Foundational Standards

At our last Tiered Algebra day, we spent an entire morning choosing foundational standards for Algebra 1 (specifically looking through the Appendix A standards that were identified for Algebra 1).  We wanted to be make sure to state that we are not choosing Power Standards.  Common Core specifically clarifies that all standards are equally important.  In our core instruction, we need to be teaching all standards.  
However, we felt it might be helpful to identify some standards that were critical to the learning of other standards.  We wanted our foundational standards to be ones that:

• would help students learn other Algebra standards

• would be necessary for life

• might help bridge between 8th grade math and Algebra

An example is that if students have trouble solving linear equations, it is likely that they would have trouble solving systems of equations, quadratic equations, etc.  In that way, solving linear equations is a foundational standard.

After much discussion we came up with the following foundational standards/groups of standards:

EQUATIONS/INEQUALITIES
A.CED.1:  Create equations and inequalities in one variable and use them to solve problems.
A.REI.1:  Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution.  Construct a viable argument to justify a solution method.
A.CED.4:  Rearrange formulas to highlight quantities of interest, using the same reasoning as in solving equations.

SLOPE
F.IF.6: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
S.ID.7: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

POLYNOMIAL OPERATIONS
A.APR.1: Understand that polynomials for a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

MEANING OF A GRAPH
F.IF.1: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of fcorresponding to the input x. The graph of f is the graph of the equation y = f(x).

A.REI.10:  Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

INTERPRET PARTS OF AN EXPRESSION

A.SSE.1:  Interpret expressions that represent a quantity in terms of its context.  Interpret parts of an expression, such as terms, factors, and coefficients.  Interpret complicated expressions by viewing one or more of their parts as a single entity.

EXPONENTS AND RADICALS

N.RN.2:  Rewrite expressions involving radicals and rational exponents using the properties of exponents.

USE UNITS

N.Q.1:  Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.

It was a morning of long debates, so I would easily say that almost all of us would argue to change something about what we came up with...overall what to you think?  Is there something you would add or remove?

-Kathryn

#MTBoS30

8/30

Coteaching--For Real!

At semester, when schedules were rearranged, I got a new opportunity.  We fiddled with a few things so that a special education teacher and I would be able to coteach an intervention class.  She has been involved in our project with the AEA, and as we were continuing to have conversations about how to help the students, it became evident that this was something we both thought would be good for the students.

It has allowed me to serve more students during the intervention time than I did previously; and with less stress.  We arranged it so that some of our lowest students are in the intervention class together.  We have 12 students and 2 teachers.  It is such an awesome opportunity for me (as a gen ed teacher) to have so few students at a time!

We had some conversation about how best to coteach, because it is not very common in our school or even in our area of the state.  But this teacher is also a reading teacher, so we thought it would work well to have her do vocabulary and then I can work on the content for each of our weekly units.  Here is a breakdown of what our week looks like:

THURSDAY:

• Opening Task:  fluency practice
• Vocabulary (as a class we make flashcards for our vocabulary words for the week)
• Very simple intro to the content

FRIDAY

• Opening Task:  counting circle
• Split Class:  Vocab and Content then switch so all students get both
• Finish content work
• Exit Ticket

MONDAY

• Opening Task:  counting circle
• Split Class:  Vocab and Content then switch so all students get both
• Finish content work
• Exit Ticket

TUESDAY

• Opening Task:  fluency practice
• Split Class:  Vocab and Content then switch so all students get both
• Finish content work
• Exit Ticket

WEDNESDAY

• Opening Task:  counting circle
• Vocab and Content assessment
• (every other week we progress monitor)

Most of the ideas for how to structure this came from the project with the AEA.  We just manipulated it to fit our situation best.  Let me know what you like or what you would change if it was you!

-Kathryn

Units for Intervention Class

I have been teaching an additional intervention class all year.  This is part of the Tiered Algebra project that our local AEA has been working with schools in our area to implement.  We had been given some guidelines, but not much, for what to do in that time.

