HW Part 2 #MTBoS30 Post 9

It was a conversation I read on Twitter last night linking this article that got me to thinking…

Where is the balance?  I have students at both ends of the spectrum…those who are college-bound & those who are not; those who have highly involved parents & those who are practically raising themselves; those who are intrinsically motivated & those who are a warm body in my classroom by court order;  those who do not work & those who go to work directly afterschool…not because they want to but because they are helping their family’s income; those who are college/career ready and those in the 15th percentile…all in the same class.

Pretty straight forward indicators of who will and who will not completed lengthy assignments.  Those who are progressing continue to progress, so its up to me to get the content infused during the class period…otherwise, its amiss.

HW/Practice is a small percentage of the overall grades reported.  However, I still see that it makes a huge impact on so many of my struggling students.  I am perfectly fine for students who don’t need it to not do it and master any quiz/test on the concepts.  But if they are able every single time, then do I need to up the level of my assessments?

Students who are not “grade getters” are satisfied with good enough.  This is my struggle.  If I set my mark at 80% and they get 60% or even lower…I require a wrong answer analysis, which gets completed IF I allow time in class, but beyond my 50 minutes…usually not.  They must show proof of practice, some action-tutoring, meeting with me, completing/redoing a previous assignment.  But if they are content with their score…there is little effort to make improvements.

After some in class intervention, I pull them out of elective classes for RTI (because after school tutoring interferes with their work schedule).  Its usually about 50/50…appreciating extra help vs. Mad at you for making them miss their electives.

When I assign HW, I attempt to make it purposeful.  Some may have more skills practice, while others are geared toward contextual problems.  If its skills practice, I choose so many and they choose so many-with suggestions based on their performance on a quick quiz in class. (Ex. If you need more practice like #3…choose from problems 11-15) Self-reflection and student choice. 

Other times, it may be to write a summary or reflection of the discovery activity / small group task of the day.

I attempted to flip using some video lessons provided by out textbook nut that was a flop.  I like the idea, but to me what I was seeing was no more than direct instruction….here copy what I do…Which is appropriate at times, just not all of the time.

There are students who simply copy someone else’s work.  Duh. Seriously.  But I see educators do it to when it comes time to submit a PGP or other documents for program reviews…and those are usually the ones who complain about students not trying/thinking on their own.  Yep. Cheating, how could teenagers do such a thing. 

I attended a session at NCTM Louisville last fall by Samuel Otten @ottensam on twitter.  The focus was on SMP but I had so e great take a ways as pertaining to HW.  Rather than the standard dry check most of us grew up doing…try some reflection.  These will easily fit in the LHP of your INBs:
Which problems were most alike? Different? Why/Explain.
Which problem was easiest? Most difficult? Why?
Give them the answer(s) and let them create the problems.

For me, its key to walk around skimming their responses, carefully select a few to share and sequence them appropriately.  I definitely am a fan of pair-share then share with whole class something you heard (not what you actually wrote) or saw from your partner.

I have even tried a question board…as students enter the room, they list problem #s that gave them some struggle.  Use this to guide our HW discussion.

As HW…assign problem to a student…they must create 2 possible student responses…one with correct reasoning, one not. Post them on chart paper for a carousel activity and students walk around Chalk Talk responding with stars (things they agree with) or  delta (questions they might ask to help student change/improve their response).  Each student gets 3 stars and 3 deltas which means they would visit 6 different responses from other students.

Another favorite assignment which actually serves as a review…
At end of lesson, they create a 3 question quiz to share the following day.  With complete solutions /explanations on back.  This can be modified to use high DOK questioning with a bit of guidance.
Or at the end of a unit, allowing students to compose their own assessment addressing each of the learning targets allows them to revisit various lessons/tasks.

Again, only some ideas of things I have found useful in my classroom…hopefully at least 1 take a way you can tweak for your students.

Give them a box…take it home, redesign/construct a more efficient box. 

#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

Interactive Notebooks

INBs were introduced to me at TMC12 last summer by Megan Hayes-Golding.  It was consistently the #1 response students stated on their evaluations as something I should continue doing in my classrooms.  They are not bulky, students like the conciseness of the information we place in them, they helped students stay organized. 

Using CWP (color with purpose), foldables, graphic organizers for note-taking allow students to develop skills that can carry over to future coursework. 

