algebra

As part of OGAP (Oklahoma Geometry and Algebra Project), I was required to have my students complete concept maps at the beginning and end of the school year.

To be honest, the concept maps at the beginning of the school year were extremely depressing.  I need to dig them back out of my filing cabinet and take pictures so you can see the difference a year makes!

As I went through the concept maps, a few things caught my eye.  And, I think they require reflection.  Since I blog about everything else, I thought I would blog my reflections, too.

These take 10 minutes twice a year to do.  They help me reflect on my teaching and my students' learning.  It's TIME WELL SPENT.  

(You have been forewarned - this is probably my longest post ever!)

Reflections begin now!

Songs help students remember!  I tried several songs to help students with memorizing the quadratic formula.  But, nothing beats Pop Goes The Weasel!

And, no matter how hard I try, I can't get my students to remember the proper names for the conic sections.  Hyperbole.  Eclipse.  Oh my...

I think this might be one of my favorite concept maps.

Algebra -> Thinking -> Hard Work -> Keep Trying -> Try Again -> SUCCESS

Last year, my Algebra 2 students had a terrible time remembering that solution, root, zero, and x-intercept all meant the exact same thing.  This year, I was a teacher with a mission.  I introduced those words in Unit 1, and we practiced them ALL year long!  By the end of the year, I could ask "What words mean the same thing as x-intercept?"  And, the entire class could rattle them off without breaking a sweat.  I saw these show up in multiple concept maps.

My students memorize and learn what I emphasize.  This summer, I need to really reflect on what I am emphasizing.  This will impact what my students learn.

Next year, our first algebra lesson is going to be on how to spell algebra!

This concept map is by a student who struggled.  A lot.  And, she didn't seek out help.  I don't quite know how to help students who don't want my help.

The more I teach, the more I learn to let my personality shine through all that I do in my classroom.  This means taking time to let kids see who I am outside the classroom.  And, I'm learning to take time to see who kids are outside my classroom.  One of the ways I've done that this year is through Good Things Mondays, Wacky Wednesdays, and Funny Fridays.  I like that this student recognized this in her concept map!

Slope Dude also got a mention.  But, that's no surprise.  It's still my most favorite video to show in class!

I try to make algebra as fun as possible.  Some days are more fun than others.  It feels good for a student to recognize this fact.  Of course, I'm sure a lot of students would disagree.

Notes are important!!!!  Yes!

I also adopted a new policy part way through the year.  No work.  No grade.  If you're going to copy off your neighbor, at least copy all of their work.  Maybe you'll learn something in the process.  Nothing drives me crazier than a worksheet on adding and subtracting rational expressions that has only answers.  I started giving students a zero on the assignment until they could produce the work that went with it.

Cruel?  Maybe.  In their best interest?  Yes.  Led to students asking for help?  YES!  And, that's my goal.  Students need to recognize that they need help, and then students need to seek it out.

Algebra II = Confusing Math

My goal next year?  Make the course more cohesive.  I think it would be less confusing for students if I designed the course in such a way that the units fit together and flowed from one to another.

Algebra is sometimes confusing.  Yes, yes it is.

Algebra requires thinking.  ABSOLUTELY!  I have done my job!

This student says that Algebra 2 is hard, boring, not easy, confusing, and something they don't want to do.  But, they also admit that there is "a lot of thinking" involved.  Thinking happens in my classroom.  Students may not like it, and that's okay.

Hardest Class Ever.  Boring.  Complicated.  Can't understand it.  Not as fun.  Hard.

Every teacher's favorite question: When are we going to use this?

Teamwork.  It's okay sometimes.

This is a start.  This is a student who hasn't been successful with math in the past.  So, for them to admit that it's okay sometimes is a major leap forward.

Sometimes.  I see this word quite a bit on these maps.  I take this to mean that my class has challenged students' preconceptions of what math class will be like.

"Sometimes fun" means that they may have never viewed math as fun before.

"Sometimes irritating" means that they may have always viewed math as irritating before.

Algebra 2 means learning a lot of words.  Yes, vocabulary was one of my areas of emphasis this year.

I'm hoping that "zero fun" is meant as homage to Slope Dude and not a description of my class.  :)

Classroom management is a real struggle for me.  This year, my management has improved.  But, that has meant that my management has been inconsistent.  I let students get away with so many things during the first semester.  And, I toughened up the second semester.

Remember my cell phone policy?  Can't talk at all.  Can't plan on your phone.  Or Ms. Hagan will take it away I know.  This student learned the hard way!

This student reflected on their previous and future mathematical plans which I found quite interesting.  They hated Algebra 1.  They surprisingly enjoyed Algebra 2.  (YAY!)  And, they won't be taking Calculus.  In a way, this breaks my heart.  Should every student take calculus?  Definitely not.  But, I teach in a district where most students think calculus is something they would never be capable of taking.  I'm slowly working on changing that.  But, it's a much longer journey than I anticipated.

Some areas of some concept maps weren't quite as focused on Algebra as I had anticipated.  But, I love learning new things about my students.

Algebra II = "Favorite Educational Class"  I'll take that!

"Hateful calculators."  This student absolutely refused to solve problems with a graphing calculator.  He was continually asking me how to solve a problem without the calculator.  When time allowed, I gladly explained the process.  I applaud his curiosity.  I wish I had more students with a desire to learn multiple methods of solving a problem!

"Paper wasted.  Glue lost."  I'm assuming he was also not a fan of the interactive notebooks.

