# Self-Monitoring

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Chatting with @druinok always gets my wheels turning.  Reading her ramblings here  on homework and grading, reminded me of a structure I used several years ago.  I think I may have actually blogged about it.  Quick search on HW and it pops up, first on the list!

The post is title Lagging Homework – I suppose that was after the summer I read Make It Stick, Brown et al, and Henri Piccotio and Steven Leinwand.  But what I remembered about the post was the Structure I planned to use for students to self-monitor their HW practice.

There were 8 problems in each practice set.  At the top of the booklet were the numbers 1 – 8.

As students completed the problem, they were asked to circle the number.  When they entered the classroom the following day, answers were posted and they were asked to mark their circles accordingly.

After sharing this with @druinok, she asked if there was some way a student could mark the question number with a ? if they had gotten stuck/had a question.  Maybe mark with a half circle, upside down – to note they had emptied all their options?

Any way – I used this for several weeks that year and I am not sure why I dropped it.  I cannot remember any major event that would have taken my time away from continuing this structure.  Anyway – I am pinning this in my to-do folder to use again.

They idea for students to self – monitor, then after assessing, allowing them to reflect similar to what @druinok shared in her post linked above.

While looking through other posts – I ran across this one – Where the idea came from – I will assume a chat.  But I don’t recall ever actually following through on this one.  A Routine for HW Practice & Retrieval with Peers

It would consist of having varied, but parallel sets = which would take some work in the beginning, but once they are done – well, they are done.  Maybe only have 1 practice set 1 day a week be varied to use this structure is more doable – what I mean Set 1 and Set 2 would be the same sets for all students, vary set 3, Set 4 the same for all students.  This would make the workload much more doable.

I love the idea outlined in the post – thank you – whomever shared it in the chat.  I can see it as being an informal assessment, no pressure, just practice quizzing.

I’m curious how you handle student self-monitoring with homework and practice sets…

# Go Fish! in Math Class

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Hey my TMC17 buddy, @kcnorojo!  This post is for you!

As an intro to reducing radicals…  I place students into groups of 3 or 4 and we play several rounds of Go Fish!  This by the way was not my original idea.  I will need to dig some to find the original post.  But I have used it multiple times with all attitudes of students and it has been a great concrete introduction.

Just in case you’ve never played.  Here are the official rules from hoylegaming.com

Each player gets five cards. If you are dealt a four of a kind, or get four of a kind during game play, those cards are removed from your hand, and you get a point. Moving clockwise, players take turns asking a specific player for a given rank of card.

I actually adjust the rules a bit in each round.  And I believe we start with seven cards as well.  Game ends when someone runs out of cards OR I call time.

Round 1:  Students must have a pair for a match.  Only a pair works.  I allow them to play for several minutes to get the flow of the game.  When the timer goes off, I ask them to count their matches and high five those with the most points.

Round 2:  Students must have a group of three for a match.  Even IF you have the 4th card in the set, you CANNOT lay it down with the match.  Again, when timer goes off, I ask them to count matches and we celebrate the winners.

Round 3:  Students must have an entire set of four cards to complete / lay down their match.  This round goes on just a bit longer.  Timer, count matches, celebrate winners.

Round 4:  I ask them to deal out the cards – and this time they must have a set of 5 to make a match.  A few usually continue to deal out the cards, but several pause and say – but we can’t!  There are only four cards of each type.  Yes!

We have a discussion about which round was their favorite to play.  Which round was toughest?  Which round was their least favorite.  Usually – Round 2…with three in a set, because IF you end up with the last card, you can never lay it down, thus never emptying your hand to end the game.  Hmmmm.

I literally draw a radical on the board and describe how it “sort of” looks like my hand when I hold a bunch of cards.  I make a big deal of the index on the radical – it tells us the rules of the game.  The Go Fish! game lends it to this part very well.  Though these are not the greatest examples, hopefully they will give you a quick idea of what the notes may look like.

