Friday, December 30, 2016

Teachers Are Stressed; They Should Fix Themselves

Someone shared this article on twitter, and I was excited that NPR thought the flawed educational system needed addressed:  Teachers Are Stressed, And That Should Stress Us All

Then I read the article.  It doesn't recommend systemic changes that are necessary to ensure teacher well being in the United States.  It just suggests that teachers change themselves by learning to be more mindful.  What a load of crock!  So I alternatively title it "Teachers Are Stressed; The Should Fix Themselves"

I'm not opposed to mindfulness.  I think it is a great tool for both students and staff at schools across the country.  I'm angered that it appears as though this massive educational problem can simply be solved by the teachers themselves.  Simply buy the book, read it, and implement.  Life will be better after that!

Would you like to know what would decrease my stress?  Here are some suggestions:

  • More days off/Year round school - I know not everyone likes this idea, but I think spreading the stress of the school year out throughout the entire year would be helpful.  Also I could take my kids to appointments without having to take time off, and then feeling guilty for taking time off.  We need regular breaks during the year; more than just weekends.
  • More prep time/collaboration time - I need time to grade papers, talk with other teachers about strategies, and develop lessons for my classes.  Those things are not automatically done, they take time.  And 49 minutes a day is not enough.
You know, that might really be all it takes.  Teachers need time.  We do a lot.  Give us time.  Give us a break.  Let us breath without 20 kids staring at us to see if we're watching while they try to get away with something.

Next time you write about teachers being stressed, acknowledge that we are not in a position to fix the system that needs changed.  That is bigger than us and so something other than us is going to have to fix our stress.

-K.

Saturday, July 30, 2016

Unit Conversions Piece

Before #TMC16, I had asked for some help with lesson ideas for unit conversions.  Anna Vance (@typeamathland), replied with this introduction that she has used


I was thinking this is pretty awesome!  How can I make it better?  How can I use it to create a cohesive lesson on unit conversions.  I got another good idea from Gregory Taylor (@mathtans) that I would like to incorporate as well:

At TMC, I got to talking a little more with Anna, and we had BOTH been trying to find a way to make the conversions a little more manipulative for students.  I was still thinking numbers, but Anna thought shapes!  And the beauty of shapes is that I can choose ones with symmetry, so that each fraction could be turned either way!!!  This to me was the awesome part.

So with a lot of trial and a little error, I created some cards that can be used to intro how dimensional analysis needs to be set up to cancel one thing and leave another.  Here are the "conversion factors"

There are 6 of them, but they could all be flipped the other way, making 12 possible options for students to choose from.  I also made cards to be the start and end of the conversion.  Nothing too exciting to see here:
Then I played around to make sure I had enough of everything, but not too much.  And I think I do.  I like that sometimes there is only one solution, and sometimes there are three.  At this point my plan for this activity would be to show the start and end I would like on my document camera and have students work in pairs.  Then if they find a solution I will prompt, "Can you find another?"  Sometimes they will be able to and sometimes not.  Hopefully some students will be able to justify why they can or cannot find another solution.  

I played around a lot with it and I don't want to put all the pictures here, because I tried to find all the solutions, but here are a few:




Start with a square and end with a hexadecagon has at least two solutions, but start with a octagon and end with a rhombus only has one.

Obviously this is not an entire lesson, so I still have some more planning to do, but I like what I've got so far and I think it will give my students some good playing and thinking about math opportunities.  I am trying to collaborate with the science teacher on this standard, so I've got a lot to do before I can be all the done thinking about it.

I have some other notes on what the rest of the lesson might be like, but really this next part is for me, so skip to the comments and throw questions or concerns up there.  I'll post links to the docs at the bottom too!

