## Green Lake 2012: Gail Burrill, Rethinking Fractions – Implications for Teaching and Learning Algebra

May 4th, 2012

This morning Gail is talking about thinking about fractions as unit fractions.  The information here is from the work done by H. Wu out of Berkley. Fraction instruction starts on a number line – not with a pie diagram or other physical model.  She is showing us an Nspire document that is counting by 1 fourths.  The idea is multiples of unit fractions.  So in the app when you are at 2 on the number line, the app shows “10/5″ as well as “ten 1/5″.  We have ten copies of 1/5.

Equality is defined as having the same place on the number line.  When we start with pie diagrams we are creating misconceptions.  For one – we wind up not being able to be greater than one.  Also we need a different circle for each fraction type.

Gail takes a minute to tell us that words in the common core matter much more than they ever did before.  When the core talks about “unit” it really means it.

Next we talk about unit squares.  How could we prove 15/6 = 5/2.  A number line model or a unit square model will work.  Now think about a unit square with 3/4 of it filled in.  That is your unit.  Then a half filled in unit square would be 2/3.  A unit square split into 8 rectangles with 3 filled in has a value of 1/2.  One and one half filled in unit squares has a value of 2.  You can see these examples here.

Here are Gail’s slides from her presentation:

## Green Lake 2012: Henry Kepner, Assessing students on the CCSSM

May 4th, 2012

Lots of states have adopted the Common Core Standards – but that doesn’t mean much.  At this point all they have agreed on are a list of standards.  How that plays out is going to be a states rights issue.

One thing we don’t do a good job of is tracking student growth.  One of the critical promises of the assessment systems being considered is that we will have a record of how students are progressing.  This is based on the assumption that all testing will be computer based so the data is easily accumulated and archived.

(The idea of college and career readiness is an awkward thing now.  There is a preponderance of soft skills that companies want (team work, communication, etc).  What they can’t come up with are the hard skills that kids need coming out of high school.)

One issue coming out of the testing that is meant to tell how students are doing, is that they are talked about being used to measure teacher effectiveness.  The danger is in using a test that is made for one thing (assessing students) to try and draw conclusions about something else (teacher effectiveness).

As Dr. Kepner shows us some test items, what we need to realize is that there are not any items ready for release – all that we can see are current items that may be something like what we might maybe see. As a side note  - in order to take these computerized tests, students will need to have practiced with these mathematical tools (sketchpad, calculator type apps) well prior to the actual test dates.  The consortium(s) will be preparing reports for each state (which will be handed to the governor) outlining the cost that each state will have to pony up to get ready.  Are the governors ready for their 5 billion dollar invoices?

Each consortium is also building intermediate assessments (benchmark assessments) that can be used any time during the year to measure where students are at.  These optional intermediate assessments will be built out of the same (similar) items that appear on the official end of the year test. So the goal should be to take advantage of whatever is done “to us” in order to use the tools we are given to benefit the students and the instruction that we create.  Dr. Kepner recommends that as much as we can, we are raising our hands and volunteering to look at items and use our kids to pilot tests.

www.smarterbalanced.org is a place that we should be looking at periodically for information on what is going on.  Their document on Content Specifications is an important one because it was given to each state that joined and then agreed on in order to move forward.  There are 4 claims made in this document: (Sample problems themselves can be found on the Smarter Balanced web site.)

1. Students can explain and apply mathematical concepts and interpret and carry out mathematical procedures with precision and fluency.  These are the types of test items that we are most familiar with.  The cluster heading in the standard is what this is aimed at.
2. Students can solve a range of complex well-posed problems in pure and applied mathematics, making productive use of knowledge and problem solving strategies. These are contextual problems which may lead to claim 1 problems.  This is the math wars – we will see nice neat clear math problems but also contextualized.
3. Students can clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others.
4. Students can analyze complex, real world scenarios and can construct and use mathematical models to interpret and solve problems.  These are long maybe 45 minute type items.

The current state of Smarter Balanced is looking like 40% traditional multiple choice (claim 1) and then 20% each of the other claims.