By creating assignments that require students to ‘interact’ with information helps them develop connections and retain the knowledge.  Often times, we would complete an inquiry task in-class, then together create a summary of what we saw/learned. By using a variety reflection tools after completing a task, students are able to self-asess any questions that remain and we can address those misconceptions either individually or in-class.

The TOC is imperative.  For teacher accountability 🙂 and it allows students to quickly locate info in their INBs.  One change I plan to make this year, is the addition of tabs as suggested in this post by Mrs. Hester.  The only change I plan to make to her suggestion, is to use the unit title. 

I really like the EOC Review glossary she shared in the post.  I believe using different techniques which allow students to interact with the vocabulary helps students develop deeper understanding of the words.  I appreciate the complete glossary, but do I dedicate several pages at the end of the INB for this?  What are some ways you incorporate literacy/vocabulary into your INBs? 

A KAGAN structure I used often in geometry this year  was Developing Definitions.  Examples/non examples of each term were posted around the room and students would carousel to each, creating their own definitions.  There was a pair-share, then whole class follow up to discuss how they defined terms to ensure we were all on the same page.  After the first time we used this task, students requested that we do it again.  They said by having to come up with the definition on their own, they were able to have a real understanding of the terms.  For a left-hand page assignment, we would often play “Draw What I Say” – another task from KAGAN.  Students would play pictionary of sorts by using a prescribed statement incorporating specific terminology.

I wonder if by having purposeful assignments within each unit of study focusing on specific terminology, then as a review prior to the end of a unit, allow students to complete those entries in the glossary, if this would have greater impact?

Another idea that developed as the year progressed, were pockets.  We began by having one pocket at the front of the INB.  However, a student suggested to have other pockets throughout.  This coming year, my intenions are to have a pocket at the beginning of each unit.  Here is an example of a pocket.  You still have room to place information.  Possibly your essential questions for the unit, a concept map-brainstorm at the beginning, then revisit as a reflection and modify it at the end of a study?

This pocket is super easy to construct!  One of my favorite things I learned at TMC/Global Math!  Simply fold top left hand corner down on a page.

Place glue or add tape to the bottom and left edge of that page.

Flip pocket top to the right and adher to the back of pocket.

These pockets are much sturdier than I gave them credit to be.

Another idea I plan to develop before the school year begins are unit organizers to attach to the back of the pocket.  I just need to figure out how to modify this

into a folded-booklet style which also includes a place for students to record their own learning progress.

I am super excited about continuing use of INBs in my classroom and look forward to developing an even larger basket of ideas to make them even better learning tools for my students!

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

Developing Definitions

I’m back!  Nearly 2 months? Yikes. Some fellow teachers on Twitter were committing to blogging once each week.  I think  that’s reasonable – besides, usually my best reflection comes during the moments I blog.  Reflection – seems to be the first thing I push aside when I just don’t have the time.  Yet, its the most valuable use of my time.

I’m sharing some successes from Kagan Geometry (one of my favorites by the way).

I was going to be out for a number of days due to being seated on the jury for a trial (give me 100+ teenagers over the courtroom anyday!).  I wanted to leave something productive.  I did short videos (<10 minutes) filling out certain pages in the INBs in addition to other activities.

The first Kagan activity was for vocabulary.  Each strip of paper included examples and counter-examples for each term.  I modified from the round-table recording it suggested.  Students were asked to pair up (a new partner for each new term) and develop their own definitions.  I loved it simply because most were terms students had previously been exposed to in middle school.

When I returned to the classroom, I ran through all I had left during my absences to address any concerns/questions.  Several students commneted how they liked (appreciated) doing the definitions this way.  Their comments ranged from – ‘You actually had to think about the terms; Talking with someone about it really helped you process what it was before writing it down;  The pictures of examples / nonexamples really helped understand the word better.’

Yesterday, we developed more definitions about angles.  When I told them what we were doing – they were excited about the activity.  Listening to the conversations – I was very happy with their discussion / questions / specifics they included in their definitions.

I remember several times in the past doing examples / non-examples, especially when using Frayer Models.  I believe taking it out of my hands/mouth and giving them the opportunity to work in pairs really enhanced their understanding of the terms.  Even when discussing HW  today – they used appropriately terminology.  Yeah!

Another Kagan activity I used as a LHP activity

from Kagan Geometry

– very similar to Everybody Is a Genius’  Blind Draw.  Students were placed into small groups and given 12 cards with written directions.  Person 1 chose a card, read the directions, gave others time to think and draw a diagram with labels.  The reader confirms/coaches/praises others’ work.  A new person chose a new card and the rounds continued until all cards had been used.  One thing I appreciated about this – another card asked students to draw a ray from E through M.  This allowed students to realize differences in very similar diagrams.

