Portfolio Reflections

The end of the year is here! 

I can't believe that I have neglected this blog so much this year...then again I can.  It was a doozie of a year.  Working with 7th grade RtI, 8th grade RtI, a plethora of classes with students needing Regents prep for mixed Regents exams, Algebra A and Algebra I Common Core... along with Student Council and all sorts of things that come along with being new to a district.  I tried my best this year!  

One thing I tried was student portfolios.  I had students keep folders in the room and periodically throughout the year, we would add to the portfolio and keep a table of contents.  The idea was to get students to not just take a test or quiz and throw it out or move on.  Good idea, right? 

I have a lot to improve on for next year with this... but this year worked out as well as it could.  I kept the artifacts to just tests and quizzes, and they had to type a reflection that included some sentence starters I provided.

These are a few of my favorites:

Student example and my comments

Student example and my comments

Student example and my comments

Here is an example of the rubric I used:

This is the rubric I used to grade them, the portfolios were a 4th quarter test grade.  (double jeopardy, yes, but the reflection was the point.  I figured an easy grade that teaches self reflection)

If you're interested in my reflection and rubric, you can download them here:

Overall, I was proud of them.  Next year I was hoping to have them pick out artifacts they are proud of.  Perhaps include projects.  I will be incorporating more student goals along the way, too, per unit, so I can ask questions like "did you meet your goals?" and "what standards are did you master and how?" etc.

How do you incorporate student reflection/portfolios??

Including Students in Interim Assessments

Holy Cow!  This year is flying by.  It has already been since NOVEMBER that I have written a post.  I have things stored away in my notes that I want to post about, so I will make a list here and hopefully provide links as I "catch up":

• Pascal's Triangle/Sierpinski's Triangle Bulletin Board
• Math Blog Fail
• Hour of Code
• Hummingbird Kits
• Racecar Lab for Systems of Equations
• INB update
• Algebra A course structure update

Hopefully in my free time I can update these rather than sitting on my couch eating Honey Nut Cheerios and watching Netflix...  I was told it takes 28 days to form a habit.  

For now, I will keep today's entry short and sweet.  I have been racking my brain (wracking or racking?  I never know which one to use...) on how to integrate students in interim assessments.  I know it is for me to help track where they are, where they've been, and what they need in order to continue moving forward, but I also know how powerful it is for me to step back and guide them as they figure out what they need.

After one of our data meetings, someone suggested that I read chapter 8 of Tools for Thoughful Assessment.  In doing so, I found the goal cards to be a great idea.  I ended up combining the two suggestions there and have created them.  I have attached both versions so you can look at them, use them, compare them to what you do or don't do already.

What are some things you or other teachers you know do to include students in looking at data and goal setting?  Am I biting off more than I can chew like my glorious Blog attempt?  Or my ineffective, overambitious grading policy?

Module 3--sequences to functions

As a Western New Yorker, I am used to snow, cold, and "lake effect".  Currently many southtowns are engulfed in over 60 inches of snow in what they are calling the "snowpocalypse" and "snovember".  Luckily (?) I am far enough south that my drive home was sunny and my roads are clear.  Strangest snow storm ever!  Happy Buffalo is getting some national attention, but sad that it is under these circumstances.  I hope people are staying safe and warm!

View of downtown Buffalo--that is a WALL of snow!  Relentless storm that dumped 60+ inches of snow.  (I did not take this photo)

The snow drifts in Buffalo-- photo credit to @JayMcKee74 on Twitter

View of my town--not NEARLY as much snow, and dry roads!

On to the math...

I have decided to skip Module 2, and save it for the end of the year.  Has anyone else decided to do this?  I know there are connections made to regressions in Module 4, but it seemed to be more logical to continue with the base Module 1 provided and move into function work, after the intense equations and inequalities study.  

That being said, I have just begun Module 3 with my Algebra 1 students.  I am still going strong with my Interactive Notebooks, ideas for improvement and modification are swarming daily.  Module 3 seems to jump all over the place.  I am anticipating spending more time on sequences than allotted, though I am constantly trying to relate it to functions (which I know is coming up in Topic B).  