## Green Lake 2012: Steve Leinwand, The Common Core State Standards for Mathematics- Hopes, Fears and Challenges as We Enter the Brave New World

May 3rd, 2012

Wow.  That is quite a title. He starts with the problem:  If you continue to do what you have always done, you will continue to get what you have always gotten.

Steve believes, as I do, that Algebra II is an impossible course to teach and it should be.  What the hell is it good for? (Please don’t tell me that they need it for Calculus.)  The point is that we have been party to the process of sorting kids out for a world that no longer exists.

Steve then showed us some data and asked what we saw? Two lists: {40, 10, 20} , {4,2,4}.  His point is that we can get a lot out of just discussing.  For example by asking what is next, we can start hearing what others are thinking and critique.  We are making conjectures and engaging in deductive reasoning and inferential reasoning.  Steve completes the table and asks us where we are.  (What?) Then he adds a first column which shows things like Roller Coster, Ferris Wheel, Fun House.  Now that we know where we are we try to give meaning to the original two columns.  They could mean anything that we can justify.  Like the number of people on the ride versus the number of riders that puke on average per ride.  Imagine the discussion.  The thing is, if you tell them from the outset what the columns are, it takes so much away from the activity.

Steve started with this (we are now 20 minutes in) to illustrate that it isn’t the standards that matter – it is the translation of those standards, it is processes that are as important a content, and we need to give kids a reason to care.  The days of being a Middle school cowboy (screw them – we’ll do what we want) are over – we have to work together to get this done.

Steve has 5 perspectives that we need to consider:

It is a great time to be convening as teachers of mathematics. Steve tells a great story about THe Bill Gates Foundation and the research that SRI and ARI did which showed he was wrong.  Check this out.  Check out Harvard student questionnaire for 8th graders which turns out to be a great predictor for future success.

Kids have nothing going for them if we don’t do what we need to do as mathematics educators.  Why are state test scores so high in Massachusetts? (Yes, high standards, but what more so?

We need to teach in a way different that we have been taught.

We have to collaborate if the Common Core is going to work. (Steve admits he drinks the CCSS Kool-Aid – or is at least very optimistic)  See page 5 of CCSSM for a great quote on how the standards are not new names for old ways of doing things.  Steve told the story of how he and others drew a line in the sand and went to Achieve threatening to use his big mouth to show how the “New” standards were nothing more that a rehash of old crap.  The final draft of the standards shows fairness, clarity and spiraling.

Learnzillion – check it out as an alternative to Kahn.

Steve talked about the amazing assessment items that are being produced.  Also about the adaptive part of it.  http://hdd.apec.org Example 4 is what will be on an 11th grade smarter balance test.  8th grade algebra is going away.  You cannot condense 6,7,8 into two years and send one-thinrd of the kids to Algebra 1 in 8th grade.  This is the 1st time in our lifetime that we have the possibility of a coherent, integrated, balanced system that we can run with.

Here are Steve’s slides from the presentation:

## Green Lake: Karim Ani – Keeping It Real, Teaching Math Using Real World Topics

May 3rd, 2012

Karim is rewriting curriculum (aligned with the common core) around real-world topics at Mathalicious.  He is going to start today by showing that a skills first approach is not as effective as a real world exploration approach.

So, skills first… traditionally we might take a fraction like six-tenths and have students divide 6 by 10 and then move the decimal place over twice.  Imagine explaining baseball to a foreigner that has never seen a game.  (I have, his name was Alexi- he was from Russia and we went to a Brewer game together.)  Isn’t the fraction example a lot like the baseball example?

So, how do we contextualize this?  Karim looked at a video clip of two guys shooting free throws.  (btw, this is from his activity “From the Line”)  The question is who did better?  Skip forward to looking at  a table and wondering who might score more when each takes 100 shots.  All of this makes sense.  We aren’t making any moves that don’t make intuitive sense to the students.  We want to minimize those times when students are wondering why we are doing a certain thing.  (Like moving the decimal place over – or even multiplying by 100).

The next activity is Wheel of Fortune – the next question is “How can we determine if Wheel of Fortune is rigged?”