• Connect it to what is happening in the Algebra class
• Don't just reteach/review what you are doing in Algebra
• Don't just have "do your Algebra homework" time
• Do more hands-on stuff
• Do more explicit instruction
• Use appropriate scaffolding
• And others, but that's what I could think of off the top of my head

So here I am, a general Algebra teacher, with very little understanding of how to differentiate in my regular classroom, now seeing 24 of my students twice a day, and doing my very best to make it worthwhile.  But I've been mostly clueless.  I tried to do a lot of pre-intervention with them... (see Micheal Pershan's argument for this type of intervention here) which looked like covering the coordinate plane and plotting points before we graphed linear functions in Algebra, for example.  But I still felt like my students weren't able to use much of what we were doing in a way that truly benefited them in the regular classroom.  Not that I actually had any real way of measuring it...

Then the AEA shared with us about a presentation they heard from a school that has a similar model in 8th grade.  They decided that vocabulary was really important, because IF THEY DON'T KNOW THE VOCABULARY, THEY CANNOT ACCESS THE LEARNING IN THE GENERAL CLASSROOM.  This was an argument I had never heard before.  Now I always knew that vocabulary was important.  And I teach it...sort of, but I've never really emphasized it.  This has changed that.  Along with other things that came from this summary of the presentation, I have changed some things, and I think it is for the better.

I now have week-long units.  These units focus on a particular skill and the vocabulary associated with it.  For example we studied exponents prior to working with exponential functions.  We had vocabulary:  exponent, power, base, exponential, reciprocal, expanded form.  We studied the vocabulary each day in different ways:  matching; create your own example; which could be used for x, which would be used for y; etc.  We also had scaffolded lessons on simplifying exponents.  We started with whole number exponents with only positive numbers.  Then we discussed things such as -2^4 vs. (-2)^4.  We simplified expressions using the order of operations (with exponents).  And finally we saw negative exponents.

I was actually able to see my students apply what we were learning in class (no actual way of measuring other than my observations).  I depended on them to lead the other students when we saw negative exponents.  This felt amazing.  I am excited to continue using this model, although I am very frustrated that it took until November for me to find something this useful for interventions.  Hopefully as I continue to apply it I will see more improvement from these students.

But I am also frustrated by the fact that it is still group all of my intervention students together.  What if student a needs this and student b needs that?  How do I make that work?  How do I know what they need?

Just for an FYI here is an outline of the exponent unit:

-Kathryn

Day 1 Lessons

Build up:

I had all summer to plan my first few days, but I just couldn't find the perfect thing.  At my school, all teachers are required to hand out the syllabus day 1, but I didn't want to spend the whole time reading it.  Last year I focused on procedures at the beginning, this year I wanted to focus more on relationships with my students and math.  I have heard from all my blog-reading that it is OK to save procedures for a few days.

So I set out to search for some good lessons.  While watching the #globalmath session My Favorites (you can view it here), I got lots of good ideas.  I knew right away that @misterpatterson 's Spaced Out sticky note lesson (you can find it an other lessons here) would be AMAZING for my intervention students.  It would address number sense and the usefulness of Algebraic thinking.  It is a perfect fit with my first unit as it also asks students to create an expression for a situation.  There were lots of other great ideas, so I followed links provided by @jreulbach to look at what other people have done on the first day. I ended up really enjoying the By the Numbers introduction that I found from @AmberDCaldwell here.  I thought I could tie it into the decorating ISNs I have seen.

So here's what I did:

For my topics/intervention classes, I modified Spaced Out to meet my student's needs a little bit better.  Here is a link to the document I used:  Spaced Out (modified by me) .  I gave a brief introduction to myself and the class and then had the students begin working.

Spaced Out (modified by me)

I really had to clarify the rule about the space on the ends being the same as the space in the middle.  It seemed a little hard for them to understand, but once they figured it out they started going.  No one was super excited about it, but when they got close and I told them they weren't being accurate enough, then they started to get that determination to succeed.  I only had 1 group (out of 4-5) in each period "pass" level one on the first day.  I made them write notes to themselves so that they would be ready to go on Friday.  For the most part on Thursday the only assistance I gave was checking their measurements and asking questions like:  What have you tried?  Why didn't it work?  Was it too much space or not enough?  What are you going to try next?

