Mar 212013
 

Nevada is one of the SBAC (Smarter Balanced Assessment Consortium) states, and the SBAC has released some questions on their website in a way that shows us how the test will look and work when it is fully released.

Guess what, I can’t get it to work at school. Why? The district is standardized on IE7, which is too “old” of a browser for the SBAC, and Chrome is too new. I had it working in Chrome one day, and then Chrome updates and it is broken again.

So, I go home and using Firefox I can get it to run. Great, how do I now get this info to my department? I know, I will use Snagit and make captures of the screens. …. Not so much. One question is actually animated. Great, I will use Snagit and make a video! Yay.

Here it is. The 11 released questions for the High School level proficiency CCSS exam. Please don’t judge the voice over. I sound like an idiot.

Aug 262012
 

Okay, all along I was promising a massive file upload for all the readers who want the Exeter materials. I will explain what each group of files are for as I go.

All files are in WORD or PDF format, and all are in a zipped folder. Downloading and unzipping the folders will speed up your access tremendously. All in all there are 44 megs of files here. That does not sound large, but word files and pdfs are incredibly small these days!

[The placement tests were posted on Exeter’s website, but they didn’t realize they were made public. Links to that page have been removed. If you are a teacher and would like the files, let me know.]

The progression at Exeter begins with a Placement test to determine what course the learner should be enrolled. These are released Placement tests from Exeter:

Released Placement tests
After being placed in the correct course, the learners then start in on the problem sets. I have 2 years archived, but I would love more if someone has them.

Problem Sets 2011-12

Problem Sets 2012-13
The current year is 2012-13, so the archive is an August download of the new materials, including the change logs. If someone has the change logs for the 2011-12 or the files for previous years, I would add them also. The live location for the current year’s materials can be found on their site.

I do have solutions to the 2009-10 problem sets (I was given these without the actual problem sets) and solutions to the 2011-12 problem sets. Will I post them? No. I know I would not be happy if a teacher posted solutions to all the problem sets I created. That is the one thing I won’t post.

During the class the learners are in, they will do hands on activities, and use Geometers Sketchpad to explore math. The Instructor of the Exeter sessions I attended was nice enough to share these. They are all written by Exeter teachers, so no poaching and claiming them for yourself. Please attribute them accordingly.

Hands On Activities 2011
(Both Word and PDF documents!)

GSP Document and Sketches
GeoSketchpad misc
If you are looking at these thinking, “Dang! That is a lot of material to go through!” You are absolutely right. The 2 docs for Alg 1 are 59 pages combined, the Geo doc is 62 pages, and the Alg 2 Hands on is 69 pages. Right there are enough docs to keep a person busy in class for a long time, and you would be learning terrific math as you go. In the GSP Document and Sketches folder, there is a document called “2011 gsp.doc” It is 101 pages of GSP constructions.

So the learners are working problem sets, they are working activities and extending their learning beyond the problems and being active with the math. Now it comes time for some assessments.

Math 1 tests
Math 2 tests 
Math 3 tests
These are all in word format, so you can edit and use them in your classroom if you like. These tests give you some idea of how Exeter assesses their learners. Something you should know is that every one of these assessments are open notes. Every problem set they have worked is available to them on the exam.

Finally, the year is over, the faculty get  together and evaluate the problem sets. What worked, what didn’t, what can be improved. And the writing committee collects all those comments and distills them down into a commentary on the problem sets for the rest of the staff. Then the rewrites happen, and the new problem sets are published, and the cycle starts all over again.

Commentary 2011-12  [if you would like the commentaries, and can demonstrate you are teacher, please email me or comment and  I can email them to you. The files have been removed at Exeter’s request.]

 

And there you have it. This is the cycle of development of the Exeter curriculum and materials. The vast majority of the work is done by the writing committee, compiling the commentaries and editing the problems. That is a huge task, and I would love to have a serious discussion with someone at Exeter just about that. Heck, I would spend a week with them just asking questions about the writing of the questions, let alone working and thinking about the problems themselves.

I hope this is of some help to other teachers out there.