Again, when I returned to the classroom, students shared how this activity was different from anything they’d done before, saying it was both challenging but helpful in that it helped to clarify certain misconceptions they had; especially with labeling the diagrams.

I have learned the Kagan strategies help students develop and process concepts.  There are “game like” activities where students must find their match and discuss.  Visual, Auditory, Kinesthetic – something for everyone.  Its not an end all – be all resource.  But the amount of HW / practice is minimal when I’ve used these strategies correctly.  I am a firm believer that they help start a strong foundation to build upon.  Hey – if students are smiling and laughing while “doing definitions” – its gotta be good.

#75FACTS week 4 – #24 I used to think… but now I know…

This week we’ve been off from school for fall break – a road trip down south to visit Winter the Dolphin in Clearwater and a few days of warm sunshine on the beach has me somewhat re-energized.  I’ll be honest, my book is still at school.  The directions for this week were to use one of the FACTS #1-10 but I haven’t been in class to do this. (Sorry)  Before leaving school last week, I chose FACT #24 I used to think…, but now I know…  as a left-hand page assignment for my Geometry students’ INB.

#24 I used to think… Now, I know…

Eight Standards for Mathematical Practices

Practice 1 Make sense of problems and persevere in solving them.  This FACT allowed students to reflect on their learning, an opportunity to share what they used to think and what they now know after working with the concept.  Students responded to this prompt after exploring in small group investigations, pair-share processing, independent practice and finally whole class discussions/questions over Triangle Congruence.  I used to think… but now I know gave students the chance to make sense of the ideas they have been working with in class.

Facts and Teaching Goals

The goal of the lesson sequence was to allow students to recognize and determine which side-angle combos were appropriate and would guarantee triangle congruencies and finally applying those ideas with informal proofs.  By allowing them to respond in writing, I was made aware of their initial misconceptions – but also able to see they had in fact realized on their own how to prove trianlges congruent with a limited amount of given information.

I learned that the AAA and HL were the two students had struggled with most but they wrote about how the activities / discussion helped them realize specifically what was needed with each combo.  Another common error they pointed out in their reflections were that order of the included sides/angles did matter with situations of AAS and ASA.

Planning to Use and Implement Facts

One reason I chose this FACT was because I am looking to implement more literacy strategies into my instruction.  This FACT provided students with the opportunity to reflect on their learning in written format – a different type of processing that just talking/telling what they’ve learned.  By the time the prompt was given, students had explored in small groups, shared verbally with a partner, practiced individually.  The writing component seemed to complete the various types of literacy strategies.  By giving students a chance to respond to this prompt, I was able to see in-depth their full understanding of the intended concepts.

Small Steps

Were your students engaged?  Yes, I was very pleased observing students as they wrote their responses.  Most students took their time to share insightful reflections.  There were a few who tried to skim by with very vague responses, I gave them written feedback and asked they resubmit their responses.  Based on their new responses, I expect those few will give their best effort first time around next time given this prompt. 

Were you confident and excited about using the FACT?   I felt it was a good opporutnity to have students share their learning in writing.  I was not as excited about the FACT until after I actually started reading their responses…

How did use of the FACT affect the student-to-student or student-teacher dynamic?  Student to teacher – I felt they were honest in their responses – and most were insightful – I was encouraged to use this FACT again because it allowed me to see into their thinking.

Was the information gained from the FACT useful to you?  Yes,  however, I don’t think I will change my approach to the lesson in the future – students were able to adjust their thinking because of the lesson format.  The FACT let me see this as a successful sequence – what a good formative assessment strategy should do!

Would you have gotten the same information without using the FACT?  I’m not sure I would have given students the opportunity to reflect had I not used the FACT.

What added value did the FACT bring to teaching and learning? Based on student responses – I believe most appreciated having the opportunity to think about their learning – it “tied up loose ends” for them in the end.

Did using the FACT cause you to do something differently or think differently about teaching and learning?   It made me realize I’ve failed to provide students with good opportunities to refelct on their learning between lessons / practice and before “official assessment” occurs.  This is something I plan to implement more for my students!  It was quick, little/no prep and offered me the chance to really see what students thought about their learning.

Would you use this FACT again?  Yes.

