Tag Archives: formative assessment

Planning for Post-It Note Assessments #made4math

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Let me just say I love Post-It notes.  @druinok questioned me last spring, “Just how many do you go through in a year?” The answer, I have no clue.  I use them once week or so on average, because like anything else, kids can get bored with them.

About 4 years ago, it was my curriculum specialist B.Wade and colleague J.Jessie who introduced me to Post-It note quizzes as a quick exit ticket tool to gauge where students thought they were. 

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@tbanks1906 blogs about it here as well.

So last year, I was introduced to this site called Pinterest, not sure if you’ve ever heard of it. 🙂  Anyway, I ran across this great reflection tool, 2-minute Assessment Grid,

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that I shared here and a follow-up Chalk Talk #makthinkvis activity here.

This issue I ran into this past spring, I didn’t have time to read/reflect on each class’ responses before the next class was filing in.  So, my #made4math for this week… I am laminating full size, color posterboards.  I already color-code my classes, 1st red, 2nd orange, 3rd yellow, 4th green, 5th blue.  I will leave one side of each board blank, but on the other, I will draw out my grid with icons before laminating. 

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Snipping some reinforced holes at the top so I can hang it on the wall using command hooks. (Thanks @solvingforx for this idea!) Students place their responses on, then I can remove their poster and replace with the next class’ for their responses.  During my planning, I can sit down and review each class separately.  Since, they are poster boards, it will be easy to store between 2 file cabinets or behind a shelf.

I can easily attach other color-coded stickies on the back side to create my Stop-light or any other formative assessment involving post-it notes, and this will allow me to keep each class section separate until I can sit down for some quality time to analyze and reflect.

Pam Wilson, NBCT
Currently Reading
5 Practices for Orchestrating Productive Mathematical Discussions, Smith & Stein
Teach Like  a Pirate, Dave Burgess
From Ashes to Honor, Loree Lough

Trig Ratios – #made4math

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Through the years, I’ve seen students struggling trying to remember which Trig Ratio is which.  I have a colleague who draws a big bucket with a toe dipped into the water.  She says she tells the students “Soak-a-Toe” to help them recall SOH-CAH-TOA.  Another has described the “Native American”  SOH-CAH-TOA tribe as the one who constructs their teepees using Right Triangles.  The most entertaining though is the rap from WCHS Math Department “Gettin’ Triggy Wit It” on youtube.

I wanted to use an inquiry activity to help them develop the definitions of the Trig Ratios.  Basically, they constructed 4 similar triangles, found the side measures, then recorded ratios of specific side lengths.  Next, I had them measure the acute angles, then we used the calculator to evaluate the sin, cos and tan for each angle measure.  Students were asked to compare each value to the ratios they had recorded in the table and determine which ratio was closest to their value.  Here’s the file https://www.dropbox.com/s/gfvhnictujfj2ik/similar%20triangles%20intro%20trig.docx?dl=0 Similar Triangles Trig Ratios.  Anyway, its not a perfect lesson, but a starting point.  If you use it, please comment to let me know how you modified it to make it a better learning experience for students.

In the past, students sometimes struggle trying to decide which ratio they need to use when solving a problem. I put together an activity adapted from a strategy called  Mix-Pair-Freeze I’ve used from my KaganCooperative Learning and Geometry book.  This book offers numerous, quality activities for engaging your students.

You can make copies of this file, Trig Ratio Cards File, then cut cards apart to use.

Trig Ratio Cards

Each student gets a card.  They figure out which Trig Ratio is illustrated on their card (& why).  They mix around the room (with some fun music would make it better), then pair up with someone.  Each person tells which Trig Ratio and why (can be peer assessment, if one is mistaken).  They swap cards, mix and pair with another classmate.  This continues for several minutes, allowing students to pair with several different people.

When I call “Freeze!” Students are to go to a corner of the room which is designated Sin, Cos or Tan.  Within the group in each corner, students double check one-another’s card to determine if they are at the right location.  Again, peer assessment, if someone is wrong, they coach to explain why, then help them determine where they belong.

Students swap cards, mix-pair-freeze again.

I like this activity for several reasons:

  • 1. Students are out of their seats and active.
  • 2.  Students are talking about math.
  • 3.  It allows them to both self-peer assess in a low-stress situation.
  • 4.  I can listen to their descriptions and address any misconceptions as a whole-class as a follow-up.