Notes for Me:
  • Me:  Shape manipulatives
  • Science:  Number manipulatives
  • Think Input/Output (where input/output have the same value/amount/quantity)
  • Me:  discuss conversion factors need to have a value of 1
  • What can we multiply by without changing the value of the input?
  • Science:  look up conversion rates
  • Me:  notes
  • Science:  guided practice
  • Mistakes?  Video?  Student created mistakes?
  • Should we make an assignment menu?  Due for both classes?  Revision encouraged throughout?
  • I want students to journal after doing the shape manipulating! Need a good prompt.
  • Introduce new shape.  Create one conversion factor that will allow you to convert this shape to any other shape in your set.  How do you know this works?  Maybe it doesn't, but you're close.  How do you know it doesn't work?
Here are the documents:

Let me know what you think!
-Kathryn


Sunday, July 24, 2016

Checklist turned Tracking Sheet

At TMC16, I went to lunch with a group to discuss SBG and Interactive Notebooks.  We ended up mostly talking about SBG, which was great because I got a new idea!  Jessica Breur (@BreurBreur) shared how teachers at her school use tracking sheets for the students to reflect on how they are doing with each target and record scores the teacher has given them.  Then at the end of the unit the teacher collects and keeps them.  I asked her to share with me, and she kindly did!

While looking at all her resources and thinking through it all I was thinking about how it would make a lot of sense to combine this with my checklist, since most of the assignments are recorded there anyway.  Also students rarely keep their checklists after the unit is over, so it doesn't seem detrimental for me to keep them.  I would just need to add quizzes and tasks to the checklist when we do them, which wouldn't be too tricky and would be incentive for students to make those up right away when they miss them (bonus!).  So instead of using any of her wonderful resources, I worked on creating my own.

I needed to break up the spots for assignments based on learning target and provide a space for students to graph their scores for each assignment, so I have a sample that looks like this:

It has room for four assignments per learning target (3 learning targets on the front, zero or one or two on the back depending on unit), and a big miscellaneous section at the bottom of the back.  I figured I would use the miscellaneous section for assignments that related to multiple (or no) learning targets and overflow if I need more than four assignments for a given learning target.  Here is a picture of the back side:


I did an example of what I would write if there were five assignments for the first learning target.

Thoughts I still have:

  • Will the stamp space be big enough for my stamps?  (I'm going to test it out tomorrow)
  • I am concerned that I will end up needed more than four assignments often, making it pointless to separate it by learning target, but I need to fit three learning targets on the front when I have five learning targets in a unit.  I am especially concerned if I am adding quizzes, group tasks & reflections, and open middle type problems to this.
  • I used to require students to have 80% of their checklist complete in order to take the test.  I could do it that same way, or I could say you can at most one missing from each section.  I want this to be a reflective tool, not just a punitive tool, but I also feel a need to hold them accountable.
What potential concerns do you see?  What things would you change?  Any ideas on my thoughts above?

-Kathryn

PS - I am on a blogging roll since TMC16, and I have a lot more ideas to come!

Saturday, July 23, 2016

Writing in Math

At TMC I really felt pushed to have my students doing more reflection, which I had already been thinking about.  I want them to have "math journals" where they can reflect on what we're doing in class, their homework, and "I see math" entries.  I didn't go to Anna Blinstein's "Journaling and Writing in Mathematics" session, but maybe I should have.  There were a lot of sessions I wanted to go to, but didn't, so I've committed myself to look over their resources on the wiki.  I wanted to take some notes while looking over Anna's slides, so here they are.  Also here is a link to Anna's presentation.  It's way better than what I have here.


Initial Thoughts
  • What do you value in your class?
Learning. I tell my students "we are here to learn" often. I also value my students. As people. I care about them and their personal growth.
  • How will doing more writing help you achieve this?
I want to have my students keep a math journal so that they can reflect on lessons and share where "I see math"
  • What concerns do you have about doing more writing with students?
I can't figure out if I want them to do it on paper or electronically and I can't figure out if/when I should read it. How I would find time for all of it and how it would be marked.

Reasons to Write in Math Class:
  • metacognition/retention
  • communication
  • fun
  • better assessment
Possible Prompts:
  • Describe the mistake.
  • Summarize today’s lesson in a few sentences.
  • Which of these is correct? Explain how you can tell.
  • What would be a good question someone could ask about this topic?
  • What’s something that’s confusing to you right now?
  • Pick one problem and explain what you did and why.
  • Which homework problem was the hardest for you? Why?
  • Would you use strategy A or B here? Why?
  • What is going well in class for you? What is not working as well?
  • How do you learn best? What can I do as a teacher to help you learn?
  • What are your goals for this semester? How will you reach them?
  • What’s one good thing that happened this week?
  • What is something mathematical about which you want to learn more?
  • Did your performance on the quiz surprise you - why or why not?
Note to Self: Differentiate (to self) whether you want journal for the day to be metacognitive/reflective or an opportunity to assess student learning. Prepare prompts in both categories and place in notebook to use. Have one selected for the lesson, but be willing to change it up.