We practice several on whiteboards and write a reflection at the end of the work.  Then I have them open their INBs and write out a few examples to complete – notate for future reference / study.  Depending on the class, I may offer a few examples if they are unable to create some on their own.

Depending on the remaining time in class, I will then pass out the Radical Rummy cards to the groups.  I have gone over how we can type in the problems on our graphing calculators – rational exponents, radicals, etc.  I explain that every card will match to form a group of 4.

When a group has gotten their matches complete, I have them create a small poster or use whiteboards to list equivalent expressions.  We then begin a notice / wonder.  I jot down their ideas, testing some as we go along, but letting them decide if their “rule” for the rational exponents holds true.

I like this task after the Go FISH! and simplifying a few radical expressions because it shows them how the rational exponents are simply asking us to find that amount of the factors.  For example, an exponent of 1/3 asks us to find 1/3 of the factors of say 8.  Since 8 = 2*2*2 and we have 3 factors, I want 1/3 of them, so 2 if the 1/3 power of 8.

There are also come GREAT discussions that arise about the negative exponents and what mathematical operations they are telling us to do.

I would love to hear how you approached these same skills and how it goes!

# January #MTBoSblog18 – Formative Assessment Strategies

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From Jennifer Fairbanks…

Happy Day – Our 1st one of 2018! Join us and blog today! Share anything you want! When you blog, tweet out the link.

Hmmmm.  WElllll.  Okkkkkkk.  What do I blog about?  Here goes…

Our schoolwide focus this spring is on revisiting what we know about good formative assessment and putting it into practice.  Eventually, we will be encouraged to ensure we are utilizing the practice of PA on a daily basis – for those not already doing it.  After speaking with our SLC, we thought it would be a good use of time for our department virtual PLC – on our NTI (aka Snow Day) – to work on ensuring that each learning target in an upcoming unit has a quality FA in place.  And if not or if it really doesn’t measure what the target is intending, then plan a better one!

As we began building the document for Algebra I unit on Functions, I was reminded of so many great strategies  learned through the years and new strategies shared by others.  Most of these have been learned through trial and error, they didn’t “just happen.”  When trying new things, sometimes you need take NIKE’s advice and Just Do It!  See what happens, reflect and try it again!  So here is a list of a few things we ran across while working this morning:

• ### Every Graph Has a Story –

When given a graph with no labels, numbers, etc. – can students devise a story that will related key features of the graph to the context of the story?

Here is @heather_kohn’s Ambiguous Sports Graph

• ### Thumbs Up, Thumbs Down –

Was reminded of this one by my colleague.  Basically, you can pose a question to the entire class, then ask for a Thumbs Up or Thumbs Down as to if it is true/false, example/noonexample, linear/nonlinear, function/not a function

• ### Green Pens –

I am super excited that my green pens arrived today!  I plan to use Amy’s idea for Bell Work, but integrate into independent practice time.  Students will have a brief practice page – when one finishes, I will check – if all good, they will receive a green pen and help me mark other papers.  After I have 3 or 4 Green Pen Helpers, I will have time to visit each table group for one-on-one help.

• ### Give One, Get One –

I believe the first time I ever used this was out of a Kagan book in Geometry.  In this unit, I plan to give students graphs of functions.  Before we begin, I will ask them to list 3 things they notice about the graph.  They will then have 4 or 5 True/False statements to respond to.  Here’s the GO-GO:  They will write one more True statement about the graph, then go visit someone else across the room, sharing / discussing their true statement, and receiving/discussing/recording their friend’s new statement.

• ### White Boards & Summary Notes

Individual to practice writing inverse function equations.  Nothing new here, I give them the function, they practice rewriting the inverse on the whiteboard, I walk around the room observing and noting…  Then I will address any common errors I see.  After reading this tweet:

and a discussion a few weeks ago with @druinok about student notes from the teacher – I was reminded…  we will discuss big ideas we noticed in our white boarding, then turn to our INBs and generate our own Summary Notes.  Since these are 9th graders, I will likely give them a few unworked Functions / Inverse examples to help them get started.  Once they have completed their Summary Notes, there will be some time later for independent practice.  Maybe even pull out those green pens again!

