Reflections of a Techie

Two Things I Learned from my Students about Scaffolding

We're studying quadratics....and even the name usually strikes fear in the heart of the most competent adult.  I didn't want it to be that way for my math students.   I wrote a good lesson plan and then I let students help me modify it---they "taught" me how to teach them better thru the interaction and feedback we gave to each other during the learning process.

I create a scaffolding technique, but students helped me add, delete and amend it until it worked for the way they think.

Even if you don't teach math, this works...because I've done things like it in science and social studies.  I guess I just had forgotten about using it.  So the trick is to create a means for scaffolding and then let students help you fine-tune it...meeting their needs.  In addition, you'll learn so much about the topic that would never occur to you otherwise.

We started off slowly using the geometric area model.  Our textbook tells us that Greek mathematicians used this method as long ago as 300BC.  I think that sort of impresses students that they are following in the steps of ancience Greeks.  We were also able to pair this ancient technique with modern-day technology using Geometer's Sketchpad and Algebra-Tiles sketch that was available in the software library.

From there we started moving into a more symbolically version of finding the "x" solutions, figuring out what this means in real life and how to even use an old kindergarten Valentine making technique.  It wasn't easy but they hung in there.

Here's what I learned.....

If I divided my SmartBoard into two areas:  one side represented what the problem we were studying and the other side represented the thinking someone would need to do in order to solve the problem.  This helped tremendously and as we worked problem after problem, they helped me refine my thinking list.  

• Look for GCF
• Look for a letter that could be factored
• Find both factors(it's a mulitplication expression after all)--usually we write something like this to remind us ---->  a product=factor * factor
• Solve for zero---finding both "x"s
• Set those "x"s equal to the x-intercepts
• If you need to find a min or max, find the line of symmetry--we would say "this is like when you folded the paper in two and cut out your Valentine heart " and we always did the hand motions!
• Use the line to find the "y" of that max or min

So all of this is on one side and then they use the other side to solve the equation.  It's scaffolding and it helps them ingrain the process in their brain.  I'm not sure they realized how much they helped me think about their thinking, but student feedback helped me zero in on what they needed me to "think aloud" for them.  Throughout the unit, you would see students able to stop look at the process list.  They could perform this procedure independently.  

To enrich the lesson, we did a one day mini-lesson that showed them the quadratic formula.  It ties what the ancient Greeks did to another pretty old mathematician....Francois Viete. He was the French mathematician that published this formula way back in the late 1500s.  Here's the second thing I learned...they couldn't use this formula on problems unless they were in the standard form of the quadratic.  Again I could scaffold this by simply writing the standard form and then helping them use

I can imagine them in high school...thinking all this was foolishness.  And it will be then.  But right now, where they are developmentally in building up their quadratic muscles, it is perfect.

NGSS are out!!!! How I see teacher voice in this collaborative process.

Super excited today as the Next Generation Science Standards roll out for the public. 

I've been a part of an amazing process to help write, revise, edit these standards as the National Research Council's 18 expert writers and Achieve have circulated draft after draft to get to this point.  My state's efforts have been headed up by Matt Krehbiel from the Kansas State Department of Education who assembled another group of teacher and industry leaders to review, comment and recommend changes throughout the process.  Let me tell you Krehbiel rocked this!!!  It was an outstanding experience...one of the best I've witnessed and I've done a lot of these kinds of committees.

Two years this process has been going on.

Simply what happened was that the writers would create a set of standards they thought would help K12 develop proficient science students....prepare them to go to college and be successful.  Those draft standards would be sent out to the lead states for their review and comment.  That's where the committee I was on would go to work.  We had teachers, representatives from business and industry and higher education on the committee.  It was really a diverse set of interests, expertise and geography (I think there was about 50+ people on the committee so it was big).  Our committee would break down things and work thru reading everything and then seeing where we could make suggestions, improvements, point out hole/omissions and identify where clarification would be needed.