Aug 232012
 

During the summer, the teachers of the math classes at Exeter get together and review the problem sets and compile a series of documents they call the Commentaries. These Commentaries are then used by the Writing Committee to review, edit, and modify the problem sets to make them better for the next year.

First of let me just say, Wow. Exeter’s commitment to the constant improvement of their curriculum is amazing. Contrast that to the situation we have in the public schools. The district spends millions of dollars on a textbook from Pearson, McDougal, or Holt and then we are stuck with those textbooks until the next textbook adoption (every 7 years in NV, unless the budget delays it.)

In the meantime, we complain about the books because we know there are better ways to teach and better ways to work with the material, but we are bound by textbooks that are bound to disappoint. Today I told my department that it would not bother me if we threw all the Algebra 1 textbooks away. It shook them up and made them think a bit about why we teach the way we do. But I digress.

Let’s take a look at a couple of problems and see how the process develops new questions, or if not new questions, new understandings of the questions.

M1:26:4 from the 2011-12 problem set
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I chose this problem because it is a pretty standard type question, used in Algebra 1 to work with systems of equations. It has multiple questions underneath, and has the zinger question in part e that challenges the learner to figure out some answers without algebra.

The Commentary on the question is:
image

The Commentary for the question suggests some methods of solving, and points out the fact that the Algebra is the best way of solving the question. The Commentary does not mention part e, which has a lot of mathematical exploration involved. But the Writing Committee clearly felt something was going on in part e that was not successful, because the 2012-13 question is now:

image

Identical question, but the committee dropped the exploration question to focus on the mathematics and the generalization found in part d.

Here is another example where the question is really straightforward and does not change from one year to the next, but the commentary is terrific in guiding a discussion.

M1:2:5 (Both years)
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Very basic question, but the commentary opens up a very different scenario with the material.

image

Wow, look at that. High school teachers I have known sometimes fall into the “why should we teach something so basic, that is a middle school standard and they should just show up knowing it, but I guess we can review it” trap. It is a trap, and it sucks you in and destroys you if you let it.

Here the Commentary shows that the trap opening, “It is surprising that some students have so much trouble…” but they don’t fall in. They point out to their teachers to look for the shy, the quiet learners and ask questions the quiet learners may not ask but desperately need. Very nice.

What the Commentary is clearly for is to show the TEACHER what traps are possible with the material and to develop better questions in the treatment of the material. Imagine a brand new teacher at Exeter with the problem sets getting the Commentary. They can work the materials easily, otherwise they would not be teaching math, but the Commentary is what allows the new teacher to develop the questions that need to be asked in class.

It is definitely a tough proposition to write the commentaries and get the information from 20+ teachers and simplify those comments down to a short paragraph. But very worth the time and effort to do so. If you are interested in the Exeter problem sets, I recommend you read the commentaries as well.

Below you will find the commentary folder for the 2011 – 12 Problem Sets and the 2011 – 12 sets. The Exeter website has only the updated 2012 – 13 sets with change log.

Commentaries for 2011-12 [link removed at Exeter’s request. If you can demonstrate you are a teacher and would like them, let me know.]
Aug 162012
 

While we did many problems and activities at the Exeter training, we discussed how the Exeter instructor conducted his exams very little. We did have a short discussion one day on assessments, and he did give all of us some files with sample exams. He does not use these exams any more, so he felt comfortable giving them, and he gave permission for me to post them.

First off, here are the ground rules for all Exeter math exams. They are open book, which means, open notes. The learners have access to their entire work history that has been done to date in the course.

Part of the exam is to be done with no calculator, and part with calculator. In addition, the assessments are designed to fairly assess the learners thinking and problem solving skills.

First, I’ll look at some problems from the Problem Sets in Math 1, then I will compare them to the assessment questions that are similar.

M1:2:5

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M1:3:2 & M1:3:5-7

image

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Math1:4:9

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And here is 1 – 4 from the first exam, no calculator allowed section.

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(I didn’t select the algebra solving problems, just looking at the number line questions for these.)

I only went through page 4 on the Problem sets, and notice that question 4C is exactly the same as the problem M1:4:9. There is nothing really tricky here, just “can you take what you learned and find it in your notes (4c) or can you extend what you know from your notes to a newish situation (4a & b).”  Problem 1 on the exam matches well with the questions from the problem set as well.