• ### Open Sort & Card Matching –

Years ago, I was taught about open sorts from a colleague who had attended John Antonetti training.  I plan to use this structure by giving students cards with several types of graphs, in the discussion with their noticing and sorting and support of reasoning – I am anticipating something coming up about dotted / point graphs and connected graphs.  In the debriefing of the sorting task, this will allow me to introduce / review the idea of discrete vs. continuous graphs.

The second part of this sort will be to place those cards inside the ziploc bag and get the other color cards out.  These cards will have various domains and ranges listed.  Again, in the discussion of their reasoning for their sorts and debriefing of the task,  I am anticipating someone sorting based on listed numbers vs. intervals, which will allow me to make the connection between the different notations for domain and range.

Finally, the matching task will be for students to match the correct domain and range to the correct function graph.  The best way for FA assessment to happen here – is to walk around, listen/observe and ask questions, never telling them, but helping them think on their own.

After some practice and discussion, I feel like this might be another great spot to have students create their own Summary Notes of the ideas shared / discussed.

• ### 2-Minute Assessment Grid

Goodness, this may be one of my favorite student reflections.  You can read about it here.  You can copy the grid and have students fill it in.  However, I like creating a large grid on my board and giving students 4 sticky notes on which to respond.  Basically Students are asked to tell ! Something they want to remember.  ? A question they still have.  @ An A-ah – lightbulb moment and + One improvement they can still make / need ot study.

• ### Class Closer Reflection

An easy, quick one sentence reflection – have students choose one of these sentence starters and complete it…  Something I’ve learned,…, Something I realized….  OR Something was reminded was of…

### Follow-Up Action is what matters most.

As with any FA – its not about the strategies – they only provide a vehicle for the information you get from student learning.  What happens next is very dependent on what information you receive.  In class strategies, you must be present, listening, allow yourself a few seconds to think through their responses / questions before responding to them with a question.  With reflections, exit tickets, target quizzes, we have the opportunity to filter through all of their responses, looking for commonalities and misconceptions – that will help us plan our next actions.  Do we need to address with the entire class?  Are there a handful we need to pull to the side while others are completing bellwork the next day?  Is everyone on the right track and ready to move forward?

# Reflecting on Feedback

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Funny how things kind of pile on to hit you in the face!  @druinok and I are revisiting Wiliam & Leahy’s Embedding Formative Assessment;  The current issue of ASCD Express is filled with articles focused on feedback and our first day back with faculty this semester- we had a PLC about Formative Assessment & Feedback.  Though this post was more about success criteria – there are several comments concerning feedback.

Chapter 5 in EFA2 was a bit frustrating.  Initially it felt like it was saying so much of the research on feedback was not useful…for several reasons.  But as I read and later watched this presentation (while sansone walking for my cardio!) – there were some big ideas that stuck out to me…well, hit me in the face.

How when done incorrectly, feedback can have a negative influence on learners.  Some things were obvious, but others were definitely worth noting.

How we should not be expected to give thorough feedback on every single thing.  He suggested the 25% idea.  25% of the work is self-assessed, 25% of the work is peer assessed, 25% of the work is skimmed by teacher, 25% of the work received thorough feedback.  Hmmm.  This feels doable.  I have felt so overwhelmed at times in recent years.  And I also wondered if by giving too much written feedback, does it become common and expected, therefore losing some of its ability to drive student achievement forward?

The article we read during our first day back AND Wiliam in this book both said without any follow-up action, formative assessment is essentially useless.  The article said – “it is not fair to students to present them with feedback and never give them the opportunity to use it.”  In his book, he said, IF its important enough for students to use the feedback, then you must find the time to allow them to do it in class.  Ouch.  But when?  We can’t possibly get everything in!!!

