Personal Reflection 3-2-1 #MTBoSchallenge

Our school district will begin using a new Certified Evaluation Plan this year.  The CEP has 2 major components: Professional Practice and Student Growth.  As part of the Professional Practices, each teacher is asked to consider various pieces of evidence and complete a self reflection which eventually leads to their individual Professional Growth Plan.

I will be completing my self reflection this upcoming week, which has had me wondering this weekend, what are my goals for this school year? 

3 things I want to learn, incorporate, practice:
I have read about Flipped Classrooms since before I began blogging.  Watched a couple webinars, read several blog posts, articles.  Its always been of interest, but I just didn’t have take the time.  I have recently begun my first Flipped Unit in my Algebra 2s.  It nothing major, I have linked to videos readily available on You Tube, but have quickly learned if students are accessing on their school accounts, YouTube is blocked.  So I am now looking for possible places to host my own videos (eventually, I want to use my own).   

My interpretation is either introduction or skills needed for problem solving which in turn allows students time in class for real application of math.  Following each video, I include 3-5 questions of the big ideas/takeaways for student self-assessment of the video.  When I begin creating my own, I intend to keep them around the 4 minute range, continue including self-assess questions.  For student who dont have access, they can come to my classroom prior to school/class and complete, but they are not allowed to participate in the days activities until they’ve completed the video or shown understanding to me.

Lesson Study – I have read some posts, been involved in a few informal twitter chats, even discussed the process with colleagues at TMC14.  I have located some resources through our PD360 I intend to utilize, but now, I have to find a friend and convince them its worthwhile to journey with me.

Talking Points -I want to ensure that every student feels like they can share their ideas and be heard.  Talking Points is the key for me developing this culture of learning.  I look forward to learning more, sharing with my students and implementing this as a classroom norm.  Here is a place to start.  Severval MtBoS have implemented them as the school year began.  I will share my experiences soon!

2 things I want to continue improving:
Literacy in Math Class- Whether reading, interpretting/deciphering informational text, writing, reflecting on their learning, verbally communicating or strategies to help studentsconnect vocabulary to prior knowledge…communication is a key skill they can use elsewhere.  Last spring, I participated in a webinar based on the book Vocabulary Their Way.  I sincerely feel providing students with similar tools will enhance their learning across all discilpines.  I plan to use some of the structures I’ve learned from Kagan resources and develop some of my own activities for student interaction with peers.

Standards Based Grading – about 5 years ago, I became very interested in aspects of Standards Based Grading.  It just made sense.  I had read, researched, even implemented some successful approaches.  I have heard through the grapevine, theres a possile push for our district to move this direction.  Even though it has not come from an official administrator, I’ve heard teacher conversations outside of vertical meetings that sounds like it may be on it’s way.  I am uber excited.  I have been looking for some good quality resources to share, should the time arise.  @mpershan shared a link this morning for a couple of good resources.  Scroll down to Garry Chu SBG.  Although, I think the Jeff Harding’s video following it gives a fun analogy to show how ridiculous some of our grading practices are-supporting Why we should consider SBG, then Mr. Chu shares some great ideas on How to implement.  I look forward to getting to move on this journey again (finally).

1 thing that’s Imperative in My Planning…
Standards of Mathematical Practices Yes, I am very familiar with them, yet I have not been so intentional in my planning and inclusion of them.  I had a major a-ha last year that I had missed the boat when first becoming familiar with CCSS.  The SMP should have been the anchoring foundation prior to transitioning to CCSS.  As I plan this year, I will be intentional and very explicit in providing students opportunities to use them.  But also in asking students to reflect on their uses of them.  I look forward to reading NCTM’s Principles to Actions, hoping it will guide me in this goal.  Another resource I plan to revisit is Making Thinking Visible.  I read it a couple of years ago, but feel it provides quality routines to enhance student learning that support the SMP.