After watching my students working through levels 1 and 2 on Thursday and Friday, I wish I had added a level between 2 and 3 that was something like this:  A table is 300 cm long, how much space will be between the five sticky notes?  Hopefully that would push them toward think algebraically instead of just through guess and check.  We will finish it up on Monday.  I set them up at the end of the day on Friday with a hint about calculating the space rather than guess and check; I'm hoping that will get things moving a little more quickly on Monday.

In my Algebra classes I used a Mrs. Freed By the Numbers matching activity to introduce myself a little bit more.  Here is what they saw:

In their group they had to assign a number to each description.  After we finished I asked them to think of 5 numbers that describe them and share them with me.  That was their "exit ticket" on day one.  Hopefully on Monday we will turn their 5 numbers into the back of their ISNs :)

I did also introduce ISNs and give them their syllabus.  I showed them how it folds up so that we can tape it into their notebooks.  Looking forward to doing that with them on Monday when I set the deadline for having a composition book!

Thanks for reading about my first days!
-Kathryn

Day 5

Today (well, yesterday by the time this is published) was Day 5 of our local Algebra Project.  We spent almost the entire morning discussing AAIMS as we will (hopefully) be using the Concept Analysis test as both an Algebra 1 Universal Screener and probe.  I'm hesitant about its potential for effectiveness as it is not written for Common Core Algebra 1, but I'm trying to stay positive.  We are getting to use it for free, which is pretty awesome.

We also talked today about what we wanted the structure of our Tiered classes to look like.  This was really hard for me to think about for some reason...all I can really say is opening, middle, closing, but I think they wanted us to develop a little bit more of a structure with options for fill-ins in certain areas. I'm still not sure where I'm at with it, even though we discussed it before and after lunch!  I know that I'm going to include LOTS of error analysis in my Algebra classes this year.  I hope that it will help them to become better mathematicians, but I don't really feel like that has much to do with structure of the lesson..  I also hope to assess each individual student in my Topics classes (tier 2) each day formatively, but our AEA staff recommended even something written from them to assess (formatively) daily.  I hadn't necessarily thought of needing something written, but maybe that would hold me more accountable to getting that formative assessment on an individual level.

We read a summary of guiding principles for intervention time.  The summary included the following:  scaffolding, explicit instruction, multiple strategies, gradual release, student interaction, meaningful practice, assessment & differentiation, vocabulary & language, and learning targets.  It was nice to have that summary because now as I plan each lesson/unit for my topics classes I can just look through that list almost as a checklist.  "Am I doing this?"  It will be good guidance if I get stuck as well!

We also looked at a rubric for Best Practices in Grading.  I really like this rubric, although I don't know who created it, so I can't credit them!  (Sorry...if you are reading this and you created that rubric, please send me a message so that I can credit you...you are awesome!)  The rubric seems aligned with all the grading research I've read so far.  I don't really have any disagreements with it at this time.  It was also reaffirming to have the changes I've decided to make reflected in the rubric in a positive way.  Progress feels good!

We completed a what do we need list.  We put down everything we could think of because they said it was our only chance to get what we need.  We feel like we've made a lot of changes in our district for this project, changes that many other school are not making, so we also want the support to make sure that it will be successful.  It is important to me that this is beneficial to students.

Unit 5 LTs (draft)

Well, here I am again, asking your advice on my learning targets!  But the difference today is that this is the last time :)  Here you go!

UNIT 5:  QUADRATIC FUNCTIONS AND MODELING

Section 5.1:  Graphing and Interpreting Quadratic Functions

                Standards Addressed:  F.IF.4, F.IF.5, F.IF.6, F.IF.7, F.IF.8, F.BF.1

5.1A:  I can find the intercepts and extrema for a quadratic function (in any form).

5.1B:  I can graph a quadratic function using the intercepts and extrema.

5.1C:  I can interpret the meaning of intercepts and extrema of a function used to model a situation.

5.1D:  I can calculate and interpret the meaning of the slope between two points of a function used to model a situation.