This is the pie in my face.  As I was planning the FALs for my classes, I realized – that giving students feedback on their pre-assessments…being intentional with the wording, expecting them to do something with it…either answer a question, extend a pattern, redo a part of the problem, look at a specific piece of their work, sketch a new picture…

Oh my goodness.  That’s it!  When we pass back the pre-assessments… usually a few common things happen…

1.  The student is given a few minutes to revisit their work and read the feedback, then attempt to use the feedback and make their response better..  then
2.   The student is paired or in a small group and they all use their feedback to create a group response to the task.  OR
3.   After the lesson, students are given an opportunity to revisit the initial task and/or a similar but different task.  I usually copy these front/back – this allows me to flip over and see their initial work, feedback and see if they were able to clarify misconceptions and correct mistakes.

How might I use this idea to implement into my other tasks/lessons?  The time to “ACT ON the FEEDBACK” was embedded into the lesson.  Lightbulb!

# Generalizing Patterns: Tiling Tables

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Last fall after instructional rounds, one of the observers asked me if I would mind having some folks visit my classroom.  Sure.  They were most interested in questioning, interactions with students and use of Formative Assessment Lessons (FAL).

When they emailed to set up a date, we agreed on January 10.  Oh, wait.  This will be the beginning of a new semester with new students.  I won’t really know them.  They won’t really know me.  Great.  Now, I’m scared.  Oh well, let’s look at the positive – this will give me a chance to try out a new lesson.

I printed off 3 lessons to look at the evening before students returned to school.  I liked all three.  Building complex equations seemed perfect, so I began to prepare for it.  We were out for weather our second day back.  As I began looking over my lesson plans, it seemed the Tiling Tables was a better fit for the upcoming unit, so I switched gears.

I had done this lesson a couple of years ago, but never taught it in class.  As I began to revisit the task, I knew I liked it.  I knew it would offer some good discussion on ways to extend the patterns.  But wait.  These students barely know what a parabola is.  Would they have a clue as to how we would write an expression for a quadratic relationship?  Would I have a clue as to how to introduce it, this early in the semester?  No.

So I pondered for a while.  I would simply use the task as a way to say, we have the knowledge and tools to do parts A and B, but part C, well – that’s what we will be learning later in the semester.  It would give us a reason to learn it later, right?  Goodness.  What a canned comment.  By now, we had another snow day, so our visitors would be in our classroom on the 4th day of instruction.  I was stressing just a bit.  What was I thinking?  Starting off a new class with a FAL I had never used before?  We needed time to build some rapport.  Too late.  Let’s go with it.

I gave students the pre-assessment:

The class was divided pretty much 3 ways – Those who doubled the number of tiles, after all – a side length of 20 is doubled to get 40, right?  The second group had sketched the designed on the the grid paper which had been provided, however, they wrote answers for the 30 cm table instead of the 40 cm.  And finally, several had the correct number of tiles by extending the pattern on the grid paper.  But I ask how efficient this strategy would be for, say 300 cm table?  Hmmm.

We began the lesson the following day by giving 3 samples of work.  Last school year, I figured out, I could save paper by having them use the shop ticket holder sleeves to hold the sample work – allowing them to draw, sketch, etc with dry erase.

These instructions would help their discussions:

The first sample was Leon:

After some small group time, we shared our thinking with the whole class.  There was one student in particular who had confusion all over their face.  I encouraged them to ask the person sharing for clarification (using our starter stems).  I believe this is important to model and have them do early in the semester, so they become more comfortable with it.  Even with more explanation, they were still not seeing the pattern.  So another student shared.  Still no help.  Finally, a third students explained how they saw the pattern.  The confused student nodded and said, “Okay, I got it.”

Now, years ago, I would have said – great and moved on.  But I’ve learned…ask them to explain it to you.  They may say they’ve got it – just so you will move on, but how do you know they understand?   This student, however, could explain their thinking and were correct – they could even extend it to the next table size.

The next student sample was Gianna:

So many more of the students picked right up on Gianna’s approach.  The confused student – smiled stating they liked / could see this one better.  For me, it was listening and watching the students discussing – that brought me an a-ha!  This is the example we will use to generate the quadratic expression I was worried about!  The total whole tiles would equal (step x step) + (step – 1)x(step-1)  Yay!