The collaborative process

For me, sometimes I worked with middle school standards which makes sense because I have almost 20 years of middle school science experience.  Other times I worked with the engineering standards because I have also taught math and computer tech.  The exciting part of working on the engineering standards was the chance to collaborate with real world engineers and high school teachers.  I can tell you that as we thought about the biology standards, for example, it was wonderful to think about how to best incorporate biotech....and right in our room was a biotech company representative.  We'd craft something and then could bounce it off her industry expertise....a real collaboration between education and industry.

Somehow Krehbiel would summarize all this input.  That is no small task because this Kansas group was very vocal, extremely passionate about what they felt was best for kids and what would promote the highest levels of learning.  So he did above and beyond to find a way to let the diversity of ideas bubbling thru in a concise way that could help Achieve and the authors.

Back and forth the drafts and reviews would go.  With each iteration, you could see the impact that the teacher's voice was having on the standards.  I think that was probably the most gratifying thing about this work.  So often things  happen to me, as a down-in-the-trenches-teacher, and I have no voice, no input, no way to influence the process. 

NGSS connected and cross-referenced to Common Core for ELA and Math

I also really like how the standards cross-reference back to ELA and Math Common Core standards.  It makes the actual document a little complicated, but I welcome that degree of complexity if it takes the guesswork out of where, how and why NGSS connects back to the skills and process of Common Core.  You'll also see that each page of standards actually "houses" the science concepts, the cross-cutting concepts (things I think we used to call the Big Ideas of Science) and the Practices.  Again....it makes this one page jammed packed and a little overwhelming to look at....but soon enough I adapted to the format and now have grown to appreciate how clever and convenient it is for a teacher that is doing their planning and lesson design.

Energized and elevated with teacher voice

But in this NGSS, I can tell you there is lots of teacher voice.  And imagine.  This Kansas committee was only 1 of the 22 states that chose to participate.  I can't tell you what went on in those states, but if it was anything like what I witnessed here in Kansas.....there was a huge amount of teacher input to these standards.  Thank goodness the State Board voted to let us participate as a lead state.  This way our input was heard (and I could tell you multiple places where I could see changes made that responded to comments that I personally helped make).  It won't feel like something that WashingtonDC did to us....it's our document.

 

 

In my state, the standards will come up for review by the State Board of Education.  I feel that they represent the best we could write.  Are they perfect?  Probably not but I feel like they are pretty darn good and will elevate the "bar" for science teaching in our state.

 

 

 

 

 

Wrapping up

Take a look.  Read thru them.  Imagine where our students will be after they've had a chance to model, use scientific argumentation, modeling of different phenomenon, investigate, compare the pros/cons of these approaches, design a tool to ________, etc etc etc.   

I think these will excite and energize our profession.

Thanks to Daily Desmos....overwhelmed but thrilled

I presented this as our class warmup today.  I displayed this graph and asked them to recreate this on their graphing calculator.  We havne't had much experience with graphs that look like this....in fact, almost none.....so it is many students first venturing out from linear graphs.

Quickly they thought they solved it by typing in y=x² and they were disappointed as they realized their graph started at the point of origin instead of at 1.  Fortunately all their linear equation background led them to realize that they could move it upwards by adding 1.

Now they had it solved.

But as we turned to the table functions, we realized that we didn't have the correct graph.  Our graph was too wide.  That lead to a discussion of how to make the graph "skinnier".....some thought we should use a different exponent and others thought we should add a coefficient to the x² .  So we tried lots of options....but were never sure that we "found" the right equation.

We needed more data beyond where y-=12.  So we've adding a comment to the Daily Desmos and are hopeful that the creator of this challenge might come back and give us some help.  This is a wonderful way to pull students into thinking and playing around with graphs....and building a "number sensibility applied to graphs".

I think students were pretty shocked when I told them I didn't already have the answer.  And they were surprised that I was a co-learning right alongside them.  It seemed to make it more enjoyable...and although they are sad that they didn't solve the problem right then and there....I think we'll make more runs at it.  And it's a good thing to learn to hang in there and to take multiple tries at the same problem.

Good stuff.  Thanks Daily Desmos!!!  We are thrilled if a little over whelmed.

Applying the test taking strategies to a real test--feedback from students

Getting ready for the test, I'm still refining and looking at different ways of prepping students to be more independent.