We talked a little bit about what percentage of the time does bankrupt come up that would make us suspicious. (We should expect 11% by looking at the wheel) We watched an episode next.  The percentage of Bankrupts was 15% of the spins.  Would a 6th grader be suspicious of this?  Probably – and this leads into an interesting discussion.

Now we are talking 7th grade solving proportions.  Obviously cross-multiplying (puke) is the preferred traditional method.  To contextualize this – if Walmart needs to produce a banner 24 inches wide that will show an iPod on it – how tall does it have to be?  We look at  an animation of growing the iPod.  One way by adding 2.2 inches and one way by multiplying the width by 1.96.  After seeing that multiplication is the way to go we now have a method for solving proportions:  What do we multiply one dimension by to get the other?

Now on to Big Foot Conspiracy.  The question: What if Nike charged for shoes based on the size (essentially weight)?  So we have kind of an incomplete  table with sizes 9, 9.5, 10, 11, 11.5 and associated weights.  The cost of the shoe is \$160 per pair.  So what if we use size 10 as a base and then adjust the other models accordingly?

Now a quick look at 8th grade.  Calculate the equation of the line going through (16,499) (32,599).  Traditionally we look rise over run, divide.  Plug slope in then tell the kids to pick either point (what?), plug it in and solve. Ouch.

The activity here is iCost.  The first question is what is the y per x?  How much does Apple charge for the iPad given the cost of two different models? The idea is that we can have a really smooth conversation about cost per GB and have it lead intuitively into the equation of a line.  Then look at a 64 GB and you see that the pricing is actually not linear.  Karim makes the claim that this activity covers 28% of the 8th grade common core (Exclam!)

Next for high school we are looking at exponential growth.  The activity is called XBOX Xponential.  The discussion we eventually have is this one: Is there a point when video games are so realistic that we will eventually plug in like the Matrix?  Do we want that? The point is that the math is what gets us to this point.

Next is the 51 foot ladder. This looks at right triangle trig.  Turns out you can climb a 50 foot wall with a 51 foot ladder.  What is the shortest ladder you would be willing to climb?

## Green Lake 2012: Gail Burrill – Ingredients for Successful Lessons – Challenging Tasks and Questions That Count. Gail Burrill

May 3rd, 2012

Gail started by playing a little game with us.  On her TI-Nspire software she drew a triangle and measured one of the sides .  Then she locked the “area” and then moved one of the points.  She asked “What do you think is going to happen?”  Ultimately: What does a trace of all the places you can move one of the points look like?  (Try it!)

Next game is what happens if we instead lock the perimeter and trace?  What do you think will happen? (Try it – your hint is that it has something to do with the sum of two of the sides of the triangle.)

Gail’s point is that the only reason we ask questions is to find out what students are thinking.  To probe or to push their thinking.  If we aren’t doing that with our questioning, then our questions aren’t worth it.  Tasks that push and probe should be our focus.  A possible task – Which glider goes farther: one that starts at 25 meters high and goes 185 meters horizontally, or one that starts at 25 meters high and goes 155 meters horizontally.  (One audience member asked which distance)  This is an example of  different context for the same concept.  In terms of the Common Core this type of task hits a lot a the Math Practices.

Next: Draw triangle ABC.  Construct the perpendicular bisector of sides AB and BC.  Make a conjecture about the perpendicular bisector of AC.  Move point A.  What do you observe?  Cool – but how can we make this problem more interesting?  October recipes from No More Cookbook Math (Harper and Edwards 2011) has a rubric for thinking about Teacher Centered vs Student Centered.

Stein 2000 talk about choosing solutions, sequencing solutions, managing solution strategies, ask questions, consolidate the math using student work.  Gail would call this “purposeful walking”.  The work on formative assessment says that hands should never be up unless the student is asking you a question.  You do the planning and choosing.

Say you poll the class on a particular problem (maybe TI Navigator style) what do you do with disparate results?  You could have a representative from each solution justify their responses…or what about just asking the whole class what the people who answered A. were thinking, and what were the people thinking that chose whatever.  Or what about pairing kids up with the goal of convincing each other that they are right.  Then re-poll the class. Now you can deal with the outlying kids one on one.