Google Form to Track RTI

Last Spring I had one block designated for RTI.  Initially our focus was on students below benchmark on their PLAN as an indicator of their ACT.  All 11th graders in Kentucky take ACT during March.  After ACT, we began to look at their Discovery Education Benchmarks for their current course to highlight students below proficiency or those not progressing at an expected rate.

When assigned to RTI the previous year, I was a mess.  I never felt I had a good grasp on my purpose and end goal.  This year, I went in with a plan of action.

For the ACT, first half of the semester,  I deconstructed 4 practice exams, looking for big ideas that correlated with suggested topics from ACTs website for students within this score range.  I used varied strategies (Notice/Wonder, visual patterns, white boarding, small groups, individual, online review options, etc) to interact with students while utilizing these big ideas as our initial goal.  Each student took a 15-minute evaluation using Method Test Prep to give me a  baseline (unless their current teacher could provide me with other evidence).  Some students had taken the actual ACT and we were able to use those results as a beginning step as well.

From Discovery Education Benchmarks, I considered the areas students were not progressing in and provided similar strategies as with the ACT above, just more focused on specific content as it pertained to their course of study (ie algebra 2 vs geometry) to help them move forward.

I needed a way to track the variety of students, so I created a Google form and placed a link directly on my desktop.  At the end of RTI, during planning or afterschool, I could quickly enter information.  This intent was just to track who I was working with, how often.  However, the goal of RTI is to provide supports for students that will enhance their learning and transfer to achievement.  As I met with individual students, we discussed where they were and I allowed them to set their own goal.  This was in their their file, they wrote it out, but I need to modify my form and enter their goal, along with final results in order to help me see the learning all in one place.  If you’re not familiar, responses to g-forms are shared with you in a spreadsheet, so you can sort by student if you like.

 

My form was simple and included the following:

Student Name.

Date. (there was a time stamp, but sometimes it may be after school or the following day before I entered their information).

Time of day – drop down menu. (RTI was 3rd block, but if a student’s schedule didn’t work well with that time, I met with them during my planning or afterschool ESS).

Topics Addressed – checkboxes with an option for Other.

Method Test Prep results (from evaluation, Practice Test 1, Practice Test 2 and/or Lessons they completed on their own time/during RTI.)

Misc. Box to enter notes of how much we completed, successful or need to continue, etc.

 

My intentions are to include DE Benchmark with subcategories and reporting levels this year as well as a place to record their goal, comments and reflection each time I meet with them.  I need to add ACT score, EOC score as well as DE Benchmark final results.

Even though I currently do not have a section of RTI assigned, this is a form I plan to modify and use within my own classroom.  I will utilize our Method Test Prep in the fall to set baselines and see needed areas for attention, then focus

 

Setting Personal Social-emotional Goals pt. 2 #julychallenge Post #17

This morning as I responded to a commented from @bpagirls on my post about an Essential Questions Board, a thought hit me, so I typed it in my reply so I wouldn’t forget…

… I have just realized as I type, why not add a spot for personal-social goal-setting on my organizer for each student to set, write and reflect.

It stems back to this post and one of the 14 ways to think about good teaching post, 3. Include social-emotional learning goals as well as academic goals.

I got that I needed to do this, but I was not quite sure how to set and record these goals.  My plans are to include a place on the back of our unit organizer students receive at the beginning of each unit.  These are formatted in a booklet style to fit our INBs.  Students can set a personal/social goal to focus on for the duration of the unit. Ideally, following the SMART goal format.  Commit to it by writing it on their organizer.  I will ask to see it, but they may choose whether to share with a peer.  Wouldn’t it be great to have accountability partners for the unit? 

Throughout the unit or even at beginning of class, ask them to read it to themselves.  Maybe even allow someone to share their progress.  Revisit them as we end the unit and write a brief reflection:  How did I do?  Did I meet my goal?  If not, did I at least move toward it? What do I need to modify?  Follow the format: 2 stars and a wish for their quick-write reflection.  Celebrate their progress, maybe through our Shout-Out Board (more on that later).

I realize this type of goal setting may be tough for students… I am hoping after completing this task, it will allow for students to generate ideas.