I used the "double and add 5" preface from Lessons 26 & 27 in Module 1, but I am not sure if that was effective.

What other ways do you introduce recursion?  How do you get across the necessity for a recursive formula or an explicit formula?  Do you have students memorize the "ways" to get an explicit formula based on additive change and multiplicative change?  

Also, what good INB pages do you use for linear and exponential growth?  

My INB pages for this section of the modules look like this:

Any ideas?! What's working for you?

Stay tuned, I will keep updating regarding this class and my Algebra A class (first year of a two year Algebra course).

It's been a while...

Phew!  It certainly has been a while since my last post.  A few things have occurred to keep me occupied:  I moved, got married, my grandmother passed away, and I am the advisor for student council, who is responsible for the homecoming court and dance.  Somehow I survived the chaos and I am barely keeping my head afloat.  I wanted to keep you all in the loop as to how things are going!

First, the blogs had to get nixed.  Things were too crazy, and class time was needed to establish my classroom goals, rather than introduce another weekly task that could perhaps drive them away from the math.  Someday, perhaps, I can get them into writing about math and analyzing math in the news.  For now, these interactive notebooks seem to be working out really well!  So far, I have created a rubric in which the students grade themselves and their progress each time, and I assess afterwards.  I grade the notebook out of 6 possible points, 3 from organization and neatness and 3 from completeness and quality.  On the back, students have an opportunity to explain their grade; for instance, maybe they were absent for a period of time and didn't know where to get the notes, maybe they had a hockey tournament and didn't bring their notebook, or maybe they are sloppy and haven't paid attention to detail.

This has seemed to work really well with the notebooks.  So far, it is the 8th week of school, and I have done 3 notebook checks.  I am trying to get in more quizzes, and thus more notebook checks, but it seems that lately I have been neglecting the notebooks.  I have found it to be very challenging adapting the New York State modules to this notebook format, but I will be so proud when I have completed it!  Currently, my Algebra 1 students just took their test on Module 1 (minus systems of equations and systems of inequalities and polynomials...I chose to make these post-test items, that would be a nice bridge to Module 3).  The table of contents of a student's notebook looks like this:

Mathequalslove has provided me with many pages of inspiration that I have added to our notebooks. Some is simply reflected in our table of contents and our glossary.  Every day, I have our learning target (the standard in "I can" form), the TOC (table of contents) page numbers, and the WWK (words worth knowing) that the students will be adding to their notebooks that period.  Students have become good at checking the board, so much so that on an "off" day, a student said "I didn't know we needed to add anything because it wasn't on the board!"

Though I have taught before at other districts, this is the first time I get to take pride on my own curriculum.  I am thoroughly utilizing the NYS modules for my lesson inspiration, and am trying to meld this with Dan Meyer activities and the ease of Mathequalslove notebook notes.  I would be spending a ton of more time if I didn't have the #MTBoS!!!

In addition, as a Common Core State, and with our state Regents exams consisting of increasingly more word problems involving multiple forms of assessment of standards, I plan on taking a day or two to address this Close Reading protocol from ELA modules to apply to the math classroom.  I plan to start with 3rd grade word problems to practice the protocol and then move into some grade level problems.  My students are "averse to word problems" as Dan Meyer would put it, and I am hoping that this is a good start to giving them access to the content.  I will also have some "lab" type activity to get them motivated!

Here is another example of how I am melding the INBs with the statewide curriculum (Compound Inequalities):

Yet another example (solving equations with 2 variables):

I absolutely love how enageny makes the connection between truth values of equations, solutions to equations with one variable, solutions to equations with two variables, and linear functions.  It truly allows students to make connections with the function work from 8th grade to the equations work from this year!

Finally, here is a student example of an adaptaion from Mathequalslove blog;

I will keep at it, and do my best to post my work!  I don't think I can do as great a job as others, but I will do my best.  In November I am attending the AMTNYS conference, so hopefully I can post my findings from there!  

P.S., look for my new name on Twitter: @kayla_cappuccio

Classroom Setup

Classroom Setup

Phew!  I survived the first week!  First things first:  I wanted to post pictures of my classroom, before and after.  I have been inspired by mathequalslove and everybodyisagenius with my room setup, posters, norms, etc.  I took over for a teacher who had retired and left EVERYTHING in my room!  The following is the "before":

I was hoping this was actually a Commodor!  Just rulers and compasses.