Section 5.2:  Comparing Functions

                Standards Addressed:  N.RN.3, F.IF.9, F.BF.3, F.BF.4, F.LE.3

5.2A:  I can compare properties of two functions (in any form).

5.2B:  I can describe and identify translations that determine function families.

5.2C:  I can find inverses of linear functions (in any form).

Thoughts/Notes

• All but three of the standards in this unit were addressed previously in unit 2.  In this unit they are to be extended to quadratics.
• I kind of would like to throw 5.1D in with 5.1A and C, but I couldn't get the wording right and so then I questioned whether it actually fit or not.  Thoughts?
• I honestly feel like this was the easiest unit...maybe that's because I'm to the point where I'm not as worried about perfection as I was at the beginning...?  Maybe that means this unit is awful...?

Once again, I ask for your feedback.  I want to know what needs to happen to make these awesome for my students.  I appreciate you taking the time to read these!  Thanks, and once again remember...ALL DONE!

-Kathryn

Unit 4 LTs (draft)

I still have a million thoughts whirling around in my head about Unit 3 based off of comments and twitter conversations, but onto Unit 4 I must go!

UNIT 4:  EXPRESSIONS AND EQUATIONS

Section 4.1:  Polynomial Operations and Modeling

                Standards Addressed:  A.SSE.1, A.APR.1, A.CED.1, A.CED.2

4.1A:  I can add and subtract polynomials.

4.1B:  I can multiply polynomials.

4.1C:  I can create equations to model situations and use them to solve problems in the context of the situation.

Section 4.2:  Zeros of Quadratics Algebraically

                Standards Addressed:  A.SSE.2, A.SSE.3, A.CED.4, A.REI.4, A.REI.7

4.2A:  I can find zeros of quadratic functions by taking the square root.

4.2B:  I can find zeros of quadratic functions by factoring.

4.2C:  I can find zeros of quadratic functions by completing the square.

4.2D:  I can find zeros of quadratic functions by using the quadratic formula.

4.2E:  I can solve an equation/formula for a specified variable.

Thoughts/Notes:

• Do I really need 4.2A?  I'm looking at A.REI.4b, which says students solve by inspection, taking square roots, completing the square, the quadratic formula, and factoring.  Well, that's a lot, so I feel like it needs more than one LT, but not 5!  And to me if you solve by CTS you are taking a square root...would basic square root equations build up to CTS?  I would prefer 4 LTs to 5 in that section...thoughts?
• I'm a little confused about how I can fully meet A.SSE.3 and A.CED.2 which both have graphing components when most of the graphing standards aren't until Unit 5 (F.IF.7, F.BF.3, and many others).  We will likely do all our graphs by plotting points or using technology for Unit 4. 
• Last year when we found zeros of quadratic functions we did algebraically, numerically, and graphically all together.  I'm a little sad that they are split up here.  :(  I like drawing all the connections, but it will have to wait to Unit 5.

Please give feedback by commenting below or tweeting me (@kathrynfreed).  I really appreciate how much everyone has helped me so far with processing these.  Every time I think my brain is over-capacity with thoughts on standards and learning targets somebody will make a comment that gets me thinking again!

For those of you who have been walking through this entire journey with me, there is only one unit left!  Hang in there!

-Kathryn

Unit 3 LTs (draft)

I promised Unit 3 LTs by the end of the week, and I think I made it on time :)  There's nothing like cutting it close.  I had hoped to have units 4 and 5 done by this time as well, but we'll just have to see where I can get.

Here they are.  More thoughts at the bottom!

UNIT 3:  DESCRIPTIVE STATISTICS

Section 3.1:  One-Variable Statistics

                Standards Addressed:  S.ID.1, S.ID.2, S.ID.3

3.1A:  I can create plots (dot, box, histogram) to represent data.

3.1B:  I can find and interpret the mean, median, IQR, and standard deviation.

3.1C:  I can compare the shape, spread, and center of data sets using the mean, median, IQR, and standard deviation.

Section 3.2:  Two-Variable Categorical Data

                Standards Addressed:  S.ID.5

3.2A:  I can create a two-way frequency table for categorical data with two categories.