Initially, I think goals can range from:
Improved / good attendance
Be to class on time
Being prepared for class
Completion of assignments
Asking for help
Asking questions or participating in class discussions.
Attend tutoring if needed
Work in a group with people I don’t know.
Share my ideas in class
Share my assessments and progress with parents/guardian
Choose better practice/study options
Listen to others ideas
Evaluate how my choices are impacting my learning.

Here is a sample of the back of my unit organizer.  I plan to insert personal goals below the unit reflection.  Here is an updated version of a complete unit organizer and student assessment tracker. Feel free to modify for use in your personal classroom. Thanks to Crazy Math Teacher Lady and Math = Love for inspiring through their posts?

My next task is to locate a fill-in the blank for a SMART to include on the first unit.  Kind of a madlibs style to get us started.

If you have a system in place or use LIM or AVID in your school, I welcome input and suggestions.

My Experience with Counting Circles #julychallenge Post 14

Still addressing 14 ways of thinking about good teaching from this post…

2.  Plan goals for both the long term and the short term.

My number 1 goal is to help students grow – personally and academically.  My wish is that they leave my classroom believing in themselves, more self-confident than when they entered. 

Ideally, I do want every student to reach proficiency, but I am also a realist.  When students come to me with *ACT-PLAN scores in the 10-14 range, proficiency is not an immediate goal…growth is, pure and simple.  My class becomes the stepping stone to reach proficiency.  Students in this range generally have major gaps in number reasoning.  They are just now beginning to develop understanding and knowledge of assessed skills.

Last year, I wanted to use accessible tasks to begin each day…Counting Circles, Number Talks (pg 4 of link) and my post, Estimation180, and Visual Patterns were staples in my Algebra 2 classes.  Students in these classes ranging from ACTPLAN scores from 10 to 23-wide range of abilities and varied confidence levels.  These tasks were approachable for all students and I feel helped in developing number sense which allowed several students to make significant gains on thier ACT.

Counting Circles (Thanks to Sadie!) was very popular in both classes.  We literally got out of our desks to create a “circle” around the room. Yes, it seemed trivial at first, but I was able to see student confidence grow as they strengthened numeracy skills.

My Routine
We have a starting number and a number to count by.  In the beginning, I choose nice numbers, then some that required a little more thought.  Eventually, I allow students choose our counting number and starting point.  I would have expected them to take the easy route.  Not at all.  They like to challenge themselves.  We also countdown.  I like to write their responses on the board for them to visually see the patterns.  When a student makes a mistake, I try to not point it out, but rather, allow students to have opportunity to voice their concerns with a response, respectfully, of course.

After going so far around the circle, I stop and ask, What will _______ (a little further around the circle) say next? 

We usually get a couple of responses, so I allow them to explain their process then, as a class, they determine which one makes more sense.

Also, I like to ask…who will say ______ ?

Side note: Later in a functions unit, while looking at finite differences, a student explained, this is similar to what we were doing with Counting Circle the other day!

Our First Counting Circle – Count by 10
I began with couting by 10 on decade numbers, by -10 on decade numbers, then on numbers like 11 or 14, counting by 10 in both directions.  It was a great way to model the routine.  Students are comfortable with it.

Next week, we counted by 2s, up and down, starting on positive and then a negative.

Several students are all in – they’ve got this!

Then by 5s.  On 15, 70, -85 then numbers not ending in 0 or 5…. 37, 128, -89. Both up and down.

I began using single digit integers then a few double digits.

Next week we worked with decimals +3.7,  starting with an integer, then moving to devimals 11.2.  One student this particular day was quickly running through their numbers.  When I asked their strategy, they responded….its easy, add 4 then count .1 back 3 times.

We also use fraction expressions as well.

I already know my stronger numeracy students-those with “high status” in class (Ilana Horn).  So do their classmates.  What I love about counting circles is choosing different students to explain.  Struggling students pick up on numeracy techniques as explained by their peers.  They are able to see those high-status students’ thinking and realize, “I can do that too.”  Its a win-win.

