Tag Archives: algebra 1

Let’s Build Some Bridges!

You’re either a genius, or the biggest idiot here.

– a colleague

Can’t I be both?


It’s the first year of Keystone testing here in Pennsylvania, and everyone is adjusting to the fun changes.  And by fun, I mean time-consuming,  nightmarish organizational hoops to jump through provided by our wonderful state government.  This year, many of our 8th graders get zapped with the testing equivalent of Haley’s Comet: state grade-level testing, along with grade-level tests in writing and science….followed by the cherry on the sundae, this week’s Keystone Exam in Algebra 1.  It’s a shock they ever have time to actually, you know….learn stuff.  Hoping our kids don’t suffer too much bubbling withdrawal at the end of this week.

We have about 400 8th graders here, and many of them will take the Algebra 1 test this week.  Some, around 80, took algebra 1 as 7th graders and have already passed the Keystone.  Meanwhile, 40 or so are in a pre-algebra course and will take the Keystone next year as 9th graders.  So, what to do with 120 students, while their grade-level friends endure a state test.  For two days, and 4 hours, I have been given carte-blanhce, an emtpy slate, to keep 120 8th graders entertained.  And money!  Well, some money anyway.  What would you do?

My BridgeTomorrow morning, 120 8th graders will meet with me in the auditorium to learn their fate.  I have split the kids into 26 groups of 4 or 5 and gathered supplies for a popsicle-stick bridge-building contest.  The concept and many guidelines came from the site TryEngineering, which provides many neat and simple tasks for kids to encourage creativity and discovery.  I have worked with a colleague from our high school, who teaches an intro to engineering course, whose students found some great resources to share with the kids to get them excited about the project.  Two short and snappy videos they found from MIT feature simple bridge designs, with Lego-men being experimented upon:  Part 1 and Part 2.

SuppliesThe supplies are simple:  each group will receive 200 popsicle sticks, a glue gun, and glue sticks.  Teams will only receive the glue gun after they have drawn some sketches and discussed a plan for their design.  Most of today was spent organizing 26 boxes of sticks, and getting groups ready.  Groups will be graded on their design, how much load their bridge will hold, and how well they work together as a team.  And about those groups….all groups have a similar mix of “advanced” kids and “pre-algebra” kids, which I have assigned beforehand.  This mix led to the “genius or idiot” comment above from a colleague.  Yep, this could go badly.  But, it could go great!  Its too tempting to not try!

So, tomorrow we start building bridges.  My coach friend Gayle and I built a bridge on our own, which you see above, and we were quite proud of ourselves.  If time permits on Wednesday, we will test the strength of the bridges.  Our bridge snapped at 7000 grams.  But I am confident the kids will do a better job.

Looking forward to a fun, but chaotic, time the next 2 days!

Load Test 1

Load Test 2


This Week’s Required Reading for Algebra Teachers!

Mid-April, that time of year where teachers and students start to see the finish-line of the school year.  Everyone feels the burdens…state testing, class distractions, covering all the “material”….teachers have a lot on their plate.  But it’s also a great time to reflect upon the past year, work in teams to consider best-practice, and plan changes for next year.  Two intriguing blog posts by Grant Wiggins this week should be required reading for all secondary math teachers.

First, Grant Wiggins rants against courses we call algebra 1.  What could be wrong with Algebra 1?  We all took it, we all agree kids “need” it, and isn’t a proven gate-keeper to college success?

Algebra, as we teach it, is a death march through endless disconnected technical tools and tips, out of context. It would be like signing up for carpentry and spending an entire year being taught all the tools that have ever existed in a toolbox, and being quizzed on their names – but without ever experiencing what you can craft with such tools or how to decide which tools to use when in the face of a design problem.

Amen, brother.  In algebra, we move from the unit of linear functions, to the unit on systems of equations, to the unit on exponents, then the unit on polynomials. At the end of each unit, we duitfully give the unit test, get some number score back, then move on to the next unit.  We have trained students to think this way:  that algebra means mastering one skill, then the next.  How often do we provide rich tasks which allow students to reflect upon their cumulative skills set?  I appreciate the work of many math folk out there to change the nature of Algebra 1 from a rigid sequence of skills to a course which encourages application and reflection, driven by interesting, authentic problems.  Some examples of outstanding math educators working to promote inquiry in math class are listed at the end of this post.


For many special education students, chunking is a device used to “help” students in algebra.  By continued pounding of square pegs into round holes, using worksheets of similar problems (i.e. solving a one-variable equation, with variables on both sides), students can achieve temporary, recordable “success”.  The students most in need of seeing auhentic problems are often those least likely to move past the chunking, and into authenticity.  Fortunately, to help sort out the madness, Grant Wiggins provided a second great article of required reading for math teachers this week:

Grant Wiggins on turning math classes into bits of disconnected microstandards.

What’s so harmful about taking a broad subject like Algebra and breaking it into pieces?  What is the consequence?

Take a complex whole, divide into the simplest and most reductionist bits, string them together and call it a curriculum. Though well-intentioned, it leads to fractured, boring, and useless learning of superficial bits.

Hallelujah!  Make sure you check out Grant’s driver-ed analogy for the full effect.  More ammunition for us to develop math courses rich with interesting, relevant tasks, where algebra is the tool, not the star of the show.

Fortunately, there are many educators out there working to develop tasks which develop algebraic thinking, and encourage the use of algebra as the tool, rather than the exercise.  Keep them in your toolbox for future planning.

Dan Meyer: the king of perplexity.  If you aren’t visiting Dan’s blog at least semi-regularly, then start now.  And check out his spreadsheet of tasks for the math classroom.  In the same theme, visit Timon Piccini, and his many on-point 3-act tasks.

Sam Shah:  Sam leans more towards the pre-calc, calc end of the math spectrum, but I apprecaite Sam’s constant self-reflection and great ideas for engaging kids in math discussions.

Kate Nowack:  sometimes task-oriented, sometimes ranting on policy, but always interesting.

NCTM’s reasoning and sense-making task library has a number of problems around which algebraic ideas can be wrapped.