Are there modifications you could make to this FACT to improve its usefulness?   I believe next time I will plan more time for students to share out their responses – maybe within a pair-share then as a whole class, possibly using the ‘Around the Clock’ appointment cards idea from Global Math Department.

Using Data from FACTs

Most students realized that AAA could only guarantee similarity amond the triangles.  There were several misunderstandings about HL I was not aware of until after I read student reflections.  I will be more puposeful in defining the included parts in the various combos, for example I shared examples with students and asked how AAS and ASA are alike / different because this was one that a few still had struggle with.  During this discussion / sharing – it was obvious some a-ha! moments occurred.

#MyFavFriday – Kagan Geometry

Last week I stood glancing at a shelf of books left behind by my colleague.  I’m not sure why I didn’t notice it before – but there on the middle shelf was a Kagan Geometry book.

Two days this week I’ve smiled at the end of the day and it felt great.  Becky Bride has compiled simple to implement, engaging activities.  I’ve read snippets about the Kagan books – but never really sat down to read/do any of the activities.

Boss-Secretary

One of the activities this week was using a strategy called Boss – Secretary.  Students work in pairs.  The boss tells the secretary what to write, explaining their reasoning for the steps/work.  IF the secretary sees the a mistake, he/she respectfully points out the mistake to the boss and praises her/him when they corrects their work.  If they work through it correctly, the secretary is asked to praise the boss, vice-versa.  After completing a problem, they switch roles.

The students have been funny with this simple, yet VERY effective activity.  Speaking of resumes, tough bosses, etc.  One asked today – do I really have to praise them when they do it correctly?  I’m really not a praise-y kind of person…  I said a high 5 would suffice.

Here is what I love about this – Students are talking/explaining their work so the secretary can do it.  Secretaries are listening, following directions, hopefully picking up on any mistakes.  I’ve heard multiple times – student exclaim – oh, now I get it.  They’ve all said they like this activity – its helped them really figure out “their thinking” – having to say what they’re doing – is difficult, and sometimes what they say/tell the secretary to write it not exactly what they meant.

This is a great formative assessment activity to observe / listen to students.  I’ve learned a lot about their thinking this week and I believe they have as well.  When students, notice plural, ask to do an activity again because it really helped them, well – isn’t that what we’re here to do?

INB LHP assignment

As a left-hand page assignment in the INBs, I asked them to pick one problem they completed as a secretary – and they had to write out the boss’s diaglogue to solve the problem.  (midsegments or isosceles triangles this week).

Another activity in the Kagan book was something I have completely taken for granted… Processing altitudes.  Students draw one of each type triangle, and are asked to draw an altitude. Pass their paper to the next person, who then draws another altitude, etc.   Even after a couple of examples / illustrated definition for reference…they still struggled with “drawing” it.  What?  If they cannot draw an altitude, how can they actually know what one is in order to use it to solve problems?

Applying Some Brain Research

Its been many, many years since I taught geometry – but I always remember students confusing medians, altitudes, perpendiuclar bisectors and angle bisectors of triangles.  I remember attending a David Sousa How the Brain Learns training several years back.  An example was shared how students often confuse concepts that are closely related because they are often times taught on the same day.  Concepts are stored by similarities, but are retreived by differences.  When we teach similar things on the same day, they are stored together, at the same time – when students are asked to retrieve that information, there’s not enough distinction between the two – therefore, they are often mixed-up, confused.  Hmmm.

So do I choose to teach each of these similar concepts (special lines/segments in triangles) on separate days – but is that even enough space between?  Should I skip a day between them?  Anyone with experience pacing it out this way – please share successes / need to make adjustments!  I really think this is an opportunity, by using Bride’s processing lessons – to make a difference, giving students the chance to build concrete understanding of these other-wise intertwined concepts.

If you’re not familar with the Kagan series – I think its definitely worth checking out.  There is very little prep time – other than working through the lessons yourself.  All blackline masters needed are included in the book!

I am soooooo excited about using more of these strategies in the weeks to come!  🙂

INBs – Graphing Stories LHP Assignment

Following @duinok’s lead, in her Favorite First Day of School post – I checked out Dan Meyer’s Graphing Stories to use as an intro to my first unit.  We viewed 8 of his videos – I asked students to sketch what they thought was the correct graph, then in a different color / style of line – I gave them time to sketch the “correct” graph.  We folded our Graphing Stories sheet and entered attached it to our INB on a RHP.  Within the discussions, we addressed choosing good intervals – a reminder of things our graphs should include from axes labels to titles.  It was a great review of good graphing techniques without actually “reviewing” – students were actually doing.