3.2B:  I can find and interpret relative frequencies (joint, marginal, and conditional) in the context of the data.

Section 3.3:  Two-Variable Quantitative Data

                Standards Addressed:  S.ID.6, S.ID.7, S.ID.8, S.ID.9

3.3A:  I can represent data with a scatter plot.

3.3B:  I can find a line of best fit and use it to solve problems in the context of the data.

3.3C:  I can interpret the meaning of the slope and the intercepts.

3.3D:  I can find and analyze the meaning of the residuals and the correlation coefficient.

3.3E:  I can make inferences about correlation and causation.

Thoughts/Notes:

• It makes sense to me to study 1-variable statistics separately, so I'm mostly OK with the organization of 3.1.  We did get a quite decent twitter conversation on whether or not students should be required to calculate standard deviation by hand.  Any further comments on that are welcome.  Thank you to those who already participated and gave me ideas.
• I had planned on doing all two-variable statistics as one section, but there is a lot there!  And it seems weird to me to have 1 standard on categorical data when the rest are on quantitative data.  Hard for me to make that fit well.  There is so much with the quantitative data though that I couldn't combine them.  I hate having 5 LTs in one section (it feels so big) but I feel like I still haven't done the standards justice.  Also I think Section 3.2 being so short will provide an opportunity for a different structure of class.  Maybe we will do a project assessment instead of a test

Please, please, please leave your thoughts in the comments or tweet me (@kathrynfreed) Like I have said with every other unit, I really truly want to make these the best goals I can for my students.  I appreciate all of your feedback whether praising my awesome-ness (not usually) or giving me advice for improvement (usually), I really like how you guys can always make me think more--even when I think my brain is dead!  Thanks for that!

-Kathryn

Unit 2 LTs (draft)

I have been working on my Unit 2 Standards.  Please remember that my big unit breakdowns are coming from Appendix A (this is because of my school's curriculum and the project I've been apart of).  The second unit from Appendix A is GIANT.  Over twenty standards.  That is difficult to manage, thankfully I had did some breaking-down of it this past year as I taught it, so I had a bit of a foundation.  I have changed a lot though, so without further ado...

UNIT 2:  LINEAR AND EXPONENTIAL RELATIONSHIPS

Standards Addressed Throughout:  F.BF.1, F.IF.4, F.IF.6, F.IF.9, F.LE.5

Section 2.1:  Functions in General

                Standards Addressed:  F.IF.1, F.IF.2, F.IF.5

2.1A:  I can find the domain and range of a relation (in any form).

2.1B:  I can determine and justify if a relation (in any form) is a function.

2.1C:  I can use function notation to describe, evaluate, and graph a function (in any form).

Section 2.2:  Linear Functions

                Standards Addressed:  A.REI.10, A.REI.12, F.IF.7

2.2A:  I can determine and justify if a function (in any form) is linear.

2.2B:  I can find the slope and y-intercept given a linear function (in any form).

2.2C:  I can graph a linear function (in any form).

2.2D:  I can define an explicit function to model a given situation.

2.2E:  I can interpret the meaning of the slope and y-intercept of a function used to model a situation.

Section 2.3:  Systems of Equations

                Standards Addressed:  A.REI.5, A.REI.6, A.REI.11

2.3A:  I can state whether or not given values for the variables represent a solution to a system of equations.

2.3B:  I can estimate a solution to a system of equations graphically.

2.3C:  I can identify a solution to a system of equations numerically.

2.3D:  I can solve a system of equations algebraically.

Section 2.4:  Exponential Functions

                Standards Addressed:  F.IF.9, F.BF.3, F.LE.1, F.LE.3

2.4A:  I can determine and justify if a function (in any form) is exponential.

2.4B:  I can find the base and y-intercept given an exponential function (in any form).

2.4C:  I can graph an exponential function (in any form).

2.4D:  I can define an explicit function to model a given situation.

2.4E:  I can interpret the meaning of the base and y-intercept of a function used to model a situation.

Section 2.5:  Sequences

                Standards Addressed:  F.IF.3, F.BF.2, F.LE.2

2.5A:  I can identify if a sequence is arithmetic, geometric, or neither.

