Two roads converged in a yellow wood, and I- I took the road less traveled by, and that has made all the difference.

From “The Road Less Traveled”, a poem by Robert Frost

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# One of Thirty Voices

# Choices

# Gwinnett County Public Schools is hiring…

# Knowledge Machines are here; How will you use them?

# New Year’s will be in August, this year.

# Reflections that push me towards next year.

# Make Problem Based Learning Disappear: Why PBL? Part Two

# Why PBL? Part One

# What do you mean, it “…can’t be solved?!?”

# Murder Mystery Solved with Trig!

# We’d like you to take over this class, six weeks into second semester….

# “It isn’t that I don’t like math. Learning takes time in math, and I don’t always get the time it takes to really understand it.”*

Through my voice, I encourage you to find your voice.

Two roads converged in a yellow wood, and I- I took the road less traveled by, and that has made all the difference.

From “The Road Less Traveled”, a poem by Robert Frost

They are looking for math, science, and special education teachers.

I work with absolutely excellent educators! We need teachers who teach students the subject matter, not the subject matter to students. There is a difference, and it matters.

Our county has been the recipient of the Broad Prize for excellence, not once, but twice. We excel. We are Gwinnett. It’s what we do.

Please put my name in the comments of your resume to let them know you heard it from me!

http://publish.gwinnett.k12.ga.us/gcps/home/public/employment

Good Hunting! Your next job is out there.

There was a time when school was about learning the three R’s: reading, writing and ‘rithmatic. Sounds like the beginning of a long ago time story, doesn’t it?

After reading this 1993 article from *Wired, *I realized that Papert’s ‘Knowledge Machines’ are, in fact, here.

Continue reading “Knowledge Machines are here; How will you use them?”

If you are a teacher, that is.

On August 8, hallways and rooms will fill with the wriggling eager bodies of their parents’ best! I can hardly wait! During the summer, I’ve been loading up on great ideas, reading about effective teachers, discovering new tech and new resources, and creating learning plans that will put them into practice!

I am teaching my students Algebra I this year; 9th graders, some returning 10th, and I want them to feel the excitement, the sizzle that I feel with math. This is a new year, a new crop of children, a new chance for me to share what I love- math – with children who never fail to delight me (and challenge me, worry me, turn my hair gray, and, well, you get the idea- but that’s another post!)

The year I have planned, this year, will be different. This will be the year that every student tests proficient on the EOC, aka Georgia Milestones. My lessons will start with Wonder/notice, there will be lots of student conversation, with roles for small group work, and conversation starter posters on the wall! My class will be fully engaged, will actually complete their assignments, will receive thoughtful feedback, and grades that really show how well they’ve mastered standards. I’ll make all the calls, on time, to the parents.

My IEPs will have clear goals, my re-evals will be works of art! I’ll handle my discipline issues with skill and compassion. This year, I’ll have strong closure routines, include literacy in every lesson, hold awesome number talks, and have nimble responses to my formative instruction.

This year, my room will be organized. I’ll have study centers, whiteboard walls, standing desks, and engaged, curious students! This year – well, this year will be everything I was hoping last year would be…

So, you see, teachers really do celebrate New Year’s in August!

As I rest and recharge myself this summer, I am like one of those little chipmunks- stuffing my cheeks with ideas, thoughts, and nubbins of lessons.

I start a list of those items that MUST go into my lessons next year: good starters, exit strategies, literacy activities… You, too?!?

At some point, I need to actually plan! And I will. But not today. Today I am going to read a book. Not a ‘teacher’ book! This one is purely for pleasure: a new mystery novel. But first, let me check out this new email from Edutopia…

…make PBL [problem based learning] disappear. In an inquiry-based school, it should be nearly indistinguishable from general instruction.

Problem based learning, inquiry based learning, question based learning… There are lots of different names for a specific type of classroom activity that places one item, image, expression, or situation in front of a group of kids and asks them to engage with it. The teacher steps back. Instruction is minimal: come up with a question, any question. That’s it. Not what type of question, not what the question needs to pertain to, not how many questions.

As a teacher, that is really hard. And it takes time to let this process happen, and, oh yeah, you need classroom rules like no judging questions, just write them down without changing them, don’t try to answer the questions, just write them down, and every question matters, so write it down even if it sounds silly or stupid.

Because when students start asking questions, curiosity is piqued.

It is okay to promise that as many questions as possible will be answered. It’s okay to go off in a direction that wasn’t in the original lesson plan. Because when students start asking questions, curiosity is piqued. *And when that happens, well, all I’m sayin’ is, never underestimate curiosity!*

Once students are curious, lessons can turn one of two ways; **you control this knob.** You can kill curiosity just as quickly as you can pique it. However, it takes courage to let this curiosity take hold, to guide it gently, and to allow the students to run with their questions.

The students have asked. The cards (one question per) are up on the board, sprinkled around the room, arranged by subject matter… However you feel they should be arranged. What next?

