Thursday, June 26, 2014

5 Practices by Smith and Stein

After finishing Mindset and reflecting on it, I chose to read 5 Practices for Orchestrating Productive Mathematics Discussions by Margaret S. Smith and Mary Kay Stein.

I first wondered if actually naming the 5 Practices would give away the purpose of the book, so I was curious how I would blog about it without doing that.  But after reading it, I know there is SO much more to the book than the names of the 5 here they are:  anticipating, monitoring, selecting, sequencing, and connecting.  The whole purpose of the 5 Practices is to best prepare for teaching mathematical tasks so that we have to make fewer decisions during the lesson where we are less able to make good decisions.

It helps me to look at the 5 Practices in terms of the big picture of lesson planning and teaching.  As most people who read math teacher blogs are familiar with The Three Acts of a Mathematical Story [Task], probably most famously, if not first, presented by Dan Meyer, I will present 5 Practices in terms of the 3 Acts...except I'm going to start before Act 1.


Before any planning can occur, the teacher must "specify a goal that clearly identifies what students are to know and understand about mathematics as a result of their engagement in a particular lesson" (p. 13).  After having a clear goal, then the teacher must select an appropriate task.  A task that can be used to meet the lesson goal while engaging the students with the concepts and that "stimulate students to make connections [that] lead to a different set of opportunities for student thinking" (p. 15).  

This part is going to be a challenge for me, because I have trouble seeing what big ideas can be learned from tasks.  I know that there are a lot of tasks available from the #MTBoS, but selecting ones that are going to best fit my goals is a challenge.

Once a goal and a task have been established, the teacher begins anticipating all the possible solution strategies.  Consider strategies that lead to both correct and incorrect solutions.  Then create good questions to ask students who are using each strategy.  If it is a strategy that might lead to an incorrect solution, questions should be redirecting students down a correct path.  ALL questions should seek to reveal what understanding students have about their strategy.

Once this has been done, a teacher should complete a monitoring chart.  Here is an example I created to match what the book suggested:

I want to add a column for questions.  It will help me remember all those questions I came up with!  Here's a link to my version of the monitoring chart. [Note:  You will likely need to download into Microsoft Word to preserve formatting.]

After you have the monitoring chart completed you are ready to teach the lesson.  So here we go into Act 1!


Nothing new from 5 Practices for this act.  Essentially distribute needed materials, read through task, and ensure all students/groups have an understanding of what they are being asked to do.  Work to hook your students into the task so they can't wait to strategize a way to the solution.


After letting the students get to work, the teacher begins to monitor their progress.  This is where all that hard work of finding as many strategies, creating good questions, and having the monitoring chart ready is going to pay off.

As you move from group to group you have preplanned questions to ask students.  Likely the major change of this act as a result of the 5 Practices is that you will take notes on what strategies students/groups are using.  This will better help you prepare for Act 3 and it is also why the monitoring chart is so helpful.

In between Act 2 and 3, the teacher has to make some decisions.  First, select students to present their strategies.  This can be done effectively and efficiently because you have all the notes in front of you.  You will likely want to select at least one student to present each strategy.  Once you have selected the students, you will need to decide on an appropriate sequencing to best facilitate the discussion you wish to have in Act 3.  There isn't necessarily one sequencing that is best, but you must choose one that will work for you.


It is time to begin the conclusion of the task by drawing the whole class together and start sharing strategies.  During this time the teacher has the important job of connecting student strategies to each other and to the learning goal.  Good implementation of this will change Act 3 from a show-and-tell, to actual mathematical discussion.  This will probably be the most challenging of the 5 Practices for me.  I definitely see it as what will turn tasks from "fun days" into "fun, productive learning days".  I also think that the anticipating I will have done with the strategies will help me to see the connections, which in turn will help me guide my students in making connections as well.


There is always the Final Act of reflecting and modifying for the future.  I think the first time I implement a task this year I will plan to do it a different day in each of my classes.  That way I have time to reflect and improve in between implementations of the task.  And since I teach Algebra four times a day, it won't hold the stress of four possible dud lessons on my first attempt.