 Each student was to prepare a practice question for each topic covered on the test.   The idea was for them to bring those questions to the study session and we'd use those to review.  I did prepare questions to throw in...and to supplement what they created, but I wasn't planning on being the main question writer for the review.

 

Quickly I realized that wasn't going to work for the most part.  The questions the students wrote were mostly done to fulfill an assignment....not to actually help them prepare for the test.  Clearly we weren't on the same page.  So we talked about how they went about writing their questions....and they admitted they mostly just wrote anything that was the least bit related so they could have their card done.

 

I can't blame them...it's what they've learned growing up and I'm trying to change that mindset.  We talked about how to take the kernels of the questions they wrote and change them into questions that they thought they'd actually see on a test that I would write.

 

So my first ah-ha of this.....I need to be more directive in explaining that the practice questions they write have to be what they expect me (as their teacher) to write.  You know....when they took on that mindset, they were pretty quickly about to re-write questions that were going to help them a whole lot more.

 

As we talked more, I also realized (and this is my second ah-ha of this) that I needed to show them a failsafe way to organize all this info.  Since we had 8 topics, it wasn't too hard to figure out to quarter fold a piece of paper and number each quarter from #1-8.  As we read each review questions, students wrote it down in the appropriate topic box, solved it....and then the person who wrote it checked their answer.  If people were uncertain how to solve it....then the quesiton-writer took the SmartBoard and showed.  We didn't move on until everyone had it copied and understood.

 

In one class period, students had 3-4 examples to work under each topic.

As I talked with after they finished their test and on the following day, I wondered if they found these techniques useful and/or helpful.

I was prepared for them telling me that it was a lame idea. But suprisingly, some of my more accomplished students actually used their study guide and think it helped them.  Now these aren't the students that really needed much help.  But if I can get these students using these techniques, and if they show that they make a difference, then I know they'll influence other students to follow their example.  With their help and trying this again and again, we'll refine the way that we prepare.

In fact, I have to share one of the lighthearted moments that happened.  When we were working on remembering how to handle the inequalities as we solved using adding, subtracting, multiplying and dividing operations.  As we were building the test notecards and then the review sheet, we started calling these "red flag" moments.  That red flag was simply to draw attention to the fact that we were about the divide or multiply by a negative number....which means that we'd need to change the direction of the inequality sign.  What made me smile is to see those "ref flag" icons written in the side margins of the tests....kids were drawing those in to help them remember.

I'm hopeful that at the end of the quarter, we'll have developed a system that seems to work for the way they think....and something that helps them become more efficient and effective in preparing for these big end of the unit tests.

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2 Test Study Skills Tips for Math

2 Test Study Skills Tips for Math

One of the ways we are trying to vertically align between the 8th grade and the high school is to reduce the amount of teacher-generated study guides and test retakes during the 4th quarter of the 8th grade year.  Fading away some of the support seems appropriate

IF

I replace the support with training on how students should do this for themselves.  We're at the place where those learning targets, which have already organized lots of class .....are becoming even more important.

First, helping students go back through all their work and identify where they've learned each target is critical.  Sounds like something we've advocated before and it's what expert teachers have done.  What I continue to learn and re-learn is that processing information is valuable....and processing it when they are prepping for a test is really helpful to students.

I crack up when we talk about a concept...and I get those blank stares that say, "I don't remember that...when we do that?"   I make them search the textbook, their notes and worksheet until they find the Big "ah-ha's " of that learning target.  It's like a big light bulb goes off and then remember what we did and what they learned.

What I've added in that seems to be the second big tip is to build a concept map of each learning target.  We use each class' collective learning to add everything we've learned about that idea.  Where possible they connect ideas together...expand to include examples.  I think the visual nature of building this map really helps different kinds of learners.

Making these learning maps involve looking at the targets and prepping note cards for each topic.   That's not easy for them...and it really takes all their skills to stick with the task and work on it.

Most importantly....these techniques will build the student's ability to help themselves.  It would be easy for me to give them a study guide.  But it isn't in their best interest and I believe this is a better path to  travel.