Rows and junk everywhere

My boxes, a projector, and a growing pile of recycling

Extremely old and rusted cabinet with disgusting things in it

Mess galore!

Now for the "after":

Set up my desks in groups, contact paper on my desk, new bookcase

Emptied old bookshelves, and a closer look at my groups

Tiny row of laptops!  My blackboard near the door.

My MTBoS posters! I had to make it smaller to fit on my wall

My daily setup, inspired by mathequalslove

My back wall with function dancer inspired by MTBoS

More of the classroom

My smartboard!!

My lovely desk, very homey.  Found a coat rack in the basement of the school :)

The whole "shebang"

My view

My setup seems to work for now.  I get lots of complements on my desk :)  The seating arrangement works well too, but I don't like that my seats are connected to the desks.  I have just ordered baskets where I am going to keep rulers, glue, tape, and colored pencils in them for Interactive Notebook (INB) work and so on.

I got the idea for my syllabus from Dan Meyer and mathequalslove with the trifold brochure to go into their INBs and came up with this for my classes:

Front/Back

Inside

I will have to finish up with the rest of my first week in another entry, I have to prep for the rest of the week now.  Thanks for all the support and feedback!

Common Core Algebra Planning (Part 2)

Wow!

It's truly amazing that we have the technology to connect with so many people so very quickly!  Thank you for visiting my blog, and for the positive feedback from all of my fellow teachers and professionals in Twitter and the MTBoS!  As promised, I will continue my musings of how I envision the first couple weeks of school.

Outline

Distributive Property

I plan on continuing my work with the real numbers as Topic B outlines, but rather than the exact lessons I hope to talk about the distributive property first.  What I love about this approach is that it ties in a lot of what the elementary grades are currently doing with the properties.  Essentially, it is "filling in the gaps" of my students, since the work we do in Algebra assumes this understanding, but based on where my students are in the education system, they have not had the instruction.  I absolutely LOVE the pictorial references of distributive property to area.  Using the below picture, instead of having my little arcs connecting the 4 to each of the addends to show distribution, it is easy for any student to grasp since they can count the squares and relate it to the expression.  The picture below that, where I show distributive property with subtraction, shows the natural progression of the area model, which gets more abstract with area.

Math Progressions

This brings up a good point about the mathematical progressions.  If you have not looked at these, and you teach Common Core math, I highly suggest that you check it out.  Though the reading is at times dense, it completely puts things in perspective when it comes to the progression of mathematics with coherence across grade levels.  I am a secondary teacher and I thought I knew elementary math (what they teach in elementary school).  I was wrong.  Digging into common core math at the most basic level makes things so much easier for me to tackle the Algebra curriculum, which looks so different than the Algebra we are used to.  One suggestion: read these progressions a little at a time before bed; if you're having trouble sleeping, it'll put you right to sleep!

Commutative Property

I love the idea of having the students interact with the operations here rather than telling them there is a commutative property of addition and one for multiplication.  Have them explore all four since we have already dug into the operations earlier in the unit.  Most likely they will recognize that they have seen the properties before, and that is okay.  I doubt they have done much more than mention the properties and not use them again except perhaps on a quiz or in passing.  I love having cutouts representing length for addition and area for multiplication.  This way they can see the commutativity!

Associative Property

I like the explanation I use in the picture for associative property.  When I was learning these properties in school, I never really saw a need to mention associative since it was similar to commutative in my opinion.  I think that having visuals really made the distinction for me, and perhaps for my students it will as welll.  I plan on making the analogy of driving down the street: the number of houses is the same, but depending on which direction you are traveling, the grouping of houses is perhaps different.  In the picture above, it would be easy to have concrete blocks for students to build numerical expressions.  Again, going back to the concrete-->pictorial-->abstract flow of mathematical progression.

In looking at module 1, there is a flowchart in Lesson 7 of the properties that kind of confused me.  I tried to make it my own, by adding color to distinguish the variables.  However, it was still very cumbersome.  At first I thought I liked it, but I am rethinking that now.  Anyone who has taught this lesson: what did you do to tie in the properties?  Did you teach lesson 7?  How did you adapt it?