I am so excited to try to implement tasks.  I think this book really gave me a way to make them a productive use of class time.  My goal will be to implement at least one task per unit.  And in July I plan to continue to develop my units, learning targets, and I will begin selecting tasks :)  

During the year I plan to create a task binder where I keep a record of the tasks I use, the strategies we find, my monitoring sheets, and other notes.  This will help me to stay accountable and to have evidence of what I have done throughout the year.  

One more thought...the book gave a flow chart for The Thinking Through a Lesson Protocol.  I plan to use this as I plan each task, but I will likely modify it to make it more usable to me in my lesson planning.  Don't worry, I'll post again as I plan my first task!



Monday, June 23, 2014

Paper Organizer

This is my first #Made4Math of the summer!


I always try to keep my desk clean, but I can never seem to manage it no matter how hard I try.  It seems like everyday after school my desk is a giant pile of papers...

So I decided to reorganize a desk drawer that I never knew what to do with before because it was so deep.  I bought one of these...

...and put it in my drawer.  (I think that is what it is just took me a few years to figure it out.)  I labeled folders for each class that say "Algebra Today."  That is where I put copies for the day so that they don't pile up on my desk.  I also keep a folder for the unit next to the today folder.  Then after school I can empty the today folder into my bulletin board for absent students and into the unit folder.

It wasn't a perfect system, but it did help keep my desk cleared off.  It even helped me to use the drawer to store my papers to grade folder and my teacher binder.  This is what it looks like right now...kind of a mess since I haven't sorted anything since school got out!

I turned a wasted drawer into something useful that helps keep my desk cleared off! It felt like a very productive change :)



Thursday, June 19, 2014

Plans for June [Update]

As I mentioned in my first Plans for June post, I have been working with a few students in order to try to help them pass second semester Algebra.  I had three students commit to attending class Mondays, Wednesdays, and Thursdays from 9am to 11am for the month of June.  The deal was that if they completed enough work prior to June 30th they would not have to come anymore. But that they are not to miss any days before their work is completed.

Of the three students, one student missed a day and has not returned.
Another student missed a day, but came they next and I allowed him to continue (Is this bad of me?...probably in some ways...)
The other student has been early everyday, gotten all take-home assignments completed, and even taken time to pick up one of the other students.

Things I like:
  • Few students means I can really meet their needs without excessive commitment on their part
  • I told them day 1 that summer Mrs. Freed was not as organized or well-planned as school Mrs. Freed and they would have to be patient with me
  • They are learning
  • I am making them responsible for their learning
  • We are working on growth mindset (but they don't know it)
Things I don't like:
  • I feel guilty when they don't show up
  • I did not stick to what I said about missing
  • Sometimes getting them willing to WORK at what they are learning is a really big challenge for me and I get frustrated (it is awesome when the still do though)
  • I have really had to analyze everything and choose THE MOST IMPORTANT and THE MOST DOABLE in our short amount of time.  Paring down when I already felt like I pared down the curriculum was challenging and I didn't really like it.
I don't know if I would offer this again.  I would have be decide after I have finished.



Wednesday, June 18, 2014

Cute Storage Containers

We stopped at Dollar Tree the other day and they had these:

Aren't they cute! I got six.  I'm very excited to figure out what to use them for in my classroom.



Tuesday, June 17, 2014

[Unit Overview] Exponents and Radicals

Here is a brief overview of the unit I just finished on exponents and radicals.  Because of time, I did not do everything as thoroughly as I would have liked to.  However, I feel the structure is something that I can hold onto and build on for next year.

Evaluating Exponents and Radicals:

I got the idea for this structure from Sarah Hagan at  Here is her post on Radical Radicals.  I liked this idea so much that I decided to apply it to exponentials as well, even though my students knew more of the vocabulary that goes along with them.


We still struggled with knowing what the word evaluate means.  That is something I hope to work on a lot more at the beginning of next year:  vocabulary like evaluate, simplify, solve, expression, equation, etc.

My File

Properties of Exponents/Simplifying Exponential Expressions:

I got the structure for this lesson from Lizzy-Sensei at  Here is her post on Exponent Rules.  I loved the structure of it, but I didn't want to print an entire page for each student for each I changed it to a half-page structure.  I also noticed that my students would fill out the table, but then stop without answering the questions.  That was frustrating to me, and I don't know how to make it better for next time.  Also by the time we made it through all the properties the students were really bored of that structure of the lesson.