Next we looked at the Nspire activity What_is_a_Solution. A simple and brilliant activity.

The Elimination Method is another activity that supports questioning and sense making.

Lastly we did a sequence activity with the Fibonacci sequence and I’ll try and recreate it here if I can find time.  In the mean time – here are Gail’s slides from the presentation:

## SLATE 2011: Steve Dembo – Learning to Speak Native

December 7th, 2011

Steve mentions we need to make sure that we aren’t doing “old things in new ways”. He mentions the TechBook and describes how it drives teachers crazy at first because there is no chapter one. We need to do new things in new ways. Beyond the textbook sort of thinking.

Steve talked about his son and the fact that he wants the opposite of what most school districts are trying to provide. He wants his son’s first and last name and location attached to everything that he does. Why wouldn’t he want that? We are all making a digital footprint, why not make the experience into a professional portfolio starting at a young age. A good example of this is College Confidential. Used appropriately, this kind of site can be used for long term planning. Colleges are sure to be looking at a site like that.

Crowdspring is another interesting place that evens the playing field for anyone. Students can be participating in projects there right now. Kickstarter is another project based place. Here students come up with a business plan and actually set it into motion in the real world. These are the places that kids need to be to work on their digital portfolios. The reality is that places will not hire unless you have a positive presence on the internet. Don’t bother with a traditional resume – it isn’t worth anything. Having no presence at all is just as harmful as having a negative presence.

Steve shared a story of a CEO that looks for his VP’s on World of Warcraft and not on the golf course anymore. If you can lead a guild on World of Warcraft, you have the same skills that you need to lead in the corporate world. If you have 10,000 followers on Twitter, that has to mean something about you as a leader.

We must be prepping students to thrive in the digital world. It is open and transparent.

Steve shared some sites that are worth looking at:

The bottom line is: How can we use sites like the ones listed above in a way that they were not intended for? We can’t fall into “Box of Legos” syndrome, where we only build what is on the box.

## SLATE 2011: Renee Disch – Google Forms for Assessment

December 6th, 2011

Disclaimers out of the way first. Wisconsin DPI has an agreement with Google that makes sure that what happens in Google complies with FERPA. Apparently that is a good thing.

Google forms have the advantage of being free, viewable with internet access, and can involve some collaboration. There are various types of forms. Just a text box the title of which can become the header of a column in a spread sheet. You can have a paragraph text, multiple choice, multiple choice but you are choosing from a drop down list, check boxes, a scale sort of rating kind of thing, and a grid which is a scale but for multiple questions at once.

Accessing a Google form is as simple as signing in to your Google account (create one here) and then selecting Docs in the tool menu. From there select Form and you are ready to go. From here on out you are playing around and making your forms.

The bigger question for me is: How can I use Google Forms to improve student learning?

## SLATE 2011: Scott McLeod – Conversations for Classroom Educators

December 6th, 2011

As a followup to this mornings keynote this session is a conversation with educators regarding the ideas from that session.

Scott started by mentioning a post-literate society: maybe there is a time ahead when many of us don’t need to read because electronic devices may be able listen to us and respond. Dependency on text is on the decline.

First topic: Worthwhile Apps.
Scott will post ideas for looking for good apps at his site for this conference.

Second topic: How do we get staff moving and motivated?
Initial urgency and maintenance urgency are the two main issues.
Scott mentioned Mind Dump which is a place where little snippets of information can be found to aid in chipping away at resistance.
Teachers are rational and have real reasons to be resistance. Those issues need to be addressed. They are legitimate.
We need to be aware of the “implementation” dip. How do we make it as shallow and as short as possible? Multiple support structures need to be in place. “There is no place you can turn and not get support.” See the book Influencer: The Power to Change Anything.

Third topic: What do we do about teaching to the top of Bloom’s (top 3 levels) and still maintaining AYP. Testing is asking us to live on the bottom.
What we remember is what we attach meaning to. Decontextualized stuff needs to live in contextualized place. We have to find ways to stay in context so we get the benefit of the top three levels and build meaning for the “remembering” of skills and facts.