Yes, at high school age, I have students who don’t want to participate, but with a bit of coaxing, they come around. It becomes a game.  Classmates encourage those who struggle.  We don’t laugh or make fun.  They celebrate when ‘that’ student experiences success.  Most of all, they smile.

Generally, it takes anywhere from 5-15 minutes depending on number choices, discussions, size of class, experience with the routine.

Suggestions:  pre-cal count around unit circle, elementary use money as a context, what others can you share?

Long term goals and planning changes with each group of students.  Having access to learning routines like these allow me to tailor toward each groups’ needs.

*In Kentucky, every student takes the PLAN during sophomore year and ACT during their junior year as part of our state accountability model.  To measure student growth from state data, students are grouped by their PLAN scores, then compared to others in this scoring band.  Once the ACT scores are available, they are given a percentile rank from within that initial grouping.  I, the teacher, can view this and whether they had high growth, expected growth or below expected growth.  The state assigns me an overall rating and this will eventually become 20% of our Certified Evaluation plan.  The other 80% is determined locally and by student growth and proficiency goals I personally set for my students early in the school year.

Time Capsule Teaching #tbtblog #julychallenge Post 13

This tweet made me wonder….

If I created a timecapsule of my teaching strategies…what would I think when I opened it? 

I read the post, Time-Capsule Teaching and within a few moments I thought…what was I blogging about 3 years ago?  I searched back and thought I hadn’t actually started yet, but there it was…

July 17, 2011

I was new to the blogosphere. 
This was my 2nd post.
TMC did not exist yet.
I was learning about standards based grading.

After much reading and discussion with close colleagues and many hours of processing what I had read, I knew SBG would be more effective in communicating student learning.  My grades prior to this had been filled with fluff, things unrelated to actual student learning…the reason some students had good grades but were not achieving at the same level.  Initially, that’s why I started blogging was to record my journey through sbg.

2 Years ago
July 16, 2012 #made4math Monday

It was the 3rd week of #made4math.
These lovely pencils for my classroom.

I did this again last school year. 15 pencils almost lasted until Christmas break.  All in all, I put out fewer than 36 pencils for the entire year.  My daughter helps decorate-cheap flowers, pipe cleaners, feathers-whatever she finds in the craftbox to make them obnoxious.  Students no longer ask me, they just borrow.  It is easier than me taking time out of whatever task I am on to hunt them a pencil. I have a mini clipboard, students signed their name and crossed it off when they returned.  Obviously, some were not returned but that’s about 1 pencil per week.  Its worth it to me, fewer interuptions, I don’t get frustrated if the same ones are borrowing a pencil everyday. 🙂

The same post I shared this handy paperclip box that I just filled with paper clips before APSI last month!

1 year ago
July 23, 2013
A Reflection Tool for PLCs from @TJterryjo “I have a dream…”

Basically her PLC was asked what characteristics a dream math student would have (in green).  Then, as teachers, what they could do to create that dream (in blue).  At each PLC, they “dotified” what they had seen in students and themselves to see if they were moving toward that dream.

This is something I wanted to do but let it go.  This is on my to-to list for our first departmental PLC this school year!

Join in!
Pick a year. Any year.  Read a post and reflect…
Not been blogging that long? Pick a favorite blogger and read one of their posts from 3 years ago…
Throw-back Thursday Blog #tbtblog

Get to Know Your Students pt 2 #julychallenge Post 12

 Get to know your students, especially how they learn and think.

Taking my lead from this post, my intent is to consider how I can improve or implement the 14 ways discussed.  In my last post, I shared how important I feel it is to know our students as real people.  This one is to share #5things that impacted my classroom and helped me know how my students learn and think.

My 3 years with Kentucky Leadership Network and my experiences with #MTBoS have changed my mindset.  The work with KLN introduced me to a new set ideas and #MTBoS allowed me to explore with others and develop a new frame of reference as I seek to grow as an effective educator.