Many of the students could not make the connection with the side lengths on Ava’s sketches in the beginning.  Then they began going back and looking at their own sketches to verify the numbers Ava recorded in the table.  They noticed the same patterns and agreed with them.

After this final discussion – we went back to see if each student had answered the task fully.  We quickly realized though there was some good, correct thinking going on in their work – they had not addressed the questions completely.  The class agreed that Ava’s was the most complete with her table.  And it was interesting to hear their discussions of how they would explain to the other students how they could expand their responses to be better and more thorough.   One student even brought up it was challenging trying to figure out their thinking since there was no written explanations of what they were doing.  (I thought – yes, this is what I feel like sometimes too.)

As we continued discussing having thorough answers – I shared Ava’s data in a graph…  they were quick to see the quarter tiles always remained four and the half tiles being linear, a focus from 8th grade.  But what about the total tiles.  How can we write an expression to model that data?  And I took them back to the slide with Gianna’s work to look for patterns between the table size/step number and the total whole tiles.  We test our thinking with different sizes and it worked.  We tested our expression in Desmos…and what?  It hit all of the data points!

They had some experiences with the visual patterns – and good feedback to me about liking them, but still having to think.  This task reinforced some of those ideas.  IN their reflections – though many may have preferred someone else’s sample work – they “saw” how Gianna’s work led us to a more efficient expression or even Ava’s approach to orgaznizing the data in a table was pretty helpful to see the patterns so we could find describe the expressions.

Total Tiles = 4 quarter tiles+ 4(n-1) half tiles + n^2 + (n-1)^2  whole tiles.

I will definitely be using this lesson in my future.  It brought just enough confusion, but great opportunity for sharing and discussion.  And the observations were great.  Students were not shy.  At the end of the day – I was amazed we had only been together for 3 or 4 days… wow, this is going to be an outstanding semester!

# Interpreting Distance Time Graphs

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On the 3rd day with a new group of students, I had visitors from some other districts in our classroom.  I was nervous – I really didn’t know these students yet and they certainly didn’t know me.  I had chosen Interpreting Distance Time Graphs lesson from MARS to begin our semester.  Although this is listed under 8th grade, it leads to some great discussions and uncovering of ideas and misconceptions.   The Keeley & Tobey book also lists “Every Graph has a Story” in the Formative Assessment Strategies.  This was the ideal lesson to introduce our first unit on functions, while trying to be intentional with planning FAs.

## Pre-Assessment

Telling students it is only for feedback, not for a grade seems to drive most of them to really share their thinking.  After reading their responses, I had some ideas of how I wanted to change the lesson up a bit from times past.  The first time I ever used this lesson was around 2011-2012.

## Let the Lesson Begin

We began our actual lesson with only the graph in this picture.  I asked students to jot down 3 things they noticed about the graph.   Pair share.  I called on students randomly with my popsicle sticks, then allowed for a volunteers (this was something @druinok and I had read in EFA2, which allows everyone to be heard).    We then read the scenarios aloud and at the table groups, they discussed which story was model by the graph.

Next I took one of the scenarios we didn’t choose and asked them to sketch a graph on their whiteboards to model it.  We had about 5 different overall graphs – I drew on the board and let them discuss at their tables which they agreed/disagreed with.  Then we shared our thinking.  Some very good sketches and great discussions.

## Open Card Sort

Many years ago, a colleague shared the idea of open sorts, something she had learned from a John Antonetti training.   I instructed students to remove only the purple graphs from their ziploc bags.  (Side note suggestion- use different colors of cardstock and this allows them to quickly grab the cards they need, ie the purple graphs, green scenarios OR blue tables.  I used to have all the same color and we wasted a lot of time sorting through which cards we needed).  In pairs, they were sort the graphs any way they wished, the only requirement, was they must be able to explain why they sorted them as they did.  Again, sharing whole class led to seeing some details we had initially noticed.  If you’ve never done an Open Sort – let go and let them show you their thinking.  You might will be amazed and wonder why you’ve never done this before.  They love to think.  We should let them.