2.5B:  I can define an arithmetic sequence (in any form) recursively and explicitly.

2.5C:  I can define a geometric sequence (in any form) recursively and explicitly.

2.5D:  I can explain why a sequence is a function.

Section 2.6:  Exponents and Radicals

                Standards Addressed:  N.RN.1, N.RN.2

2.6A:  I can find powers and roots.

2.6B:  I can translate between exponential and radical expressions.

2.6C:  I can simplify exponential and radical expressions using the properties of exponents.

A few of my thoughts:

• I want my students to understand that a function has multiple representations, and I want them to be comfortable moving from one representation to the next.  This is why I put "in any form" in so many of the learning targets.  I think it's obnoxious, so I think I will take it out...but for now I need it to remind myself of that crucial important concept.
• I think Section 2.6 actually fits better before Unit 4 (when quadratics are introduced).  For Unit 2 all I need is the definition of an exponent, negative exponent property, and the zero exponent property to go along with exponential functions.  I don't think it's worth doing all properties that far ahead of when they can be used in context.  So I will likely break slightly from the recommendations of Appendix A and place this with Unit 4.
• [Edit 7/28]  There is nothing specific in here about comparing linear and exponential functions, but we do it as we explore exponential functions, and also with sequences.  That's one of the reasons why I chose to not integrate sequences into the other sections.  We will discuss similarities and differences, and I will ask students to compare on assessment (we have "advanced" questions so I can ask an extension of a LT fairly).  Does that make it OK that I don't have it as a specific LT?  I just feel like there are SOO many...

PLEASE, PLEASE, PLEASE give me feedback.  Either by commenting here or by tweeting me (@kathrynfreed).  I want feedback from you no matter what you think.  Making decisions like this for my classroom is a little terrifying for me, so your feedback helps me know what I need to change to make this the best I can for my students.

-Kathryn

Unit 1 LTs (draft)

This is a follow-up to this previous post on Unit 1.

I (finally) have my first draft of Unit 1 LTs ready to share.  I am very eager for feedback, as I want these to be as good as they possibly can!

Section 1.1:  Reasoning Precisely with Quantities

Standards Addressed:  N.Q.1, N.Q.2, N.Q.3, A.CED.3

1.1A:  I can choose appropriate units and interpret units for a given situation.

1.1B:  I can determine an appropriate level of accuracy required for a given situation.

1.1C:  I can use dimensional analysis to convert units in the context of a problem.

Section 1.2:  Reasoning Precisely with Equations

Standards Addressed:  A.SSE.1, A.CED.1, A.CED.2, A.CED.3, A.CED.4, A.REI.1, A.REI.3

1.2A:  I can create equations and inequalities and use them to solve problems (1 and 2 variable).

1.2B:  I can graph equations and choose an appropriate scale.

1.2C:  I can solve an equation/formula for a specified variable.

Please, please, please give me any feedback you can! (I'm pretty much begging you.)  Whether you think I dominated unit 1 (probably not) or think I totally screwed things up (much more likely), I want to hear your feedback so that I can improve them before the school year starts!

You can comment below or tweet me (@kathrynfreed) to give me your thoughts!  Thanks!

-Kathryn

Day 3

We had Day 3 of this project and we got to present right at the beginning of the day (Well after a Kid President video--he's hard to follow!).  We shared the key points of our action plan...almost like what I posted previously, but not the "why?" part.  I figured that part would be better to share verbally if the conversation went that way.

But I have to admit I was totally wrong in my assumption that people wanted to know why.  Most teachers are totally on board with the plan.  They want to see it happen, they just need help figuring out the logistics.  What was best about presenting was all the questions that came from this.  Everyone is trying to figure out how to make it work and so not all of the questions were addressed to us, some of them were addressed to others, too.  And that helped us realize some of the things we still have to figure out.  What great collaboration!