"Learned a lot o' math."  Yes!

"A long journey completed."  "Hours of sleep lost."  Some of my students needed to lose a few more hours of sleep so they could actually complete their homework...  

Slope Dude strikes again!  I made my students always pronounce "undefined" as if they were skiing off a cliff.  "Undefiiiiiined"!

And, the circle that says "fun" may not be very large, but I'm happy to see it there!

Apparently, Algebra "sukkz."

I'm really hoping that "EOI'z wur hard" was an intentional misspelling.  They also noted that they were often ineligible in my class.

Algebra - the study of "invisible numbers."   I'm pretty sure they meant imaginary numbers.  Must work more on vocab next year!

Colorful writing.  Songs.  Notes.  Graphing Calculators.

I hate how many times EOI shows up in these concept maps.  But, I guess that's my fault.  Our students focus on what we emphasize.  From the beginning of the year, I told my students that they had to pass their EOI.  In Oklahoma, students are required to pass an EOI in Algebra 1, English 2, and two other subjects in order to be eligible to receive a diploma.  Each school is graded based on how students perform on these tests.

Can we just please do away with high stakes testing so I can get back to focusing on math and problem solving strategies and higher level thinking skills instead of test prep?

Long division is time consuming and surprisingly easy.

EOI -> passed -> happy feelings  

Notes = Study Objects

Words cannot express how much I love reading that!

Let's just say we learned a lot of stuff in Algebra 2 this year!

This map wasn't as large as some, but I adore it.  First off, they drew their own mapping diagram of a function.  This student made the highest score in the school on the Algebra 1 test.  I guess I shouldn't be surprised that produced the most educational concept map of the day.

I love how this student couldn't remember what the E stood for in PEMDAS, so he described it instead.  And, functions are all about inputs and outputs.  I call that a win!  

Learning.  Entertaining.  Fun.  Irritation.  Worksheets.  (Okay - not so proud of those last two.  I don't want worksheets to be the thing that my students remember about my class.)  Hexahedron.  <- My students were super excited about the origami!

Algebra = life.  I agree.

People cry.  I have made some students cry this year.  I don't think I made this particular student cry, though.

Feelings get hurt.  This makes me sad.  My classroom should be a positive, happy place.

And, I hate that they wrote sitting on their concept maps.  I try to get students out of their seats as much as possible.  I need to do a better job of this, though!

Want to know the meaning of life according to one of my students?

People fly.  People die.  People try.  People cry.

This map is depressing.  Algebra is useless, a waste of time, meaningless, and dumb.

Math is "hard work" and a "lot of fun."  This one makes me feel better.  I shouldn't take these comments so personally, but I do.  As an education student in college, I thought I would reach 100% of my students.  No students would slip through the cracks.  That's a fine ideal, but that's not reality.  I can only help students that want to be helped.

Fun Work.  Fun Games.  Fun Projects.  I'm liking the sound of this!

I would't call myself the best algebra teacher.  But, I try.

Thanks for sticking with my reflections this far!  Have you ever done concept maps with your students?  I'd love to hear about it!


  1. Sarah, would you mind sharing the prompt you gave students so they would create these? I absolutely love the idea, but I'm not quite sure what to ask the students to do, so that they'd understand the task but there would be room for creativity in the responses.

    1. Sure! Here's the instructions I was given to do the concept maps.

      Ask if students are familiar with content maps, flowcharts, that kind of thing. Tell them that we’re going to be asking them to make a map related to algebra…but first…
      …just to make sure that we all start on the same page, we’ll do a short practice one on a concept familiar to nearly everyone: Teenagers.

      Draw a circle on the board with Teenagers written inside it, and collect student input as to ideas related to teenagers. As they give you input, put it in the appropriate place – either directly connected to the main concept (teenagers) or as an offshoot of a sub-concept. Do not go into detail about the structure of the map beyond ensuring that you have illustrated both the spider-type map and at least one hierarchy.

      Illustrate how their ideas go on a map…and note that, if we finished it completely, we’d have a map of all the things that were important about teenagers.

      Please get out a clean sheet of paper.

      Please put your first name and last initial in top right-hand corner. Put the date under your name. Put the name of your teacher under the date and OGAP under your teacher’s name.

      Write ALGEBRA or GEOMETRY in the center of your page. Tell them they will have about 10 minutes to make a map of everything they know about algebra or geometry. Remind them to connect words or phrases with lines so that we can follow them. Ask them to do their best work and remind them that this is an individual assessment, so please don’t share anything about their maps until everyone is finished.

  2. Sarah - you mention Funny Fridays and Wacky Wednesdays in your post. I am intrigued! Do you have other posts explaining these days? I was unable to find either when searching. Thanks for sharing your ideas and resources. LOVE your blog!

    1. Hey Tish! Thanks so much for reading my blog. It means a lot to me! I can't believe that I've never written about Wacky Wednesdays and Friday Funnies. I wrote a blog post specifically about them today to make up for it. Enjoy!

  3. Great ideas to use concept maps to measure how much they learned! I also use concept maps and I have learned some tips on How to Make a Concept Map using Lucidchart and it is very helpful and user friendly! Check it out!

  4. I truly love reading your blog. These concept maps were a great idea! I also agree that I have to reorganize my algebra 2 curriculum to flow better as well as prepare for the parcc March and May test. Do you have any ideas? Thanks!

    1. We're no longer a PARCC or CCSS state, so I'm at a loss for advice to share with you. Good luck! And, thanks for reading my blog!