Ways to get buy-in:
  • share student work (with class, parents, admin, on classroom, twitter, blog, wall)
  • respond to their writing
  • Share purpose
  • Give them interesting problems to write about
  • use during assessments?
  • Give feedback:
    • short is OK
    • coach on how to improve
    • acknowledge progress
    • ask students to reflect on their journaling
    • short and frequent is most important!
Note to Self: If I decide to ask for formal write-ups, there is a structure outlined on the wiki

Assessing Journals:
  • Two sentences: acknowledge something good, suggest improvement
    • more detail
    • clearer explanation
    • connect math/writing
    • better justification
    • more precision
    • more math vocab
    • include examples
    • extension
    • look for connections to other content
  • Scoring:
    • Foundational: student reflection responds to some part of the prompt and generates some insight about self and/or math (this is a 2)
    • Proficient: student reflection engages with the prompt; uses reflection to plan and reach goals (this is a 3)
    • Exemplary: student reflection yields insights, connections, and specific areas of need; student reflects deeply as part of process beyond specific prompt (this is a 4)
  • More scoring rubrics on wiki
Note to self: I could have students "redo" if they don't show foundational. Also, do I really want to score them? How would I connect to standards? SMP?

Thoughts Now:

  • What would you change about your responses?
Still have same concerns
  • Do you have any new ideas or concerns?
Lots of ideas on assessment, buy-in, questions to ask, and ways to give feedback
  • What do you need to do in order to be able to include more writing in your classes?
I need to decide if/how to score, how to have them keep their journal (notebook or electronic), when to check, and some prompts to give. I also need to set up notes to myself about the structure in my notebook.

Where do I go from here?
  • Ask Anna, Carmel, kristen about journaling on paper vs electronically
  • Select some common prompts and organize into my notebook
  • Determine goal frequency of journalling in class (twice a week?)
  • Talk with Nicole about scoring or not (when we go back to school)
  • When lesson planning: select prompt for lesson, timing, and method for increasing student buy-in
If I follow-through with this, you should be hearing more about journaling on this blog. Ideas, suggestions, comments, please leave them below or tweet me (@kathrynfreed). I'd love to continue this conversation, because I still have a long way to go with it.

-Kathryn

Friday, July 22, 2016

Algebra 1 Learning Targets and Reporting Standards


I've been working on my learning targets for this coming year and linking them to reporting standards.  My goal is that the learning targets will be somewhat evenly spread out among my eight reporting standards.  I'll present them unit by unit here, but first I should let you know what my codes for my reporting standards stand for.

NQ = Number and Quantity
SSE = Seeing Structure in Expressions
ER = Exponents and Radicals
CRE = Creating and Reasoning with Equations
IBF = Interpreting and Building Functions
LER = Linear and Exponential Relationships
SID = Statistical Interpretation of Data
SMP = Standards for Mathematical Practice

I've got 10 units set up for next year.  Hoping for five each semester, but I could also probably do four first semester and six second because we have more time second semester and starting out the year always goes slow.  I'm also hoping to give a performance task each unit, but I don't have them all the way planned out yet, so that's what you'll see at the bottom of each list of learning targets.

Numbers and Units


Functions


Linear Functions


Exponents and Radicals


Exponential Functions




Sequences


Polynomials


Quadratic Functions


Solving Equations


 Statistics


So this is the basic plan.  Questions, comments, concerns can be left below or by tweeting me (@kathrynfreed)

-Kathryn

Friday, June 17, 2016

Practice Structures

So, Sarah Carter and I chatted on twitter some about practice structures, and she totally beat me to blogging about it.  Read her post here.  She also calls for you to submit the practice structures you use.

My goal is to generate a reasonable list of practice structures that will be efficient for me to use and also beneficial for my students.  Ones that make them think, move around, and engage in their learning.  Efficiency is an issue because I don't want to always spend 15 minutes explaining a new structure.  There are lots of options out there and if I'm always doing new things then the focus comes away from the learning.  Here is my list so far, and I'm going to explain how I have/plan to use them and what the benefits I see are.  I'm also interested in how these can be incorporated into student notebooks.