So nothing really tricky, just an honest assessment of knowledge. Now granted, this is only the first exam, not an exam from later in the year where the material is tougher, but it does set a pedagogical pattern for the assessments.

In the first test of the year, there are 5 questions w/o calculators and 5 with. If we look at the 5 with calculator the pattern holds.

image

Notice the heavy reliance on the problem solving, and the methods of problem solving discussed previously.

The exam treats the problem solving very straight-forwardly and even suggests to the learner they SHOULD be using the table system. Then, in question 10, a little extra credit is dangled for taking the problem from guess and check to the generalized answer.

Nice.

All in all, I would say there is nothing ground breaking or earth shattering here. It looks like the Exeter teachers assess their learners like I assess my learner, and like many / most / all teachers are taught to create good assessments.

The lack of multiple choice is the real difference, but the reliance on MC exams is a crutch because of huge classes (30+) and the stupid demands of high stakes testing foisted on public schools. Doesn’t make it right, just makes it what the ‘reformers’ want.

Below you will find a zipped folder for download of some out of date exams used that used to be used at Exeter in Math 1.

Aug 132012
 

This is a post that can not be written without a better understanding of how Exeter structures its school year. First off, they are on a 3 term schedule; 3 ten week (approx) terms per year. This is a FABULOUS schedule, and I can speak from experience. It is a similar schedule to what Knox College (where I attended college) uses .

The benefits of the 3 term schedule are many, but some of the best are the sense of urgency it places on the learner and the ability to be more flexible in scheduling. The sense of urgency is terrific. You have 10 weeks in your class, and you are counting down right from week 1; “9 weeks left, 8 weeks left … oh crap, finals are next week.” You are never allowed to kick back and think, “nah, I have time, I don’t need to worry about that project / assignment / test yet.”

The second benefit, flexibility, is the one thing that truly is what I want to discuss here. I asked our instructor how many new learners Exeter gets each year. I was thinking that they probably didn’t have many transfers in after the first year, but that was not true. The Freshman class starts around 250 each year. Then, each year, approximately 50 learners are added to the class until the Senior class graduates with around 400 learners. [Of course, these numbers are not set in stone, they were given as an example only.]

That means that Exeter has a huge problem each year. The Freshman class is coming in with a wide range of ability levels, and then every year after that they get more learners who should be at one level, but in reality may be way way below that level or even above that level. This then is their dilemma, how to place the learners in the correct course for their level of ability.

First off, they have a strong system of placement exams for the learners. Wow. Imagine that, a learner placed into the class they should be instead of the class that all Freshman or all Sophomores should be in. Of course, given Exeter’s commitment to sharing what works, they have put some old placement exams online for everyone to see and use. Sweet! [Turns out, they weren’t old placement exams, but an internal site that was made public on their end.]

Secondly, they teach all three of the Math1 and Math2 classes each term. If Math1 is broken into 3 pieces, which I will call 1a, 1b, and 1c, then during term 1 of the Freshman year, all three classes, Math1a, Math1b and Math1c AND Math2a, Math2b and Math2c are taught all 3 terms. Wow.

This means a learner might be placed into Math1c as a freshman during Term 1, not every learner is required to start with the first Math1a class. This is HUGE! Now you don’t have to worry about the bored learner sitting in class causing problems waiting for the material to catch up to them.

Okay, can this be used in the public schools? After all isn’t that the point of this? I am not sure.

This kind of system works for a private school (and Knox is a private school as well).  because the system is not set up to provide an education for farm laborers. You do know that is why we have long summers off, right? Because the kids in school were needed to work in the fields during the summer. That hasn’t been true for 30 years, but we still have that long summer break. Sue provided a link to the myth of the summer break below in the comments. It is worth reading and following up on.

It certainly could not be adopted because of the extremely underfunded nature of public schools. We are lucky to have 1 math teacher per 30 learners, while a private school can charge as much as they need to in order to cover the extra teachers to teach the same course every semester and hold the ratio down to 1:12.