I like this moment. While the questions are being shared, I am gaining new insight into the minds of my charges. What do they know? What connections are being made to the image or situation or equation (not necessarily a math connection, by the way)? How do my students think? Where are the questions going to take us? And my teacherly question… Where are we in relation to the knowledge I want my students to gain from this? Will we get there, or (and this is the scary, let go and teach part) will we get somewhere else just as valuable?!

Making PBL disappear means building this type of student led inquiry into every part of the course and creating a daily attitude of curiosity.

At this point, I would take a moment to address the title of this discourse. Making PBL disappear means building this type of student led inquiry into every part of the course and creating a daily attitude of curiosity. What are we going to explore today? What are we going to learn how to do today? Students come into class prepared to ask questions, questions that they know will be answered.

This is not a pipe dream. This does take a belief on the part of the teacher that the students’ questions are worth exploring, discussing and answering. It also takes a little bit of classroom setup- students need instruction in the rules of the game and, most importantly, the focus for the lesson – that picture, equation, situation, idea – needs to be well-chosen, the possible questions and directions prepared for, and the possible math directions imagined and worked out ahead of time. This kind of lesson takes time to prepare, a commodity in short supply for most of us.

How do we get from using PBLs as sometime specials to a technically invisible way of doing business in the classroom?

The biggest thing I can say is that no teacher has to do this alone. The body of resources is growing by leaps and bounds. There are informational blogs with ideas, examples of lessons, stories of actual class experiences (some with scans of student work), videos, websites, and instructional books. There are multiple teacher groups on Twitter that share ideas and discuss lesson results. These teachers are more than willing to give feedback and help.

Having said that, integrating PBLs into the classroom requires:

1) a knowledge of the standards you want to teach, translated into “I can” statement goals,

2). A willingness to encourage student led questions and discussion,

3) A portfolio of PBL activities that cover one or more standards,

4) the ability to facilitate “what happens next” and use the questions generated by students to unwrap the ideas that will lead to understanding of the standards, AND

5) the courage to let students choose how they will investigate/learn what you are setting before them.

Why do our children have to complete four PBLs in a two month period, separate from their ‘regular’ schoolwork? Why can’t their ‘regular’ schoolwork be taught in such a way that they learn and can draw parallels to their world outside of school?

Not that the content should match their lives, but the way they learn that content; the way they organize and make it a part of who they are in school should have some relevance to how they organize and deal with the stuff outside of school.

These two parts of their lives should mesh, not be two such disparate worlds that they cannot be reconciled.

Here is one solution:

I came across an Algebra I review problem the other day on Classworks. The challenge was to solve a quadratic using the Quadratic Formula. One of the answer choices was “can’t be solved.” *Which I did not notice.*

I was working with three students who did not understand what to do. Once I wrote out the quadratic formula, (actually, all I had to write was the negative b plus or minus!) they began to remember. One boy immediately told the other two how to find a, b, and c. That required a discussion about standard form, so we had to do a little rearranging of the problem given on the screen. Once we got the formula equal to zero, the second student plugged the numbers into the correct places! The third began offering solutions to various parts. I thought we were doing pretty good! Until we came up with a negative under the radical.

Like the music in Jaws… Dum, de dum, dum… They looked at me, dumbstruck.

“What do we do, Ms. Maxcy?”

I asked them if they had learned about imaginary numbers. *(Of course they hadn’t – yet. This was only Algebra I! But sometimes I forget which level I am teaching… Which is another story altogether!!!)*

Still not checking the given answer choices, I blithely proceeded to give them a brief ‘reminder’ lesson on real and imaginary numbers. They continued to look at me blankly.

As I magically (to them) unraveled the answer as 2 plus/minus 2i sqrt 11 divided by 3, they stared at me. Then they stared at their answer choices. They looked back at me.

“It’s not there, Ms. Maxcy.”

At this point, admit it, we teachers think, “it’s got to be there, that’s the right answer; why is it not there? Gosh, did I do it wrong?” And then we doublecheck our answer. And then it hit me. This was Algebra I. We don’t teach imaginary numbers. Yet. It was then that I finally looked at the answer choices…

The correct answer was there, but *it wasn’t the correct answer at all! *

Right there in front of me, there was the answer that the students were supposed to choose: choice “D) Can’t be solved.”

Right there in front of me, there was the answer that the students were *supposed* to choose: choice “D) Can’t be solved.” This is a terrible choice! It’s not the right answer! It’s not a good answer! Okay, so we don’t teach them imaginary numbers in Algebra I, *why don’t we just list the result with a negative under the radical as the answer?!? *

The kids get used to seeing the beast (negative radical) and we teach them how to simplify in Algebra II or geometry, depending on your school system. But, please, NOT *“can’t be solved”!*

That is just setting them up for trouble ahead! Lay the foundations, don’t build a wall that will have to be torn down later. Please!

Rant finished. Thank you for listening.