For the rest of the morning we split into groups:  Math teachers, Special Education teachers, and AEA staff. As Math teachers we continued our work to unpack standards in Unit 1 and find appropriate assessments.  We were working with 1-2 other teachers on a standard of our choice.  I worked with a teacher I had never talked to before, and we picked a standard she had worked on previously.  I felt as though it was much more productive this time.  She and I communicated well together, and I was able to be a little bit more flexible about the whole process.  I tried to avoid the things that had stressed me out too much previously.  We made some progress and we will continue to work on Unit 1 and maybe Unit 0 next time.  I hope that we can get the first part of the year planned prior to the beginning of the school year!

In the afternoon we discussed standards based grading in a little bit more detail.  This is one area that I feel like I have a good start to because of our school's PD, but there are lots of flaws that we need to work through.  I felt like the conversation we had around this were good, but I feel pressure to iron out the flaws prior to next school year.  I have to put my grading plan in my syllabus, and I want to have something fair figured out the communicate to students and parents.  This is a big challenge that I discussed with some of the AEA people.  They understand and also want to work to find a solution for us, however not all participants are going to fully jump into this shift next year, so it is going to be challenging to meet the needs of all the schools/teachers represented.

To conclude our day we got to be students in the lesson DVR Dilemma from Yummy Math.  The purpose was to get us to think through the practice standard that we are working on improving.  We have been challenged to work to improve our teaching strategies to better address this for our lesson plans in the upcoming week.  I will be working on teaching students to multiply polynomials...it's really hard for me to think about how to use this to help students "Make sense of problems and persevere in solving them."  But I've been thinking about it a lot after that challenge...maybe I will post again about what I decide to do and how it goes.  Going to be a big risk!

Presenting our Plan

We were asked to present our plan for implementing instruction at three levels at our Day 3 meeting.  Not sure why us or what part of it most people are interested in, but we met after school today to look over our plan again and discuss our presentation.

There are two main aspects of the plan:  assigning students and scheduling classes.  I will give some highlights of each below.

Assigning students to the Tier II and Tier III courses:

• Students who have addition math instruction as a requirement of their IEP will receive Tier III instruction
• Students will be identified for intervention (Tier II) using a variety of sources:  Algebra Aptitude Test, IA Assessments, Previous Course Grade, Teacher Recommendation.  We will likely choose a cut off for each of these and then flag students who are on the list for 3 of the 4 identifiers.  This may include IEP and non-IEP students.
• Our principal, the math team, the special education instructor, and AEA representatives will all participate in selection process
• Currently we have no official universal screen or progress monitoring in place

Scheduling, Planning, and Instructing Tier II and Tier III:

• We are on a 7-period day, with 51-minute class periods (and a 17 minute homeroom)
• As the Algebra teacher, I will give up all my non-Algebra classes next year (currently consisting of 2 periods each day) to provide tier II instruction.  So I will teach 4 periods of universal instruction and 2 periods of intervention.
• I have requested that the tier II classes be schedule at the beginning/end of the day so that all students in the class will have had same universal instruction
• My dropped courses will be taken on my the 2 other mathematics teachers we have by increasing enrollment in advanced classes and no longer offering Pre-Algebra
• Tier III will be given to students during their Guided Studies time.  It will mean of their 51 minutes of GS, 30 minutes each day will be Algebra instruction given by the Special Education instructor
• I will be planning (with the help of all my peers in this project) the universal, tier II, and tier III instruction
• We have requested 1 day each week to collaborate on the instruction for tier III students
• Students will receive elective credit for tier II and tier III algebra.  Will be unable to shift in and out of course as needed (not seen as a potential problem).
• We have a special education associate who will be able to facilitate instruction during universal, tier II, and/or tier III

Why?  I honestly think that is what some people want to know.  "Why are we willing to go to all these lengths to provide something like this?"  I would have to say because I can see that my students need it.  I have many students in Algebra currently that I desperately wish I could provide this opportunity to.  I see the need and I address as good as I can, but without the additional time and the smaller class sizes I cannot do all that is necessary.  

These are the ideas we are going to try to get across within our 10-minute time frame, as well as providing an opportunity for others to ask questions.  I hope this will help others find a way to make this successful in their schools as well.