## List 3 Things

A couple of years ago, I began asking students to list 3 things they noticed or knew about their graphs – anytime we were interacting with a graph.  IF you ask them to do this enough, it eventually becomes habit.  I also like this approach because it gives them a chance to survey the information in the graph before they start worrying about / answering questions.  Today, I asked pairs to label their whiteboards A – J and I set the timer.  They had to share/discuss/jot down 3 things about each graph.  Once again, I used popsicle sticks to randomly call on a few students.

## Graph & Scenario Matching

Using the “rules” listed in the lessons powerpoint, students were then given time to discuss and match graphs to the scenario.  This went so much quicker than times I’ve done this lesson before.  I believe it was because they had already interacted with the graphs twice…they were not “new” to them.  I will definitely use the Open Sort and Name 3 Things before matching tasks in the future.

I gave them a chart to record their matches.  We then shared out our matches.  Each time, I neither confirmed or disputed their matches, but rather would call on a couple of other students to agree/disagree.  After some discussions, I came back to the original student to see if they agreed / disagreed with their original match.

One of my favorite graphs is this one –

And our final sorts…  And again – Scenario 2 is always up for some debate.  It reads: Opposite Tom’s house is a hill.  Tom climbed slowly up the hill, walked across the top and then ran down the other side.

Though every student did not get every match exact, there were several a-ha’s during the lesson and questions asked.  I look forward to reading their post assessment.

I’ve used this lesson as written many times with much success.  However, just making some adjustments prior to the matching made a vast difference in the amount of time students needed to complete the task.

Let me know how this lesson has gone / goes for you if you use it.

# Revisit of Two Books #MTBoS12Days Post 5

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Since much of my goal this spring is on Formative Assessment, I felt a need to review some of my past readings…

Looking forward to a revisit with these books over the next few weeks.

Looking through my notes/markings in the #75FACTS, I have used about 30 of the strategies outlined in the book.  It has been about five years since I really dug in to this book and the conversation about a volume 2 released earlier in the year, makes me want to revisit this one.  I plan to skim those not marked to see what ways I might be able to implement in my planning this spring.

The #EFA book – seems I made it to Chapter 5 and never quite finished.  I believe this was the year were we on 7 period day and I had 5 sections of Algebra I (3 levels) and AP Stats, the semester got a hold of me and wouldn’t let me go. ha.  After skimming the TOC and my notes, I feel this is a good book for me to be accountable to better quality FA this spring.

While looking for the Wiliam/Leahy book, I paused to look through the stacks I have at my house…  so much good reading in recent years thanks to the encouragement of my #MTBoS friends!

# 2017-2018 #GOALS #1TMCthing #SUNDAYFUNDAY

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NERVES. Anxious.

We have opening day for teachers and open house tomorrow night.  I am always nervous to meet new students and parents.  Scared.  Because I want to be great for them, I want to value their time.  I want them to learn and think and be challenged.  Somewhere in the mix, I want them to at least not *hate* math.

The past couple of years have been, well, not my best.  I chose to disconnect – because things were happening out of my control and I quickly became bitter.  So as not to spread that ugly, contagious monster at school, I added space between myself and most everyone in proximity at school.  I trusted no one.  I gave up.  I walked into my classroom and I left.  It was miserable.   This is not the work life I wanted, but it felt safe to isolate.  It seems selfish looking back now.  But I needed time to heal, forgive.  Sadly, my students did not get the best me and that breaks my heart.  I apologize.

Last year in an effort to dig my way back, my friend and I read a book Choosing Joy (kindle is only \$0.99 right now).  Its a 52-week devotional with a 4-page format.  Easy, but challenging.  I was reminded that no matter what, I get to choose.  I plan to pull the book out again this year for frequent reminders.