I cannot be grateful enough to all those who have challenged me and help me grow.  But as I think of the experiences that have opened my eyes to see better ways I can consider my students as learners, these are the ones that first come to my mind.  #5things for getting to know how my students think and learn…

Wait Time II
I learned about this routine from 75 Practical Strategies for Linking Assessment, Instruction and Learning (Keely, Tobey 2011).  A simple adjustment.  Yet it forced me to really listen to my students.  You can read more on a previous post, here.  Basically, it allows  the students AND teacher to process a student response.  We were all told in undergrad to wait 3 seconds after asking a question before calling on a student.  Some people actually think this deters the class flow.  I disagree. The idea with Wait Time II is to wait again, after the student response.  It allows the responder to consider what they said, the classmates to process what was said and the teacher to consider next steps, questions, etc.  A bit uncomfortable in the beginning, but once I explained the rationale to them, they got it, as did I.  Waiting and listening adds value to what students are saying.

What Makes You Say That?
Making Thinking Visible, (Ritchhart, Church, Morrison, 2011)
A chat with Liz Durkin challenged me to consider ways I could implement these routines into my high school math classroom.  It was the question “What makes you say that?”  that helped me begin drawing out student thinking.  What were they seeing? What evidence supported their statement?  With this routine, I began learning new ways of seeing problems myself.  Students’ ideas, strategies and approaches are way more intuitive than my own.

Notice and Wonder
I was first introduced to Notice & Wonder with Max Ray’s Ignite talk sharing The Math Forum’s simple, yet impactful strategy.  You can read more in Powerful Problem Solving (2013) as well.  When I pose a problem, scenario, graph, students may not readily know where to start.  But they can tell me what they notice.  Its a starting point.  Everyone can share something.  When we listen to what others are saying, that ignites other ideas as well.  And they begin sharing their “I wonders” which are great transitions to explore more.  Its great.  Its simple.

This routine carries over to standardized tests as well.  Students shared how they didn’t know how to approach certain problems on ACT or their EOCs, but they looked at it, thought about what they noticed, connected it to something they knew and was able to at least make an educated guess. 

Friendly Class Starters
After reading What’s Math Got to Do with It? and completing the Jo Boaler How to Learn Math course last summer, I knew I needed to find ways to invite students to think differently about math in my classroom.  Some major a-ha’s and sad realizations as to why so many kids are down on math.  I began with things like Number Talks she presnted during one session.  Amazing how many different ways students can see / approach a single problem.  When I invited them to share their thinking, they owned the math.  This past year, I implemented Counting Circles, Estimation 180, Visual Patterns as well.  These resources were primarily used as bell ringers to get students in math mode. However, there were days it lead to deeper, richer discussions and I was flexible enough to go with it.  My students’ confidence began to grow.  Their number sense was developing.  They were sharing their reasoning without me asking them to.  I saw some big gains on benchmarking and standardized testing for several students and I attribute them to these “friendly” and accessible resources.

Small Groups and Discussions
When I completed my initial National Board Certification in 2002, I quickly realized small group discussions provided a definite means to seeing student thinking.  It was a chat last summer, that made me realize I needed to quit butting-in.  I would hear a misconception and jump to add my 2 cents rather than allowing them to reason out if they were correct or needed to adjust.  I was stealing their learning opportunities! Yikes.  I began listening more-offering questions rather than telling them the direction they should go.  It was frustrsting for some students.  They despised me answering their questions with questions.

5 Practices for Orchestrating Productive Mathematics Discussions (Smith & Stein, 2011) is a quick read that offers samples to incorporate into your classroom. The 5 practice provide structure to help you develop discussion based tasks rather than step-by-step inquiry lessons.

Another valuable resource for me are the Formative Assessment Lessons provided by Mathematics Assessment Project.  Most lessons follow a similar format to the #5pracs.  I used to struggle offering questions that would move learners forward.  Though some disagree with scripted lessons, this resource supported me with sample questions for specific student misconceptions.  As a rssult, I began asking better questions on my own.