However I do know that I would plan on formatting it just a little bit better for my notebooks next year.  Also need a box around where we actually put the rule, because when I had them look back in their notes for the rule, they didn't know where it was.  I'm also thinking about reorganizing the columns in the zero and negative exponent property ones because students kept thinking that the rule should connect the first and the last column, rather that the ones that showed the zero or negative exponent.

Also students struggled to put what they had learned into practice.  It seems that they needed much more practice as they went.

My File [Reformatted as a Book]

Translating between Exponentials and Radicals:

I did an intro to try to help show WHY this is true, but I don't think it was very good.  This is something I really want to think through developing a good discovery-type lesson for my students next year.  For this learning target we put the rules into our notebooks and then I had a matching activity for them to do.  I asked them to write down their matches on the bottom of the page.

Simplifying Radical Expressions:

We added, multiplied, and simplified radicals.  We did adding multiplied, added, and then simplified to show that we could add things we didn't know we could add.


Adding Notes/Practice
Simplify Cards

I knew that was a lot in a few short days, and I had just read Kathryn Belmonte's post on Coloring Relay, so I made my students a coloring sheet with the answers written in.  I allowed them to work individually telling them that they could color in one section once they had completed the problem that had that answer...yes some students mostly colored and didn't do a lot of math.  But it was Friday and I wasn't feeling great, so it was a compromise I was willing to make.

This is not my favorite unit.  I think it is a lot of stuff to put into one unit.  But really it is only a couple standards, so it is hard for me to balance that.  It has taken me a long time to share this because I'm not very proud of this unit.  However, I put a lot of work into it.  I created and modified everything.  It was a lot of work, but hopefully now that I have things to this point I can make it better for next year.


Note:  All files must be downloaded in Microsoft Word to get correct formatting.


Monday, June 16, 2014

Thoughts after Year 1 of ISN

After a full year of using interactive notebooks in Algebra, there are three main things I want to work on doing better in the upcoming year.

1.  Hold students accountable for them

I chose not to include the notebook as part of the students' grades for several reasons.  One being that I use standards based grading, and I feel like a notes grade would be more a compliance grade than an understanding grade.  The other is that I teach about 90 Algebra students each year.  That would be a lot of notebooks to check.

I had told students that I would hold them accountable because when they asked for help the first thing I would do is ask them to take out their notes.  If they did not have their notes completed, then they would have to complete them before I was willing to help them.  I did OK at this, but I must not have done well enough, because even at the end of the year students were frustrated when I was making them copy notes from earlier.  And this actually meant that some students just stopped asking for help. :(  Not really what I wanted...

My notebook--no papers sticking out :)
Student notebook--lots of papers that should be glued in :(
My notebook--filled out TOC :)
Student notebook--empty TOC :(
My notebook--worked out problems :)
Student notebook--answers with no proof :(
In discussing this with the Algebra 2 teacher at my school, she suggested some accountability in a different way.  She recommended that I require students have their notebooks completed for the unit before I allow them to take the unit test.  I tried this with a review assignment later in the year and it didn't work out well, less than 50% of students had it completed on time... But she thought if I started with this at them beginning of the year students would come to expect it.  I know that I need to hold students accountable, but I'm not set on this as the way...however I do know that I could make this work.

I envision checking notebooks the day before the test while students are working on review stations.  Doing a 100% or 0% check like Sarah Hagan does (see here) would hopefully make the checking process faster.  If students do not have their notebooks complete I warn them that they must complete their notebooks before the test tomorrow.  When we start the next day I pass out tests only to the students who have completed their notebooks.  Other students must get on a netbook and work to update their notebooks.  If they don't get it done in time, then they have to take the test on their own time (before/after school) another day.

Like I said, I'm not sure this it what I'm going to do, so I would like feedback on this idea, please :)

2.  Be more organized 

One of the reasons why it was hard to hold students accountable was because I did not have a good organization system in place.  I figured out a decent system right before 4th quarter started, but I didn't share it with the students because I wanted to see how it would work.  It worked well enough, and with a few adjustments I think it will work great.  I shared some of it here.

I plan on including a monthly calendar on my bulletin board instead of writing on the folders, I can write on the calendar.  This will help if students want to see something more than a few days in the past.  I have a small file cabinet that I will use to store older papers.  I will have to try to organize the file cabinet a bit better than I did this year...I also think I might make one copy of each paper a specific color (ie. yellow) and then students know not to take that one, but to make a few copies first.  (I also want to write the page number that the copies go on before I make copies.  I read of that idea from Type-A Mathland here, and tried to implement it from then on, but mostly forgot.)