I almost didn’t attend TMC17.  Even being a veteran, the voices in my head – nearly convinced me I shouldn’t go.  I had submitted my proposal way back when – I wasn’t sure if anything I had to share would benefit anyone.  I have such respect for this community, I didn’t want to waste their time.  My friend, the book fairy said, “But you love math camp.  It re-energizes you.”  She was right.  Its what I needed.  A BIG, jumbo shot of mathy-filled joy to jumpstart this school year.

## START

I had 2 things on my list I wanted to learn more about and experience #talkingpoints and #clotheslinemath.  I’ve dabbled in both, but never saw them completely through for what they can be.  So, my #1TMCthing will be these 2 actually.  I teach Algebra I – basically 3 levels CP using Springboard Curriculum, Algebra I – using our own resources, and Collaborative with Co-Teaching Model.  I am excited to see how each of these routines / tools will play out with all of my students.  My goal to implement each one time in each unit.

This may seem odd, I see both of these supporting my goal of intentional vocabulary / literacy strategies.  Several years ago, I worked hard at implementing ideas with this focus – I need to refine and focus on these as well.

## STOP

I need to be very intentional about my self-care.  In order to be my best for my family and my students, I need to make better choices for my health and down time.  Ideas:

• take a 5-10 min brain break to recharge somewhere in the middle of the school
• read for pleasure throughout the school year.
• journaling my food.
• #FitBOS to work towards my activity goals. S/O here to @sarah3martin for always including me in fitbit weekly challenges.  Thank you.

So I will protect my self-care time by including it on my calendar, sadly this gives me permission to do it without guilt.

## CONTINUE

I have worked very hard for several years learning about formative assessment, questioning and closure activities for reflection.  I intend to continue working to improve these and keep using some that I have found to be very beneficial to my students.  But improving and being more intentional with my follow-up tasks to the formative assessments.

I would also like to continue implementing some of the big ideas from our chat on #Makeitstick a couple of summers ago, that Anna does an amazing job of sharing in her posts and presentations.  Spaced practice, interleaving, being intentional and explicit about retrieval practice.

And I will continue life-lessons in my classroom – that’s what kids will take-a-way in the end.  (If you have questions about this poster, just ask.)

When I was younger, I remember wanting to “Be a Barnabas” – yeah. That too.

# Better Questions Week 3 #MTBoS

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I’ve pondered this challenge for a couple of days.  So many options!  But a tweet from @mathymeg07 led me to a post from @MrAKHaines blog Math Pun Pending.

The post was celebrating a variety of strategies his students had use to answer the question:

He wrote:  When I wrote the question, I had anticipated that students would use a couple of different strategies. What I didn’t know was that my 25 students would use a combined seven correct solution strategies to solve this problem.

Two parts to my post:  1. How can I make this an open question and 2. How can I use student samples to develop a better lesson in the future?

How can I make this an open question?

A.  Name a point that is NOT on this line.

B.  Name a point that this line passes through.

Thanks to @PIspeak‘s TMC14 session in Jenks, I urge students to “Support your claim with evidence/reasoning.  I want to see your thinking!”

How can I use student samples to develop a better lesson in the future for my classroom?

I appreciated the fact that he never explicitly taught “the teacher’s efficient strategy” but allowed group discussions and support to drive the lesson.  Students shared ideas.  The last paragraph  in his post says, “My students are acting like mathematicians, y’all. They’re using their toolkit of math ideas to solve problems flexibly. I couldn’t be happier.”

In the end, that’s what we all want – students thinking on their own, making sense and being confident enough to explore a problem with their own ideas.  So, how does this tie in with the Better Questions prompt?  My outline of the lesson feels a bit like those I’ve used from Formative Assessment Lessons, but I feel it lends itself to students doing the thinking, talking – I only provide the materials and support to make desired connections that will lead to the learning goal.