 

To clarify, the intent of this activity is for students to determine what information they are given in relation to a given angle, then decide which ratio it illustrates. It is meant to help students who struggle deciphering what information is given.

Representing Polynomials FAL & Open Card Sorts

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After an assessment last week, it seemed to me what I was doing wasn’t sticking for my students with polynomials.  So let’s just scrap plan A.  Plan B – I pulled out my Discovering Algebra book, came up with a box-building data collection that lead into the FAL I have linked  below.

Formative Assessment Lesson – Representing Polynomials

Thursday, students were given a 16 x 20 piece of grid paper and asked to cut out square corners and create a box with the largest volume possible.  We combined our data as a class.  Recording the corner size removed, length, width and height.  Students were asked to observe the data and respond I notice…  & I wonder… and that’s where our class began on Tuesday.

We shared out our responses, some adding ideas as we continued the discussion.  Work with our data on TI84s – we saw a connection between our constraints 0, 8, 10 and the graph of the regression equation.  This was not new, during the discussion, a question was brought up about what values would result in a volume of zero.  Students were able answer that with confidence and a reasonable explanation.

The FAL pre-assessment confirmed my students weren’t quite ready for the full blown lesson.  With discussion of rigor and relevance the past few days, I wanted to offer students something engaging but not so over their head, it was a flop.

I backed up and did a bit of prep work yesterday – with the following discussions in class:

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Following with whiteboards / sharing for this slide from FAL:  FALreppoly3

and a simple practice set to ensure they were on track.   FALreppoly4

 

We began class today with a quick check of the 6 practice – with a focus on similarities / differences.  Noting the double root of #5.

Prior to the actual FAL, I decided to use the same equations and graphs they were to match during the FAL, except I would have them do a card sort.  Originally, I had planned to ask them to sort cards into 2 groups.  While pondering how I could make it better, I recalled a colleague sharing ideas about open card sorts from a John Antonetti training she had attended.  So, this is what I did.

I told students I wanted them to sort the 11 equations – any way they wanted – they just needed to be able to share out their reasoning behind their choices.  After a few moments, I called on different groups and we looked at their sorts.  I should have snapped pics / documented their responses.  I was amazed – not that they did it – but how well they did it.   The things they were looking at – were much better than my original idea to sort in to 2 groups.  Students were asking students – why they put one in one group instead of another. Pausing after we had the cards sorted on the board – giving other opportunity to look others’ groups…some were obvious, others were not.   I even had groups who had the exact same sorts, but with completely different reasoning.  Wow.

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At some point we began talking about “What does that tell us about the graph?”  Almost everyone was engaged and comments added to the discussion.  Next we went on to the graphs to sort.  Again, any way they wanted…just be ready to share reasons.

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Most of the sorts were better than ANYTHING I would have suggested.  My eyes were opened – I could see their thinking.  And others did as well – it was obvious in the eye brows raised and head nods.  In both classes, there was one equation that never seemed to “fit in” the other sorts – but students were confident suggesting it belonged to a particular graph (& they were correct).

When I realized the sharing took more time than I had planned – I ran copies of the equations and graphs to send home with students and asked them to match on their own.  My plan is to put them back in their pairs for the actual pairing of the FAL.  They also had blank graphs for any without a match.

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I learned so much listening to my students today…  I am looking forward to the assessment of this standard.

I didn’t feel like I taught anything today…

…but I did feel like my students left with a better understanding…because I chose to step aside and give them the opportunity to share their thinking…

It was a great day.

 

 

Always, Sometimes, Never – #75FACTS

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I’ll be honest, I’ve only truly dug-in to reading the first 6 FACTS of Keeley & Tobey’s book over the past 2 weeks.  Through KLN – Kentucky Leadership Network, I’ve explored several others over the past year.  But I’ve gotten very drawn in to processing the descriptions, suggestions given on the first 6 (by the way, they are listed alphabetically, didn’t know that until someone pointed it out in twitter chat).

This past week, of these 6, I’ve attempted some form of Agree/Disagree (#1), Always Sometimes Never (#3) and Comments Only Marking (#6) in my classroom.  I’ll share more later on A/D and Comments.

