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My CLMS Speech: It’s a great time to be a teacher!

8 Dec

I was recently given the honor of California League of Middle School (CLMS) Educator of the Year for my school. I was asked to give a speech that responds to the following prompt.  Transitioning to Common Core State Standards:  How do you engage your students and colleagues in changes to the classroom?    I was initially underwhelmed with the prompt, but in the end I was pleased with my speech.  I hope you enjoy it. Here it is  (of course, left off my preamble of thank you’s).

It’s a great time to be a teacher. Why? We are having a Renaissance in education. I started teaching about 10 years ago. I had my overhead projector, my colorful Vis a Vis markers, and, of course, I spent many an hour cleaning those darn transparencies. Over the years, tools entered my classroom to make my life easier: the document camera, the LCD projector, the iPad, and even the Smart Board. But the tools, in themselves, didn’t improve my teaching or the students’ learning. Things don’t do that, ideas do. The common core practices inspired me to question and reflect on how to best help kids discover, think, collaborate, model, and explain their thought process. Coincidently or perhaps not so coincidently, there are additional factors currently impacting my perspective and teaching style: the growth mindset (that mistakes are a necessary part of growing the math brain), the maker movement, STEM initiatives, expanding my expertise through MOOCs, and sharing best practices with the larger teacher community through blogging. It sure is an interesting time.

I’m a math and STEM teacher. As a math teacher, common core gave me some room to go deeper into topics, letting the students learn more authentically, investigating certain ideas, working on projects, sharing out their observations. A popular new practice in many math classrooms, including mine, is number talks. It’s where kids mentally strategize how to work out particular puzzles, patterns, or numeric expressions, such as 21 x 19. It’s amazing the learning that happens during these sessions. Kids are decomposing numbers, rearranging them, putting back together. You hear kids say, “What, you can do that?” Talk about AHAs, they’re rolling in. So how do I engage students in changes to the classroom? I ask them questions that make them think, and then I listen.

As a STEM teacher, it’s fascinating to watch my students connect what they learn in their core classes with hands-on engineering projects. My 8th graders are designing 3d models, printing them out on our 3d printer, building robots to accomplish particular tasks, learning how to code, getting first hand experience with the design cycle, and presenting their creations to their peers and others. They are little engineers! It’s funny, about 10 years ago I left my engineering career to go into teaching, and now my teaching career is going into engineering.

By the way, it’s not just a great learning time for our students, but us teachers are really walking the talk of being lifetime learners.   Out of all the confusion and initial frustration with common core, came the best collaboration I’ve experienced as a teacher. Now, practically everyday my cohort of math teachers talk about: what, when, why and how we’re teaching what we’re teaching. It’s so motivating to be surrounded by forward-thinking colleagues who get excited when we discover more effective ways to teach and reach our students.

So yes, I think education is experiencing a Renaissance; a rebirth of ideas, and it’s exciting to be part of the community, shaping it and breathing new life into it. It is a great time to be a teacher!

Pperfect Squares: Breaking the 1000 barrier

12 Oct

It’s always so much fun teaching the namesake of this blog, pperfect squares.  I printed out the lyrics of the song, and together my students and I sang it. The next day, I had them, in partners, list out all the perfect squares beginning with 1. For the next 10 minutes, they were to list as many as possible, in order, on the big white boards. Can you break the 1000 barrier?  The kids work so hard to do this, and about 75% did! Some stayed after the bell to get it.  A week later when we learned about perfect cubes, a student, who loves to rap, created a pperfect cube rap and performed it for the class. It was so entertaining!

Here’s some pics of the kids breaking the 1000 perfect square barrier:


Yes to Retakes and No to Zeros

18 Feb

Back in 2008 I attended the ETS conference on Assessment for Learning, and Ken O’Connor’s breakout on grading  had a lasting effect on me.

Regarding retakes, he gave the compelling argument regarding parachute packing. Do you want to use the parachute from the packer who was doing excellent packing work but recently got sloppy with the packing, or the packer who started off badly, but has been doing perfect packing in recent weeks? I would go with the latter. What matters is that the student eventually learns how to master the topic, and not all students learn at the same rate. Here’s my retake philosophy this year:

  • Only one retake allowed (from my experience if a student doesn’t study and get help before first retake, they don’t do it for subsequent ones either)
  • Students must retake assessment week following original (implemented this because students were waiting too long)
  • Retake score overrides original score (good or bad; this encourages studying)
  • In the gradebook, in the comment field for that student’s test grade, I document that the student retook the quiz, and I state the original and retake score.