On the LHP, students were asked to write a brief reflection of their graphing experiences.  The second part to the assignment was one I held my breath on…  would they actually do it.

Create your own video / story.  Include a graph to model it.

The next day, I shared a scoring guide with them.  We talked about reasonable deadlines – I passed around a sheet and they chose their due dates.  With only a handful – who came to meet when they were not going to be able to meet their deadline, they were anxious to turn them in.

Several chose to write a story – but many of them made videos – I had a student running up the side of a house – sitting for a moment before jumping back to the ground (yes, it was interesting), another student running at different rates, someone tossing a ball back and forth in a store, a student doing a standing back tuck, a student swimming laps in a pool.  These are only a handful of videos I saw – but this was exactly what I wanted – students taking something of interest to them and connecting it to math.

My plan is to attach their graphs to the LHP.  I have smiled & laughed a lot while watching their videos.

INBs – A New Adventure – “Flip 4 Answers”

INBs – A New Adventure

All summer long I searched for ways to improve my literacy in math class – I learned so much chatting with my tweeps during our #lit4math book study.  It helped me redefine what literacy is / should be in math class – not just about reading.  And writing.  Not about creating something completely new – but improving what I already do to emphasize communication – discussing – giving students opportunities to make connections.

As I ran across various posts on the Interactive Notebooks – I knew this was something I wanted to do.  At first I had the wrong perception – thinking the interaction was between student and teacher – I struggled, wondering how in the world would I find the time to “grade” and evaluate that many notebooks efficicently and effectively and keep them in students’ hands for continuous learning???

After reading – mostly from @mgolding – I realized I had it all wrong.   The interaction was between the students and their own notebooks – to provide them with opportunities to engage with the information I gave them.  I was overly excited when I saw @mgolding would be presenting at #TMC12 – then crushed to find out my session was at the same time. boo. and I would miss out.

Listening to conversations that came out of her session and reading more once I returned home only confirmed my decision to move forward with INBs.  My science colleague had decided to pursue this learning tool as well – so grateful to have an in-person to collaborate/share ideas with too!

During the first Global Math Department meeting, she brought calm to me – answering so many of my questions in her session that night – thank you, thank you, thank you @mgolding!!!

I have begun my venture with INBs.  I feel a bit stronger in one class than the other – but I have been upfront with my students – this is a learning experience for me as well.

Some things I’ve quickly learned:

1. I MUST keep my TOC up to date – its easy to get off track if I don’t!
2. I MUST do the INB along with students – having completed the pages myself – knowing exactly what I want to go on them;
3. I MUST practice any foldables / graphic organizers to make sure they’ll fit/work.  I may have a great idea in my head – in theory anyway- but I have to put it to the paper to see if it will acutally do what I need it to do!
4. I MUST think about what I want to accomplish with the LHP assignments.  This is the one I tend to struggle with some…thankfully I have lunch with my colleague and bounce ideas to get feedback.

Flip 4 Answers

I plan to blog my list of RHP ideas later, but for today, I want to share an idea that came from my students.  Its similar to something I saw @mgolding share at #TMC12.  She had used post-its to cover hints/work/solution to an assignment she left with a substittue teacher.

When asked to create a practice quiz, one of my students used an index card to cover their work – thus “Flip for answer.”  When  I shared the student’s example, I never dreamed others would follow.  Yesterday during our first cumulative test – I oberved several others started playing off the concept.

   

As I look at the sample below, a CWP (color with purpose) would be VERY easy to assign…I think on Monday – that may be a good warm-up – turn to page 12 and CWP…  positive or negative or zero or undefined, even identifying which letters model parallel & perpendicular.

 

Another idea I think I’ll lean toward using for my LHP assignments – is the use of “Open Questions” – an idea I got during a book chat last fall from More Good Questions Small/Lin.  The second part of RHP 12 was an example of this…give coordinates of two points: with zero slope, undefined slope, positive slope, perpendicular to the slope in part c.

I believe the INBs require me to be more organized in my example choices.  It helps students be more focused / organized as well.  Looking through INBs yesterday – those who were having some trouble with their INBs / not completing their LHP assignments – seem to be the same (few) students who were struggling to make the connections I need them to.  This confirms to me the choices I am making – since most are finding great success.