Dateline: April 14, 2016

*The murder of Maria, whose body was conveniently found at right angles to Leg Streets A and B, has been solved! Investigators found the weapon across the river, apparently thrown there by her assailant while he was running down Leg Street A in an attempt to escape. A quick thinking officer (who had majored in math at the police academy) was able to* *calculate an angle measure for the angle made by the throw from the perp and the street leading to the victim. Another savvy investigator was able to determine the distance from the suspect to the location of the attack.*

*With the mathematical evidence in hand, investigators were able to triangulate a conviction. Math teachers everywhere weighed in, saying it has the proportionate ability to change the way investigators do business!*

*Dimensions of the prisoner’s defense will be released at a later date. Film at eleven.*

Okay, so I don’t really have film (we forgot to assign the job of reporter!) What I do have are a room full of kids who can now set up the proper proportions for trig problems!

Here’s how the crime went down:

Scene 1: Before the murder, I handed six students a few props:

Each student had to use the prop to arrange themselves into a triangle. The other students watching were, um, helping. (that’s what they called it!)

A short q&a followed:

*Me: *Okay leg A, are you opposite or adjacent to angle b?

*Hapless Student holding Leg A sign:* “I’m opposite, um, no, I’m right next to him *(indicating student holding the angle b sign)*! What does adjacent mean, again?”

We were able to sort out the definitions, and the students holding the leg signs got pretty good at determining whether they were “opposite” legs or “adjacent” legs. A big moment came as students noticed that they could be opposite OR adjacent. More importantly, they were able to articulate WHY the status would change.

More importantly, they were able to articulate WHY the status would change.

Scene 2: The next six students were given the cards. This time, I stood back and let the first group help position the players. A little skirmish ensued as Leg A and Leg B were being positioned. After a brief discussion about whether or not leg locations could be interchangeable (did Leg A have to go in the same place as the first triangle?), it was decided that as long as a leg were placed on each side of the 90 degree angle, it didn’t matter what we called them.

The opposite and adjacent discussion began again. It was fun watching students correct these new players, or making them guess by giving them tantalizing clues!

(If you ever want to know what you look like teaching, give your students the reins. Mimicry is not dead!)

Scene 3: With everyone up to speed on definitions, the murder could now commence! Maria was positioned. Ryan was immediately suspect, as we put the crime scene tape in his hand and instructed him to escape a bit down the hall. The “weapon” was given another piece of crime scene tape and told to take off in the opposite direction. The “hypotenuse” was asked how far the “perp” had thrown the weapon. We stretched the crime scene tape from the suspect to the weapon location. It was at this moment that I heard several students say “Hey, we made a triangle.”

It was at this moment that I heard several students say “Hey, we made a triangle.”

*(Scary, I know, right?)*

After a bit more discussion, the students determined that we needed an angle and we needed the distance from the body to the suspect to set up a proportion to solve for the distance. Two students were dispatched with the piece of crime scene tape that had been held between the victim and the suspect (Leg A, for those of you following along). Twelve inch square floor tiles assisted in the crime scene measurement. I used my oversized protractor to come up with the angle measure, and we were ready to set up some proportions!

Back inside the room, our eager detectives checked their trig proportion info sheet (yes! They used their NOTES!) and settled on cosine, adjacent and hypotenuse. I stood back and watched them argue over who was going to set up the problem, exactly how to set it up, and how to enter the information into the calculator. Then I watched them convince one another which answer was correct.

Concrete to representational to modeling AND peer tutoring…I love it! I would say that a murder wasn’t the only thing that got solved today!

Six weeks into second semester, I was asked to become the teacher for a group of Algebra II students.

I met the Continue reading “We’d like you to take over this class, six weeks into second semester….”

How many more of our students feel this way, but instead of telling us with words, they distract, joke, sleep, or skip class:

…Math is such an interesting subject that can be “explored” in so many different ways, however, in school here I don’t really get to learn it to a point where I say yeah this is what I know, I fully understand it. We move on from topic to topic so quickly that the process of me creating links is interrupted and I practice only for the test in order to get high grades.

Taking Time Learning Math:A Student’s Perspective by Evan Weinberg

**Would I want to come to my class?**

This question haunts me. What are my kids seeing, feeling, thinking? Why does this kid come, but stay totally uninvolved? Why does this child talk, constantly, but about anything but math? Where did curiosity go? Is my class a class I would look forward to?

My personal enjoyment of math comes from the struggle with ideas and the satisfaction I get from my connection of and understanding of the relationships among those ideas. It’s like a huge puzzle that will take the rest of my lifetime to fully understand. The student’s comments in Evan Weinberg’s post resonated with what I see happening with my students. They are not learning math so much as preparing for a test about math.

They are not learning math so much as preparing for a test about math.

The current situation of ‘learn how to do this; learn how to do that’ mentality is slowwwwly changing over to ‘understand why this is so; why does this relationship work’ exploration. It will need a shift in how we teach, letting kids struggle and connect ideas (we must facilitate this exploration, but not down some tightly designed path), and changing our view of grades and mastery. I can’t say I don’t have the answer- I am working on an answer that works for me and for my students. And I’m sure I am not the only one teacher who has found the path that is taking them closer to the ideal.

This post grew out of my response to Evan’s column. His response,

“I completely agree that this is a shift, and it is ongoing. Clearly, despite the changes I’ve made to the way I teach, students still get the sense that the test is the important part, which means there is still a great deal of improvement yet to be made!”

*Taking Time Learning Math:A Student’s Perspective by Evan Weinberg

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