So the short answer is no, we can’t do it like Exeter can. That is a cop out though. How can we do something similar?

How can we personalize the instruction so learners who are advanced can forge ahead?

How can we implement and use placement exams to tailor the instruction?

Kahn Academy is getting some traction on this, even though the videos contain mathematical errors and mistakes because it is a way to personalize instruction. Can we, as innovative, driven math teachers figure out a way to do it better?

I am willing to bet yes. Once we are willing to throw away the books and embrace the standards, then we can simply say, Johnny knows standard 1, 2, and 3, so an A on those, but he needs to work on standards 4, 5, and 6.

Next we need a way to assess well, and finally we need a way to locate those standards out all of the standards that are part of the problem sets.

Once we have these elements, then we can at least try to individualize.

Jul 012008
 

So one of the biggest problems with using skills based assessment, or standards based assessment, or any of the other names that can be given to the process that Dan Meyer has been educating us on is that Alg 2 is just way to darn big.

I mean, really.  Rational functions?  Composition of functions?  If we break these down in to the smaller, little skills that are part of either of these two concepts, then we will never actually assess the larger skill that is essential.

This is a problem. H. already discovered this, and she was very willing to say so.  A couple of other people have said the same thing in the earlier comments on my blog.  Given the previous experiences, should I scrap my idea of using this for Alg 3-4 or should I forge ahead and figure out a way to do it?

I vote for forging ahead.

I already posted a Concept checklist for Alg 3-4.  It is still a rough draft, and I will be editing it and refining it. ESPECIALLY given my most recent idea.

I was introduced to “I Can” statements a couple of times this year, both in different contexts.  What I thought of doing is making the learners do “I Can” statements and then using those “I Can’s” to create assessments based on my Concept Checklists.

Yes, the learners would have to keep track of two different things. They will have to keep up on what they Can and Can’t do AND keep up with how they are doing on their Concept Assessments.  The Concept Assessments need to be linked to the “I Cans” very carefully and justified very well. If they are not justified both directions, then the reason for doing all of this work goes out the window.  The learners will see it as busy work and throw away the paper on their way out the door.

 Posted by at 9:27 pm
Jun 262008
 

Before I really get into this one, I must first say that I will use the terms Alg 3 to mean the first semester and Alg 4 to mean the second semester of my District’s second year algebra class.  I am specifying this because as I have talked to and grown in my understanding of Math, I realized that every district does this differently.  This is my attempt at mitigating  a little of that confusion.

Right, so before I can post the third (and far from final) draft of my Alg 3-4 Skills checklist, I think it would behoove me to first share what my starting point is.  Here are my district’s expectations for Alg 3 and Alg 4.

First off, ignore the dates at the bottom.  This class has not been updated with either the new standards (adopted a year and a half ago) or been re-formatted to be standards based instead of textbook based.

Does anybody else see a difficulty with what I am trying?  Some of the topics here are HUGE!

So, I needed some ground rules.  First off, I can not assess everything I teach.  This is vital, and essential.  Second, these skill assessments can not be the only assessments I give.  I am going to have to assess in a comprehensive manner. in addition to my skills assessments.  Finally, my skills list must fit on one page, single sided.

Okay, that last one seems kind of arbitrary, but it is not.  Part of my goal with this assessment strategy is to give the learners a recognizable and achievable set of goals, even if, or ESPECIALLY if, they hate math.

Giving them a three page list of skills the first day of class is saying to those learners, “you are going to fail this class because the amount of things to learn is ginormous”.  I can’t do that.

One page, even if I have to leave off some skills, even if I have to double up on some skills, is still better than overloading my learners.  Now the burden is on ME to focus my efforts and make sure I don’t leave off some important aspects of the math.  Their burden is to learn.

So, here it is. 

I tried to match my District’s blueprint, since that is what the CRT is based on.  This is not a final draft, by any means.  I am very open to suggestions and criticisms.

 Posted by at 4:55 pm
Jun 242008
 

First things first.  Everything I discuss here is specific to EasyGrade Pro 4.0.  Why?  That is what our district is standardized on.  I am sure that everything can be modified to any gradebook, however.