I’ve been following the #T3Learns chat from Wiliam’s book.  In chapter 3 of Embedding Formative Assessment, it suggests using student sample work. How might I structure a lesson, utilizing student samples of this question?  In Principles to Actions, MTP3 states Effective teaching engages students in making connections among mathematical representations to deepen understanding of mathematics concepts and procedures and as tools for problem solving.

1. Begin with the same question. Allow students to write a response. (3-5 min)
2. Place students into small groups and allow them to share their approaches. (5-7)
3. Allow groups to explore student samples, making note of different ideas, what they like/ways to improve, questions they’d like to ask the student. *maybe as a gallery walk? (15-20)
4. Discuss their findings as a whole group. (10 in)
5. Connections to/between the different mathematical representations. (5-10 min)
6. Written reflection:  (3-5 min. possibly use as a start up / bell ringer to begin class with following day – providing an opportunity for retrieval of previous days information?)
• my strategy was most like:____
• the strategy I liked most was ____ because ___
• the strategy I found most difficult to understand was ___ because ___
• Which approach was most efficient?  Why?
• What do you think was the BIG IDEA your teacher intended for you to learn/understand?
7. Transfer…provide a few, different contextual problems that allow students to connect the mathematics to something tangible, maybe in a problem posing situation (should this be small group?  individual? ) (5-15, would this be better as follow-up the following day?)

Timing is often an issue for me.  I want to provide students with enough time to make sense/discuss, but not so much time it feels long and drawn out.  Are the times I have listed appropriate?

Please offer suggestions.  How have you used a similar approach successfully in your own classroom?

# #MTBoS My Favorite: Open Questions & Level-Up Quiz

Standard

Goodness.  I think this is where I fall apart.  I have so many favorite things I’ve used in my classroom, at times I cannot focus and choose one.  I become distracted, thinking I have to use EVERYTHING.  I have to pause, think about the learners in the classroom and what will be best, most effective for them.

Our second week back after Christmas break was very productive.  I chose to combine 2 ideas and focused my energy with them.  One goal I had set was to use open questions.  (Older posts – first attempt, more good questions – about strategy from Small / Lin).  Rather than giving students more inequalities and asking them to graph.  I gave them a point and asked them to create an inequality whose graph would “capture” the point.  Students had to think differently in order to create their response rather than following a procedural step by step or copying a classmate’s work.

The other was an idea someone had tweeted that caught my attention and I wanted to see how it would work in my classroom…level-up quizzes.  Since the target involved graphing inequalities, I gave each student a paper with 4 empty graphs and space in margins to write inequalities and verify.  Here is a sample of the criteria I gave them:

I told students I wanted everyone to be at level 3 by the end of the week – Level 4 was using multiple measures to verify their responses.  If students were at 3 or 4 early in the week, I posed a challenge to them to create two inequalities that would both capture the point.

This task accomplished several things for me.  It was obvious where students got stuck, it allowed me to give feedback or have a conversation about the symbols, which direction to shade, helped point out when/why to use the = if the point was on the boundary line or not, could quickly address issues with graphing key points of the line.  It allowed students to move on without waiting on their peers.

There were a couple of students in each class who continued to struggle-mostly students who had chosen NOT to put any time/effort into practice the prior week or who had been absent, but the rest of students made gains and improvements with this skill.  By the end of the week, majority of students were at or above the level 3.

The big thing with verifying I saw was students using (0,0) to test in their inequality algebraically as opposed to the actual point we picked.  I feel this was due to us graphing inequalities the prior week.  This year, I opted to encourage evidence of their claim by having them test a point to determine direction of shading as opposed to just saying above/below.

With only 1 response for every student each day, I was not overwhelmed, but able to give feedback.  I made notes of most common errors and addressed them as a whole class prior to passing the quiz back.  For many, I simply wrote a number corresponding to the Level-Up criteria.  Students knew the first couple of tries “didn’t count” but were opportunities to learn and level up by the end of the week.

My concerns after reading about Rubrics in Embedding Formative Assessment –  have I made it more of a skill-ckeck list?  By presenting it as an open question, is that enough to allow for student thinking?  Thoughts on how to improve are welcome!