I think it was Ken O’Connor who also introduced me to the no-zero grading policy. Why are grades A-B-C-D all separated by 10% point while we give the F a 50% band? If a student falls into this F abyss, they may never get out even after they have worked hard their grades begin to get better We all know how averages can be skewed.  For more information on this, read Douglas Reeves’ article, Case Against Zero. Here’s my no-zero philosophy this year:

  • Apply no-zero philosophy on assessments
  • If students get a 25% on a test, I put 25% on the test that I hand back to the student; however, I enter 50.25 into the gradebook. This lets me retain the actual grade info while still giving them a 50% F.

Both of these policies, retakes and no-zeros on  assessments give students a second chance to succeed. They are also great discussion points when talking with parents on how their child can improve in my class. There is never a time when a student should lose hope.

Constraining Horizontal/Vertical lines via Desmos

18 Jan

Students seem to always have trouble grasping that x=2 is a vertical line, and that y=2 is a horizontal line. I understand their issue with this;  x is the horizontal axis yet x=2 is a vertical line. Boy, that’s confusing! In class we talk about how it’s counter-intuitive, and we repeat the “x=2 is vertical because it cuts through the x axis at 2”. To help the students understand this more, and to get in more domain and range practice, I had them write their initials in Desmos. A good structured yet open-ended activity where students could go simple with basic block letters or get creative with more curves (parabolas), etc.


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My students get creative with Desmos

30 Nov

Last week I introduced my students to Desmos. After doing a short lesson to show off the power and “what-if” capabilities of desmos, I pretty much let them loose on creating equation-driven art. My main objective here was for students to get a deeper understanding of linear equations, and specifically more experience with restricting the domain and/or range of a linear equation. So I showed the students how to restrict the domain and range, and my only requirement of the art is that they include at least one instance of a restricted domain/range.  Very soon the kids wanted to know how to create and manipulate parabolas, circles, sine waves, etc.  The students absolutely loved this activity; I was hearing comments like “Desmos is the best app I ever”, and “oh, now I see how that works”.  I gave them two class periods to work on their art, and told them they can complete it at home and save it to the  google folder they have shared with me. Here’s some of the artwork I received back. This first one, the Hunger Games’ Mockingjay uses 40 equations and the student worked on it for over 3 hours.


To see Mockingjay in all its glory in Desmos:


To see butterfly in Desmos:


To see Birds by the Sea in Desmos:


To see star in circles in Desmos:

Halloween: Scary Graphing Stories

31 Oct

This was a hoot! A couple of weeks my algebra students and I were going over graphing relationships. I had a story about Bob driving a car to demonstrate a speed .vs. time continuous graph. Later we used the example of a squirrel gathering acorns to demonstrate a discrete graph. The students started mashing the stories together to create a story and graph of Bob chasing the squirrel….it didn’t end well.

Anyway, scary graphing stories were born. So today for Halloween, I created this Scary Graphing Stories worksheet. After the students created the stories, we shared out. Here’s a small sampling of student work:

What makes my classroom uniquely mine? My ears.

12 Oct

What makes my classroom uniquely mine? Well, my students would probably say my occasional rapping and our many choral response ditties.

But when I think about what I do that I am most proud of, I think about the questions I pose to them and how I listen to their ideas… (btw, these are all a work in progress):

— Really listening to student ideas and learning from them!  I try to follow their train of thought, and I try to  be open to allowing them to  adjust my thinking. This reminds me of something interesting that happened a couple of weeks ago. I gave the students a MARS performance task  where they had to create an equation for a situation. The graph of the situation was a horizontal line (constant > 0)  that  at a given point increased linearly. The rubric expected the students to create an equation for the linearly increasing piece only.  So when one of my students said he had created an equation for the entire graph, I listened although I was, inside, skeptical, that it would work.  As a class we tested his equation, and amazingly it works. The equation included an expression in absolute value, and it was really brilliant. I am so glad I listened.

— Asking open-ended questions for the students to think about. When they respond to a question, I try to ask clarifying follow-up questions. It’s exhausting sometimes, but worth it.

— Lately I’ve been trying to get the class to answer each others questions more.  I’m trying to follow the advice: A teacher should never answer a student question that another student in the class can answer.

— Each week, as part of their homework for the week, my students write about a reflection topic that I give them. These are topics where they either synthesize information we’ve gone over recently  or think more critically or creatively about a topic. Some examples are:

  • What’s the difference between 0/x and x/0? Is there a way to prove why they evaluate to differently?
  • Create a math story for the equation 3(x+2) + 5 = 23 . What is x in your story? Solve equation. Does the solution make sense for your story?
  • Summarize the conditions for when you would get a compound inequality, a single inequality, no solution , or all real numbers as the solution for an absolute value inequalities.

I love these. I think it gives students a chance to use the math vocabulary in their own words, to organize their thoughts, and to respond creatively in order to make more sense of a topic. A little time consuming to grade, but many of these response put a smile on my face. Math teachers don’t get to see original written work like this enough.