Day 2

Our second meeting (also known as "Day 2") was packed full of thought-intensive analysis of multiple things. We started by discussing "Understanding by Design" lesson planning, where focus begins with the desired result.  There are 3 stages of this planning method:  the Desired Results, the Assessment Evidence, and the Learning Plan.  This process can be challenging because only after a long time looking at the standards and choosing an assessment method can the instruction planning actually begin.  As teachers it is hard to wait so long to plan instruction!

After discussing this method, we broke into groups and began unpacking various standards from Unit 1 of Algebra 1 as defined by Appendix A of the CCSS with this template to guide us.  This is really challenging!  At first we were supposed to base it off of our professional understanding of the standard (which is not always clear), and discuss our understandings.  Then we could look to some other documents, but there are few resources available from the authors of the CCSS to help us unpack them.  We spent all morning doing this!  It felt very unproductive to me for two reasons.  First, because we were working in groups with people we didn't know very well, and so it was hard to respectfully critique each others' ideas.  And secondly, because we did not define "understanding" and "knowledge" prior to getting started.  All in all a challenging morning for me.

We were actually supposed to do one more thing before lunch.  Choose one of the practice standards to focus on for the rest of the year--yikes!  I remember hearing someone say that the first four are the most important, so we chose to go with #1:  Make sense of problems and persevere in solving them.  Then we had the opportunity to change the rubric for it.  The rubric we were given was not structured the way I like to have rubrics structured, so I redesigned it with the help of my coworkers present at the meeting.

After lunch we created a proposal for how our district should implement Tier II of the instruction.  We had already had quite a few conversations with our principal and other math teachers in our district, so I felt as though the proposal was just formalizing all of those conversations.  The goal/plan is for me to teach only Algebra next year.  Four periods of Algebra (tier I) and two periods of Strategies (tier II), while a special education teacher would teach the students receiving tier III instruction during their guided studies time.  My hope is that I can have the "strategies" courses at the beginning/end of the day, so that the students have had the same instruction from the Algebra class.

Once we completed that, we discussed the benefits of standards based grading.  My district is already in the process of developing standards based grading, so we have an idea of what it is, what it might look like, the benefits, and the drawbacks.  However I still found this conversation to be very rewarding.  I jumped into standards based grading this year without all the background work that teachers in my district have done, so it was good for me to step back and remember why they chose to move in this direction.

The last thing we did is to split off as Algebra teachers (special education teachers did something else) and look through 7th and 8th grade standards that we might have to teach during the transition to the common core.  These are the standards that are necessary to meet the Algebra standards, and may not get mastered in 7th and 8th grade.  I think it was important to acknowledge that it is a transition to the common core, because at times I feel pushed to move my students over to it too quickly.  It is important to get there, but we also have to remember that we are in a transition time.

So when I left Day 2, my brain was working in many different directions, but I felt that all were beneficial for the future of our students and their mathematical learning.  I sometimes just wish that it didn't take so much work, but in the end it really does.  In which case it is important to remember the purpose--student learning!

Day 1

I attended day one of our Tiered Algebra 1 Action-Research Project.  We got an overview of the project including the components that will be involved:  Iowa Core Standards, Standards-Based Grading, and Tiered Instruction.

We spent a lot of time discussing the tiered instruction because that is the newest idea for most of us.  This is based off of RTI, or Response to Intervention, a method used to keep students performing at grade-level and provide assistance when they fall behind.  There is not much information published about implementing RTI at a high school level, especially for mathematics, so we took a look at the basic structure of the program.

We will provide three tiers of instruction.  The first is universal.  All students receive the first tier of instruction.  The second tier is for some students (10-20%) that for a lack of a better phrase are "chronic mathematics strugglers".  These students need to receive an additional 30 minutes of instruction everyday in small groups (7-10 students).  The third is for a few students (1-5%) who have IEP math goals, with additional mathematics instruction written into their IEPs.  These students will also receive an additional 30 minutes of instruction everyday in even smaller groups (1-3 students) with a special education instructor).

Oh to think of all the scheduling issues this creates!  Thankfully our math department had already been discussing the need for intervention and brainstorming ways to make it work.  All that brainstorming with this guidance for how best to help those students allowed us to see this not as an impossibility, but a challenge we would have to work around.