Last year, I began experimenting with the Formative Assessment Lessons from the MARS site.  Sorting Equations and  Identities lesson asked students to sort mathematical statements into categories – always true, sometimes true, never true.  Part of the task was to justify their choices.  After using this lesson, I realized students really struggled with these statements.  In fact, they hated them – moaning/groaning each time one would pop up.  Which said to me – they were having to think.  I began embedding them in lessons/notes – class discusses/questions – especially in assessments.  By the end of the year, students were “not afraid” to face ASN questions as before.

This week, I gave geometry students 15 statements about quadrilaterals/polygons, in which they had to answer ASN.  When they arrived in class the following day, I had areas of the room designated A, S, N.

Depending on the FACT, it may help to explain to students why you are using the new strategy.  Part of this discussion was that when someone makes a statement, it may seem true, but we should check it out to determine if in face it always applies, sometimes applies or never applies (page 57).  Through the activity, students were able to share counterexamples if they disagreed with another student’s statement.  Great discussion (even a few semi-heated arguements) occured!

Mathematical Practice – #3 Construct viable arguments and critiques the reasoning of others.

Were students engaged?  Definitely – from the time they walked in, they saw the A, S, N posted and KNEW what was coming.  Most were engaged during the activity.  At least those who didn’t want to think – had to at least choose an area to move to in the discussion.  I used my “name cards” to call on students to ensure everyone needed to be ready to share their justifications.

Were you confident/excited about using the FACT? Yes.  I’ve found a new love for always, sometimes and never statements – though I remember detesting them a particular college geometry course – now I realize what a great learning tool they can be.

How did use of the FACT affect the student-to-student or student-teacher dynamic?  I tried to allow students to share their own counterexamples – but when one was stuck, I would question – referring back to properties we had investigated, drawing figures on the board, presenting a what if… if needed.

Was the information gained from the FACT useful to you?  I realized some students still confused a few of the rhombus, rectangle, square statements.  Mostly, that students often only considered the “obvious” – but this activity was great because others were able to share their “what about…” with their classmates.

Would you have gotten the same information without using the FACT?  In the past, I would have likely made the same realizations but only after giving the unit assessment.  This FACT helped clear up some misconceptions during the learning process rather than at the “end of the learning.”

What added value did the FACT bring to teaching and learning?  Students had to think about their thinking, jusitfy their reasoning, could be critiqued by classmates’ thinking – great opportunities for discussion / sharing!

Did using the FACT cause you to do something differently or think differently about teaching and learning?  During the task, I was able to use student comments as a springboard for whole class discussion, pointing out examples that made it true and examples that made it false (great piece of learning to impact understanding of counterexamples).

Would you use this FACT again? Yes.

Are there modifications you could make to this FACT to improve its usefulness?  This FACT lends itself well to written work, whole class & small group discussions.  Follow up is key – probing students and guiding them to consider other examples – if not shared by classmates first.  Even after arriving at what seems to be class consensus, ask again – challenge their thinking – don’t settle for the first correct responses – ask why – let them justify their reasoning.

Thoughts on #75facts

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As I read SimplifyRadicals #75facts post this morning, it really got me to thinking…about things I do and how I could use “Create the Problem” in my own classroom.

I’ve given students the answer before and asked them to write a scenario that could model the problem.  But reading her refelction and suggestions for modifications helped me realize a couple of ways I could improve the way I’ve done this in the past.

The FACT reminds me of ideas from More Good Questions, Marian Small & Amy Lin.  Give students the answer and they have to come up with the equation/problem.  Example, the slope is 2/3, what are 2 points that could give you this slope?

As suggested in the FACT#11 description, providing students with an open ended task takes their thinking to another level.  Student examples generate whether they know why a computation is performed rather than just knowing a procedure.  But this FACT actually asks them, not to find the computation/problem, but to give a scenario/context where this strategy could be used to solve the problem.

The key, as with many successful strategies, is sharing student ideas.  Not just allowing them to talk about their examples and how their story matches the solution, but the teacher asking the class for feedback on whether it is a match, if not, how could it be changed/made better (pg. 81)?

This reminds me of another FACT I’ve used in class before “2 stars and 1 wish.”  however, when I first saw this a couple of years ago, it was called 2 +’s and a delta…two positives and one thing I’d like to change.  Playing off of My Favorite No, I ask students “What do I know this student understands?  Give me 2 examples of what this student did well.”  By focusing on the correct parts first, especially if I’m using a student’s example (anonymously) – the student can see it wasn’t completely wrong.