What other lessons do people have for the properties that really gets students engaged and thinking about structure?

Common Core Algebra Planning (Part 1)

First Blog!

So here I am, starting a new job as an Algebra teacher; 1 section Common Core, some sections of year 1 of a 2-year algebra course, and some lab sections in the second year of a 2-year algebra course.  I have been completely transformed by what I have seen online on other teacher blogs, the MTBoS, and Twitter Math Camp.  People like Dan Meyer, Sarah Rubin, and Sarah Hagan have completely transformed how I view teaching math.  I know this year is going to be the best year yet, and I will only continue to learn more!

I am overwhelmed with ideas of classroom posters, interactive notebooks, three-act-math tasks, and first day math activities.  So far, I have begun my notebook, but I am trying to adapt our New York State modules to fit my style and my approach to laying the foundation for algebra.  

Sorry for the faintness of the writing, I feel nervous to commit to the outline!

Outline

For those of you using modules, I have really been able to dig into the progressions of K-HS math and the structure of the modules themselves.  I have even ordered myself a color, teacher copy of the modules that can be found here! Anyways, based on how things have worked for others this year and what I know, I have decided to not do Topic A.  Instead I have decided to modify Topic B and consulted an algebra textbook from the 1950s similar to the one below...

...in order to review the deep-down basics of numbers, properties, and operations.

1. I want to review math as a language.  Music, German, and Klingon are all languages.  "Like other languages, Mathematics has its own vocabulary, grammar (principles that govern the correct use of a language), syntax (the part of grammar that concerns rules of word order), synonyms, negations, conventions, abbreviations, and sentence structure" (Esty).  I love, love LOVE this quote!  So inspiring and relevant!
2. What is a number?  Is "12" a numeral?  What is the value?  Why wouldn't we use "(8-5)*4" to represent "12"?  I want to have rich discussions, or even arguments, over what a number is.  In 9th grade, students think they know what math is about, but I guess I want to shatter that illusion.
3. Sets.  What is a set?  A set of dishes, a set of tools, a set of numbers...I think this a good flow into the different number sets like the natural numbers, whole numbers, integers, etc.  I am not afraid to use the notation as in college either, I have made a poster!
4. Operations I love this progression found on the math page here.  Again, kids think they know what operations are and how they work, but they really don't!  I also think this is paramount for making connections from integers to polynomials like the modules do.  As for the Order of Operations?  Forget PEMDAS!  I love love LOVE the "Boss Triangle" (also on my math posters).  I got the idea from this article from NCTM.

I am also going to start a weekly student blog for my math journals, called "Writing Fridays".  I know it's not a catchy title, but I think that it is a good way to instill some literacy in the math classroom.  So on Fridays I am thinking of posing a task, or question to the students.  They have parameters to answer over the weekend (due Monday) and respond to at least two other students (due the following Friday).  We will develop a rubric, but I love the idea of allowing the students to be creative with their responses and "critique the reasoning of others".  I, of course, will monitor responses and posts to make sure it is appropriate.

For instance, the first Friday I have a "Write your Mathology".

Students can pick from these prompts (borrowed from here):

• How do you feel about math? Do you like or dislike it? Why do you feel that way?
• Are you "good" at mathematics? Explain.
• Do you like some areas of mathematics better than others? If so, which ones do you like or dislike? Why do you like or dislike them?
• What makes math great or horrible for you?
• What experiences in math have you liked? Why?
• Describe your most memorable experience in learning math (good or bad).
• How do you feel about taking the math class you are taking this year? What do you expect to learn about?
• What type of things do you think are important to help students learn math?

The next week, they will answer "Is math the language of the universe? Why or why not?"  Here is a cool article that references this video that students can watch to whet their appetites:

I will have to write another blog on the entire next week I have planned, including properties, equality, expressions...

I told you, my mind is SPINNING with ideas from the #MTBoS!!!!

Esty, Warren. "The Language of Mathematics." (n.d.): n. pag. AugustMath. Web. <http://augustusmath.hypermart.net/LMSection1p1.pdf>.