Card Sort:  I most often do this individually where each student gets the whole set and sorts and glues into his/her notebook.  I like that it is a sorting activity, so good for organizing the learning in the brain.  I like that it goes well into the notebook.  I don't like that students don't have to explain.  One idea on making this better is to have them do the sort as a group and pick a few each to put into their notebooks with an explanation.  Which gives fewer, but more meaningful, examples in their notebooks.

A few times this past year I made a whole class card sort where students each got one card and had to find their match.  If the class had an uneven number then I would leave one out on a table and one person would match the table.  As they match up they come check with me.  Sometimes I time them and they compete class period to class period.  Fun, but each student does not see all matches.

Quiz-Quiz-Trade:  I'm not really sure I do this correctly for it's given name...but I give each student a problem, have them work it out.  Then after a set time I make everyone partner up, work their partner's problem (which becomes their problem), and talk through it together.  (Maybe I could call it "Do-Trade-Do-Talk"; DTDT for short.)  Then after a set time, new partners, repeat.  There might be some benefit to having a student keep the same problem as "theirs" the whole time, but I'm not sure yet.  Good practice.  We often do 4-8 problems when we use this structure.

I have a handout (pictured below) that they use and keep in their notebook pocket for the unit.  This means that the students probably don't look at it ever again, but I feel like this past year my students were better at that, so perhaps I can help my students develop that better.  I would suspect it would be easy to get students to put this in their notebooks as well.



Stations:  I have 6 table groups set up in my classroom, so I usually do 6 stations.  Students rotate based on my timer from group to group.  I usually post answers on the back of the next station so students can check their work themselves.  I don't always have great participation in stations, but it might be because I haven't found a good way for students to record their work.  Sometimes it's just on whiteboards, so maybe they think it's less important?

I have had some thoughts of making stations a more challenging structure - more than just rinse-repeat practice problems.  This would make it more important for students to work together as a group, hopefully getting better involvement.

Jigsaw:  I have only done this a few times, and I think it was all last year.  But I use this as a way to jump-start a class discussion where I want students to "notice" and "wonder" about a new idea.  Each table group would be given a problem or group of problems to complete and present to the class, afterwards as a class we discuss patterns and try to draw a conclusion.  It would be possible to have discussion questions for groups of students as well, but I generally facilitate the discussion as a class.  Perhaps a well-written "talking points" could follow the sharing part and precede the group discussion.  I want to use this more in the future as it seems to be a good use of class time.

Posted Problems:  I tape problems up to my walls and students do whichever they want in whatever order.  I usually post answers for them to check as they are working.  This gives them movement and the option of working alone or with a partner.  Also works pretty easily in their notebooks.

Scavenger Hunt:  This is where problems AND answers are posted throughout the room.  Students work a problem, then find the answer (to the one they just did) attached to the next problem they are to work.  It is self checking (AWESOME), students can start anywhere because it just does a big loop, and makes kids move.  A lot like "posted problems", but a little more work to set up and get students to understand the structure. Since I usually post answers so matter, I'm not sure the benefit of one over the other.

Coloring Page Worksheet:  Like a worksheet, but includes a picture to be colored as the problems are worked.  Answers are placed in spaces in the picture and when students get an answer to one of the problems they find that space in the picture and color it.  It is very calming for students to color, however I often have some students who just color and some students who just do the math.  The students in the former group are the ones I'm concerned about.  However, I feel it beats just a regular worksheet, which I use sometimes, too.

Add Em Up:  I'm sure I learned about this from Elizabeth at TMC14 during our morning session, but she has blogged about a complex number placemat activity here.  I've done this once or twice and I need to do more of it.  I just don't have a good answer to "What if I have a group of three?"  Also it's a lot of paper to give each group all the placemats to do their work.  Often I use whiteboards, so I could probably make that work better.

If you haven't done it before, students work problems in their group in "rounds" and they are told what the sum of each of their results will be.  In that way it is self checking.  Each student does their individual work in the corner of a "placemat" which gets them focused together as a group.  If their sum doesn't work out from the beginning then they have to check each others' work.

The Mistake Game:  I found this from Kelly.  She actually has several posts on this structure, but here is The Guide.  Simplified, groups of students present solutions to problems that include at least one mistake.  If they accidentally include more mistakes it is better.  The audience has to find the mistakes.  This is more engaging for the students.  Read her post for more details.