Then for the delta (wish), I ask students not to point out the mistake, but to think of a question they could ask the student to help the student realize their mistake.  Sometimes, this is a tough task, depending on the mistake that was made, but by asking a question, students, again, are having to think on a different level.

In several of the Formative Assessment Lessons from the MARS site (Solving Linear Equations in Two Variables) – the lesson format actually allows students in small groups to evaluate different levels of student work.  On a slide in the projector resources for this lesson, Assessing Student Work, students are given these questions to guide their discussions:

You are the teacher and have to assess this work.

Correct the work and write comments on the accuracy and organization of each response.

•What do you like about this student’s work?
•What method did the student use?
Is it clear? Is it accurate?  Is it efficient?
•What errors did the student make?
•How might the work be improved?
My thinking, use the FACT #11 – Create a Problem as an exit slip.  Divide the responses into different levels.  On overhead, share different levels, both correct/incorrect, as well as different approaches, using the above questions as a guide for class discussion.  Then present students with solution(s) and ask them to create a problem.
Thanks to Simplifying Radicals for getting my brain to churning so early this morning!

 

#75facts Book Chat Begins Monday 9/24

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Mathematics Formative Assessment: 75 Practical Strategies for Linking Assessment, Instruction, and Learning

Mathematics Formative Assessment: 75 Practical Strategies for Linking Assessment, Instruction, and Learnin

Page D. Keeley (Author), Cheryl Rose Tobey (Author)

They refer to the strategies in the book as FACTS – Formative Assessment Classroom Techniques thus the hashtag #75facts.

If this will be your first online book chat – its simple – read assigned material, log on at designated time and share!  I’ve heard from several of you that you’ve gotten your books in hand – so let’s get started next Monday – September 24.  Meet up on Twitter at 8:30 cst and use the hashtag #75facts in your posts.

I know this will be a great opportunity to share and learn from others!  Several of the FACTS may be strategies you currently use – so there will always be opportunity to share what this looks like in your classroom.  The FACTS may also trigger a new idea on how to modify and improve techniques.

There are 75 FACTS which means this chat has the potential to continue the entire school year – so, if you are new – please join in!  We want you to be a part of this!

Overview:

This book is a bit different than ones we’ve used in the past, so you are encouraged to get started and read ahead – getting ready for implementation – however, we’ll begin our chats by discussing 1 chapter each week.

Chatper 1 Introduction – defines FACTS, shares research, making a shift to a foramtive assessment centered classroom.

Chapter 2 – Integrating FACTS with Instruction and Learning

Chapter 3 – Considerations for Selecting, Implementing and Using Data from FACTS

My initial thoughts are to focus on 3 FACTS each week – you can choose 1 of those 3 to implement (or any prior FACT), reflect and share during our discussions.  We can see how this goes and always modify as we see fit.

Chapter 4 – Getting the FACTS is where the 75 FACTS are presented.  Each FACT covers 2-3 pages, so the reading is not the time factor here – implementation is where your time will be focused.  Don’t let this overwhelm you – if you don’t get one implemented, this by no means implies you should skip the chat!

Each FACT follows the layout:

  • Description
  • How it promotes student learning
  • How it informs instruction
  • Design and administration
  • Implementation Attributes
  • Modifications
  • Caveats
  • Uses with other Disciplines
  • Examples, Illustrations
  • Notes/Reflections

If you have not already, please enter your name in the form so we can ensure we keep you posted!

I will get a form in place for you to share any blog posts about #75facts soon!

Online Book Chat – Math Formative Assessment

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Are you interested in an online book chat?  If you’ve never participated and wonder – how does that work?  Its simple, we’ll set specific parts/sections to read; meet up online and discuss what we’ve learned; share what we’ve implemented; reflect/collaborate!

Mathematics Formative Assessment: 75 Practical Strategies for Linking Assessment, Instruction, and Learning

Mathematics Formative Assessment: 75 Practical Strategies for Linking Assessment, Instruction, and Learning

Page D. Keeley (Author), Cheryl Rose Tobey (Author)

They refer to the strategies in the book as FACTS – Formative Assessment Classroom Teaching Strategies thus the hashtag #75facts.

Get your book in hand and we’ll be posting more information later!