One more thing I can do to help make things more organized is to post pictures of my notebook on my website.  This will help hold students accountable, because I only have my one noteboook and when multiple students need to make up notes (or when students want to make them up at home) they will have the ability to get on a computer and view them.  This will be a significant amount of more work, but I think I could choose to do it first thing during my prep each day and I would be OK.

3.  Give more opportunities for student ownership

I was hesitant to have students do reflection activities in their notebooks since I wasn't really holding them accountable for it.  The few times we did do reflection things I really, really liked it.  I think that students were willing to think and process as I was asking them to.  But I need to start out doing those things in the first unit, so students learn to develop those thinking skills.  Here are some examples of reflection-type things we put into our notebooks:

Students had to write own steps for calculator
Students had to finish sentences on their own
Another way that I can give students ownership of their notebooks is encouraging them to use color purposefully.  I didn't encourage this at all this year.  I did it myself, and some of my students did it too, but I think it is something all students would benefit from.

An example of my use of color
So those are my goals for next year...hopefully I can handle that :)


Friday, June 13, 2014

Mindset by Dr. Carol Dweck

I just finished reading Mindset by Dr. Carol Dweck and before I choose my next book to read, I want to make sure I do a thorough reflection.  That way I will have put in some effort to actually process the book and allow it to best affect my life.  These are essentially my notes.  I would highly encourage you to read the book.  It will affect both your teaching and your outside life.

That was written approximately a week ago...I haven't gotten much farther in my reflection, so I decided "thorough" was perhaps an inappropriate goal.  I need a book to read tomorrow (and I will not have internet), so I'm going to write a short summary...

Mindset refers to the way that you approach challenges and learning.  There are essentially two different mindsets, but it is not a dichotomy.  It is more a scale.  And it is not a set, constant distinction.  A person may exhibit one mindset in one case and the other in a different setting.  But for the purpose of the book, the two mindsets are presented much more separately than they may appear.

One is called the fixed mindset.  When a person has the fixed mindset, he/she feels that the ability to do/know ________ is set in each person.  That causes people to see failure as something that cannot be overcome and may give up.  People who are in a fixed mindset feel threatened by challenges because it shows their lack of ability.

The other mindset is called growth mindset. When a person has the growth mindset, he/she feels that the ability to do/know ________ can change based on how hard a person works.  That causes people to see failure as something that can be overcome through a lot of hard work.  People who are in a growth mindset feel that challenges are a learning opportunity, and relish a good challenge.

Bottom line:  our students need to have a growth mindset in order to do the most learning.  Everyone will achieve more with a growth mindset than a fixed mindset.  That is why this book is important for everyone.



Saturday, June 7, 2014

Summer Joys

Here are some things I have enjoyed so far this summer:

  • swimming at the pool
  • singing in the shower
  • going to the zoo
  • sleeping in
  • cooking supper
  • reading books for fun
  • reading teaching books
  • playing catch outside
  • riding bikes around town
  • visiting the library
  • catching and appreciating the moments that make me smile over and over again
I'm sure there are more, but those are the ones that immediately come to me this morning.



Friday, June 6, 2014

Summer Reading List 2014

I wanted to share the books I plan to read this summer.  Please comment below or tweet me (@kathrynfreed) if you are planning on reading any of the same books.  I would love to have someone to keep me accountable!

by Dr. Carol Dweck

I actually started this one this spring and just finished it.  It is a compilation of her research on fixed vs. growth mindset.  Despite talking a lot about research, it is written familiarly and is not too intense of a read.  It will make you think about everything you think and say all day long though!

Read my reflection here.

Powerful Problem Solving 
by Max Ray

5 Practices for Orchestrating Productive Mathematics Discussions 
by Margaret S. Smith and Mary Kay Stein

Read my reflection here.

Good Questions 
by Marian Small

I am looking for ways to motivate and hold my students accountable for doing the mathematics themselves.  I want them to want to challenge themselves mathematically every single day, whether they are in the classroom or not.  I am hoping that I have selected a good group of books to help me do this better in the future.