First thing, set up the categories we will be using to grade with.

grade book setup 1

Notice that only 15 percent of the grade is due to any assignments, and it is not labeled as “homework”.  We are committed to trying to get the freshmen to work 100% of the time in class so we don’t have to assign homework.

Not sure how that is going to work out, yet.  The “Panther Math” category is a required element of our school.  Every learner does a Math Proficiency practice of some sort every day until they pass the proficiency exam.  This begins the first day of class as freshmen.  It has been showing results so far.

Notice that 70% of the grade is tests!!!  The Comprehensive exam is to make sure they are ready for our district’s CRT.  They will get 3 comprehensive exams, 1/3 of the way through, 2/3 of the way through the semester, and then the Final CRT.

Next, the way of inputting into the gradebook.

grade book setup 2 Notice the “Complete” and “Not Complete” names.  Those are how we decided to communicate the success of the learners.

 

 

So, here we have 7 fake learners.  When they demonstrate mastery on the “A” exam, they get a “COM” or complete worth 100% of the points.

gradebook w gradesThe learner does not get a score in a “B” test until they passed or “Completed” the “A” exam.  Notice that Frank is doing well.  He completed objective 1, but he scored 0 out of 4 on the “B” for objective 2.

John, on the other hand, is doing poorly.  He is not even close to mastery, and his grade reflects that.  Jean has mastered 1 objective, so her grade is higher.  Shelly has mastered none, but she is trying and because of the trying has a solid C.

This system gets past the point values to the importance of COMpletion and MASTERY.  For the teacher, COM’s are good, points are indicative of remediation.  I think this will alleviate the problems H had (see her posting here.)

Okay, ladies and gentlemen.  If you have any thoughts, criticisms, suggestions, lay them on me.  We go live with this with 4 Freshman Algebra 1 teachers, at least sixteen sections of this, starting in August.

More on this will follow.

 Posted by at 6:17 pm
Jun 242008
 

Okay, so we have some philosophy down to guide our decision making. We have some rules and procedures, a way to communicate the test questions across multiple teachers, and some basic forms so our freshman will have a consistent set of handouts and standards. 

Now all we need is some way for the teachers to know exactly what he heck we are doing and tracking the same way.  One thing to note when looking at this.  In our district Alg 1 is split into semesters, Algebra 1 and Algebra 2.  So our Alg 2 class is called Algebra 3,4. (yes, it does cause confusion when talking to people in other districts / states.)

Great, we have standards aligned with each topic, those standards are aligned with the district CRT’s, so hopefully we have all our arrows pointing in the same direction.

We spent quite a lot of time massaging this.  We are not assessing everything that could be assessed.  For instance, we are not assessing 1 step equations.  We still have to teach it, but if the learner can do 2 step and multi-step equations, then they can do 1 step equations.

 

What I will not post here (for obvious reasons) is our excel spreadsheet with the questions in it.   We used Microsoft Equation 3.0 to construct our problems, so they are objects that can be copied and pasted into the following file.

This is our Test Blank

that we agreed to use.  Copying and pasting the problem into it gives us a very structured way to give out tests.

Finally, we agreed to a rolling 3 in class assessments. This means that every assessment will have 3 presentations to the class.  The first time will be an “A” assessment, and the second and third will be “B” assessments.  If the learner passes any of them once, the “A” assessment is complete.  They only need to do the “B” assessment for full credit.

Gradebook next!

 Posted by at 5:56 pm
Jun 222008
 

Okay, so we sat down (five of us) and hashed out some of the mechanisms and details we will use on our assessment journey.

First, we all agreed on the principles that Dan documented. Yes, I said some bad words when I read his three principles, because he scooped me on something that he had not written about (yet) and I thought I would have something truly unique to offer.  Oh well.

Next, we got down to the nitty gritty.  How many questions on each assessment?  What constitutes mastery?  How do we decide?  Where will these questions come from?  How do we create a continuity across four different Alg 1 teachers?  What standards are we going to actually address?  Do we have to assess everything we teach?

Answers below the fold in order to conserve space.

Continue reading »

 Posted by at 7:24 pm