Another aspect of the FALs is the way they suggest grouping students, not by ability, but similar thinking – whether it be similar misconceptions or approaches to a problem.  This supports what I have been reading this summer with Ilana Horn’s Strength in Numbers (2012).  She presents how social status in the classroom may actually hinder student learning and achievment.  I believe grouping students homogenously by approach and thinking puts them on equal playing fields to share and build their ideas. 

By observing student responses and listening to their discussion, I am able to select and sequence ideas for them to share that will allow more engagement from the class as a whole.  Students are able to listen and view strategies similar to their own, but also consider new approaches which in turn builds their own skill set and toolbox for thinking.

The common thread is to not to do all of the talking, but to sincerely listen to my students and their thinking.

#readthree Summer Challenge #MTBoS30 Post 22

Last summer I wrote a post after a tweet from @burgess_shelley (she’s married to that Pirate guy)…but I enjoy reading her journey and experiences as an educational learner and leader!

Time to read the blogosphere is sometimes put on the back burner during the school year.  I hate this because interacting with #MTBoS challenges me to be a better teacher.  But it happens.

So today, I offer this challenge (again) to myself, but feel free to join in.  Read posts from 3 people you follow on twitter.  If you cannot do it daily, set a goal for yourself. I am challenging myself to 4 days a week and one day to reflect and share my take-a-ways by compiling my to-do list for next year. 

My intentions for next year are to incorporate more hands-on labs/data collection, focus on vocabulary and literacy strategies to empower student reasoning (writing and summarizing, @druinok!), providing more purposeful interactions/discussions (Strength in Numbers, @tchmathculture!) and planning more engaging tasks/activities.  Hopefully these goals will guide my focus in this challenge.

I am looking forward to reading from some new bloggers as well as catching up with those tried & true!

Feedback & Perfectionism #MTBoS30 Post 5

I’ve had some major a ha ‘ s this spring.  Mostly about myself but as I dig in to reflect, I realize I am not so different from my students.

As part of my Master’s program 15 years ago, I earned my certification for Gifted & Talented Education.  Quick shout out to Dr. Julia Roberts of WKU’s Center for Gifted Studies.  She was an amazing instructor. Everything we did pertained to our classrooms, our students. She helped me build an even stronger foundation in my educational beliefs.

I quickly realized so many of the topics we discussed and strategies we learned could apply to all of my learners, not just those identified as GT.

One is perfectionism.  I have struggled with more students this year failing to complete tasks.  As I dug for reasons why, many shared the fear of doing something wrong, so they chose not to do it at all.  OR when faced with a challenge, they felt their end product wouldn’t be high standard so they chose to let it go.

I say I believe growth mindset.  I encourage my students to learn from mistakes.  But do I truly live it myself? 

My philosophy, if it’s worth doing, do it right the first time.  Meaning to put every effort in up front, planning before I begin the task.

Step back.  When is the last time I challenged myself to really try something just beyond my reach?  Something that I could not achieve on my first attempt?

It’s hard to experience failure.  So is that why so many students give up before they ever begin to try?  Even with nudging and attempting to support a culture of growth in my classroom, I feel that I have failed certain students.  So what can I change to move forward again?

Another A-ha for me this year…  Are my students not moving forward because they are waiting for feedback?  Rather than reflect for themselves, are some waiting for my “seal of approval” before the next step?

Ouch.  Timely feedback.

If I expect it, then I must model it.  Rather than awaiting pending approval, it’s time to sit down, make end of year adjustments and keep moving forward. 

It’s my classroom. They’re my students.  Ultimately, their progress is in my hands.  I am a professional who can reflect on my practices and make decisions that will have the greatest impact for my learners to move them forward.

Yes.  This post is a bit out of frustration.   It’s just that sometimes we ask for fresh eyes not to tell us we’re good teachers and class went smoothly that day. I ask for feedback because I am constantly trying to improve my craft.  If I have even one student not moving forward…I want to do better and I need to do better.

Knowing the How but Not the Why

Guilty.  I can do a lot of procedures, but when asked to put it in a context or explain WHY it works…I may or may not be able to do it.  Or at least at that point in time. 