I have done this with my freshmen and my upper classmen.  It works really well with my older students, however I don't think it's ever worked well with my freshmen.  I'm not sure why.  Maybe I need to persist and do it more often?  I try to get all students to ask questions and present, but some are really hesitant and expect the other students to find all the mistakes for them :(  What usually happens is it ends up taking FOREVER to find the mistake and then a student blurts it out instead of asking a question.  Or the same student finds mistakes in 12 out of 15 problems.

I really, really, really like this, but I need to find a way to make it work better in my Algebra classes.

Open Middle Style:  This is where #mtbos is compiling problems of this nature.  These problems require a lot more thinking and tinkering with the mathematics than regular practice problems.  I would like to provide students with at least one problem like this for each learning target we have.  (Maybe these types of problems would work well as stations...hmm...) Sarah has posted some she has created here and here, and I have a few I might share as I work through my functions unit.  However, there are a lot on the open middle site I linked above, so check them out!

So those are the practice structures I use/have used/want to use.  Some of them I want to use every unit (card sort, quiz-quiz-trade, stations, jigsaw, add em up, open middle) and some of them I'm not sure I want to use at all (scavenger hunt, coloring page, mistake game), but now I have a starting point as I work through my units.

Please let me know your thoughts on any of these practice structures!  Ones that are great, ones you don't like because..., ones I'm missing here that I should definitely include, etc.  I would like to know so that I can use the best ones for my students.

-Kathryn

Monday, May 30, 2016

Restructuring...Again

Well, I'm at it again...trying to figure out how to make my classroom and curriculum better for my students.  I like a lot of things about a lot of my units, but I found myself wondering if it would be more engaging and connected for students if I reordered some of the units.  SO...this is what I'm thinking:

Unit 1:  Numbers and Units
I am hoping to collaborate some on this with the science teacher.  We will teach unit conversions together.  It will be interesting as I have never done something like this before.

Unit 2:  Functions
This is the big change.  Instead of doing all the standards that are "close" to 8th grade standards first, and then starting functions second semester, I'm going to start with functions right away.  I want have a more "function" focus throughout the year.  I also really, really want my students to develop a lot of flexibility with their functional thinking, so hopefully having more time will help. (Some of the flexibility I want to see:  evaluating from equation, graph, table; understanding function notation and y= are similar; find average rate of change and tie it into slope; thinking about "characteristics" of a graph:  x/y-int; increasing/decreasing; extrema)

Unit 3:  Linear Functions
So after a broad introduction to functions, we will focus on various types of function on and off.  Linear is first!

Unit 4:  Exponents and Radicals
As a preface to Exponential Functions unit next, we will manipulate exponential and radical expressions (hopefully with and without variables).

Unit 5:  Exponential Functions
Back to another big function group.  Going to discuss the characteristics of an exponential function algebraically, graphically, and numerically.

Unit 6:  Sequences
Here we tie arithmetic sequences to linear functions and geometric sequences to exponential functions.  Hopefully my students can see the domain of each of these functions will be restricted to the natural numbers.  Also want to make sequences more challenging by including variables in the terms.

Unit 7:  Polynomial Operations
Adding, subtracting, multiplying, and factoring polynomials.  I LOVE polynomials.  I need to make sure my students see more than just quadratics here, but it's OK if it's my focus.

Unit 8:  Quadratic Functions
I have a lot of good things here, but it is not quite a cohesive unit yet.  Needs a little bit more work to develop into that.  Hopefully by not being THE LAST unit I will be able to be more cohesive.

Unit 9:  Statistics
Saving statistics for this point will allow application of the three types of functions we study.  We can do some fun regression for various functions.

Unit 10:  Solving Equations
This will include solving linear equations (which we will constantly review throughout the year, since it is 8th grade, too), quadratic equations, and systems.  I think I'm going to like that systems can involve quadratics :).  We might have to discuss why we don't solve exponential functions yet in Algebra 1.

Five units a semester seems doable, right?  Better than 12?  I think we did 8 this year.  I'm hoping some intentional unit-specific planning this summer will allow me to progress better throughout the year.

Let me know what you think!  Am I missing something big that won't work with this?  Have you tried it this way before?  How did it go?  I'll post learning targets and unit outlines later in the summer (hopefully)!  But probably not chronologically.

-Kathryn