Aside: Where do keyboarding skills stand? It should start as early as possible. Keyboarding may be replacing cursive handwriting in terms of time and necessity. In 10 years though keyboarding may not exist.

Fourth topic: What do we do about filtering?
Logging software may be useful.
We spend way too much time locking stuff down instead of teaching appropriate use.
We typically lock 95% of people down for the sake of the 5% that are the problem.

Fifth topic: How can we implement changes in the structure that we currently have?
Imagine that we start with 9th grade. There are no bells, class schedules. You give 15 teachers and every student a laptop and the current curriculum standards and that’s it. What can you build? What can you do?

Sixth topic: What would you implement for 1 to 1 initiatives?
Not an iPad. Not enough content creation – they are mostly content consumption devices.
Maybe a Netbook. Best option is a laptop.
A BYOD policy mirrors what happens in the real world, however there are equity concerns.
See Scott’s link (above) for a research brief on 1 to 1 initiatives.

Seventh topic: How do you know when you have to take a step back and avoid burnout.
Be aware that you need to either give stuff up or find more support structure. See this.

## SLATE 2011: Eitan Benzaquen – Digital Learners Becoming Digital Educators

December 6th, 2011

How do we take a school through the process of technology integration? How do we get teachers excited and how do we become good technicians of implementing change?

Prezi is the main tool being used here. Also Poll Everywhere.

Screenagers today are hyper-connected. How do we make learning a freeing experience, rather than a dictated one. RSS feeds, Wiki’s, blogs, etc. Any of these tools must be used with high expectations of quality.

## SLATE 2011: Scott McLeod – The lines are blurring. Translating changes…into school practice

December 6th, 2011

Everything is Scott’s presentation this morning is available here. We can also follow whats going on at TodaysMeet.com/mcleod This is a nice way to follow #slate2011 tweets.

Scott started by introducing #pencilchat as a hash tag where educators take pokes at excuses for not integrating technology into the classroom. Pithy stuff.

Scott’s first point is that We All Now Have A Voice and his second point is that We Can All Find Each Others Voice and then We Can Easily Work Together. This has to change the way we do things. Access is completely mobile now and we can get it anywhere. The lines are blurring now, say, between work and home or between local and global. Google’s Art Project is a great example of blurring the lines. So is Google maps in terms of being in one place but seeing another in “real time”.

We now live in an era where a 12 year old guitarist can get 90 million hits on youtube. That kind of thing used to be reserved for huge record contracts. Lines between producer/consumer and expert/amateur are clearly blurring. Another line that is blurring is the one between Us and Them. What kind of jobs are location dependent versus location independent. The internet is destroying geography. The jobs that we are going to grow and not see disappear because a robot can do them are
those that involve critical thinking, problem solving etc. This needs to be the focus of our classrooms. Not things we can look up on Google. Dan Meyer puts it best when he says “The robots are going to eat our lunch if we are not careful.” We need to spend classroom time doing the things that the robots can’t. Making connections, diagnosing and treating misconceptions, creating perplexing problems that create patient problem solvers, etc.

The University of the People and MIT Open Courseware are blurring the lines between formal and informal learning. Can a student learn on-line all they need to know to pass a bunch of AP Exams and get college credit for that? Why or why not?

Next part of the session Scott challenges us to discuss how we operationalize changes in our schools that actually lead to student learning. What are we doing to combat low-level, wrote memorization, naked skill pedagogy? The first premise is that we need to invent our own solutions. The answer is not “out there”. We need to work it out and make it happen. Do it.

Next we took a look at this Mission Impossible: How do we get rid of textbooks? Each group put ideas into a Google Spreadsheet and then each group looked at someone else’s spreadsheet, identified 2 good ideas and put them on a summary page. We did this as a discussion around textbooks but also to see the value added by doing this is a digital way.

Scott also did a short segment on his iPad and looked at some really decent apps:
Algebra Touch is a great looking app for the iPad for Algebra.
So is Word Wit for English.
iMuscle for kinesthetics.
NYPL Biblion for History (The World Fair).
The Waste Land for Poetry/literature.