For example, a colleague who subs in our building is finishing up an education certification. As part of that program, they are currently enrolled in a math methods/problem solving course.  They had a question about a problem…

2/3 divided by 4/5

Getting an answer was not the issue.  We both knew to invert the 2nd and multiply.  They were asked to put it in a context and then follow up with a different interpretation as well. 

I thought for a bit and said, there is a lesson sequence in the Vn de Walle book but mine is at home.  “Oh! I’ve got that book!”  So they ran to get it.  By the time they returned, I had found an article I remember running across a couple of summers ago.  Measurement and Fair Sharing Models for Dividing Fractions by Gregg & Gregg. It was essentially the same lesson, modeled after the Van de Walle lesson.  Christopher Danielson has a very nice post here that references it as well.

Basically, I went through the lesson sequence.  Just as when we teach procedures, if we don’t provide opportunities for student thinking to develop, they are stuck with meaningless, rote steps.  As part of this sequence, I realized how much easier it was for me to divide with like denominators.  Honestly, I had never considered it before.  Shameful, I know.  But noone had ever led me to do it that way and I had never taken the time to consider it. 

Along with Jo Boaler’s course, I wonder how spending some time thinking about how elementary and middle grades teachers develop concepts would impact my own teaching.  I realize how important it is to allow time and provide a structure for students to make those meaningful connections on their own.  I am there as the support to help them along their way.  But in order to be successful, I might need some of my own productive struggle in order to answer the WHY and provide some meaning.

#WTPW Simplifying Radical Expressions-Rationalizing Denominators #tlapmath

I am not sure how exciting this lesson is, but I believe the idea beats the run of the mill take notes-practice on a worksheet.  It gives students opportunities to notice patterns on their own, a chance to share and discuss those ideas as well as consider ideas from their classmates.

I appreicate Math Equals Love Walk the Plank Wednesday post and will definitely use some of her ideas with the “why” we do this.

My goal is for my students to be able to determine if expressions are equivalent, so I am beginning with a simple card matching task.  As students enter the room, they will receive a card with a radical expression either simplified or not (similar to set A).  As we begin class, they will be asked to find their match…without verbal communication…while I post attendance, etc.  They will come to me with their match and I will confirm if they are correct.  Yes, I will allow calculators.  I know, not too high level on the thinking scale.

I will have several sets of cards similar to those they matched.  Each group will then be asked to complete an open-card sort.  This simply means, I do not give them any direction on how to sort their cards.  The only stipulation is they are ready to explain why they chose to sort them as they did.  When the timer goes off, we will share sorts (both volunteers and any I find that are interesting to me).

Part C, I will have concept attainment cards placed around the room.  Each card will contain examples of radical expressions labeled simplified and expressions labeled not simplified.  Students will carousel to different cards, noticing patterns, trying to develop their own rules.  After a set time, they will do a quick pair-share to summarize their findings before we have a whole class discussion. 

Hopefully their ‘rules’ will encompass all we need to know, but if not, I can always use their ideas to lead us to our goal.

We will create a set of notes for our INBs.  Part of their HW will be a LHP assignment to give examples of expressions that are simplfied and not simplified from their earlier carousel work.  Ideally, they would create their own expressions.

If students need practice with skills, an idea from a workshop several years ago…on a page of say 30 problems, I pick 5 I want them to do, then they pick another 5 or 10, whatever I/they feel is necessary.  By giving them this option, I have more success getting them complete the practice.  I would much rather have 10 complete than 30 incomplete or not even attempted.

An idea for formative assessment…return to card sort from Part B.  They should sort into groups of simplified/not, even match up equivalent expressions.  One person stays with the sorts, while others go to different groups to peer assess.

Possible written assessment questions, a) give a bank of expressions to match equivalents, noting simplified terms; b) given a simplified expression, create an unsimplified, equivalence.

This is a very generic layout, but I can use the sequence with whatever level of Algebra I am working with.

I will post again when I have sets of cards completed. 

Feedback to move forward, ideas  for improvements are welcomed.

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