Reading in Math Class

For years, I have tried to share a related article as appropriate with my classes.  Often times it was a news article related to a data collection lab.  However, I feel more impact for reading in math class is from informational reading with graphs/data related pieces. 

One day each week, I plan to use a “Laker Literacy” article (named penned by data team in school wide iniative last spring) or  Stat Rat (Graph or Data related piece).

Today, my Algebra 2s read this article from a Quality Core unit on Patterns and Sequences. 

I asked students to number the paragraphs 1-6.  After time to read, they were instructed NOT to answer the questions on the back, but rather as they read each question, make a note of which paragraph from the article could be used in helping them respond to that question.

We will be using the article and questions next class. 

Math and Kentucky Program Reviews (Art, Writing, PLCS)

In Kentucky, we have Program Reviews for Arts/Humanities,  Writing a nd Practical Living / Career Studies (PLCS).  My interpretation… the idea is to ensure all teachers across disciplines are integrating concepts, strategies into their classrooms on a regular basis in efforts to make connections with student interests and enhance their learning experiences. 

I have used many routines from Making Thinking Visible over the past two years to improve writing-to-learn and writing-to-demonstrate learning opportunities for students.  I feel they will tell you our reflection and analysis of work through writing and discussion makes their learning stick more.

As I plan to revisit these routines with @druinok and some other stats peeps, I was exploring this and ran across Artful Thinking.

Definitely check out the Thinking Routines and Curriculum Connections links for some insightful resources that can help other content areas find purposeful, quality connections to art for their courses. 

Finally, a tweet from @approx_normal the other morning provided these awesome classroom tasks focusing on Career Technical Education.

Hope this provides some helpful information for teachers looking to make connections in the areas of Arts, PLCS and useful thinking routines to help with Writing implementation. 

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

Representing Polynomials FAL & Open Card Sorts

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:

 

Following with whiteboards / sharing for this slide from FAL:  

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

 

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.

 

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.

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.

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.

 

 

Station Activities – Geometry first attempt

Geometry Station Activities by Walch

With little time to plan, I jumped right in to a set of station activities for my semester – block Geometry classes!

My first run was with the parallel lines / transversals stations (I know its a bit out of order, but it will be okay!).

I instructed students to take out one sheet of graph paper and we folded them in half, labeling Station 1 & 2 sections on one side and Station 3 & 4 sections on the back side.   Students were in groups of 3 or 4.  I know the big idea is to move around to the various stations – but my new room is too small :(.  Rather than running a ton of copies, I made 3 complete sets of the statin instructions and placed them into page protectors.  Students completed their work on the graph paper.  When complete, they would exchange their station instructions for another station set located in front of the room.  This way students do not have to wait on other groups to complete before moving on.

Using a different color for each station, I highlighted the station # and any Words Worth Knowing (thanks everybody is a genius blog!).  Two of the lessons called for spaghetti, I used toothpicks.  Each student will also need protractors.  The stations are not dependent on one another, so order of completion did not matter.

The discussions were great because students’ angle measures were not equal to their group members’ but the same “patterns” occurred.  I probably like the discussion questions component of the activities best.  Each student responds to a given set of questions in writing.  Then they must pair up with someone who was not in their original group to discuss their responses.  Simple misconceptions are quickly cleared up during this time.

The layout of this lesson allows students to talk about and look for patterns during the station groups.  They process their new information as they write responses and allowed to share verbally again with a partner.  Finally, as a whole class we debrief the entire lesson(s).   This format really supports the literacy strategies discussed this summer in our twitter book chat #lit4math.

I like that no prior knowledge was required for students to successfully learn about transversals and the special angle relationships formed when parallel lines are present.

I have compared the listed CCSS for Geometry Station Activities to the suggested Geometry standards of Appendix A and this book addressed over 75% of those standards.  Only the measurement and any probability suggested for Geometry are not included in this book.  There are 16 station sets and I have my students for 18 weeks…my thought is to use at least one per week, as appropriate…  I’ll share more as we get in to the semester.  But for this first run, I say 2 thumbs up.

*Station 4 deals with corresponding angles – and I reworded Question #1, because it was misleading.  Anytime you use investigations, you should definitely go through the entire lesson / activity before presenting it to your students.  (duh?) I see this happen too often, teachers just pull out an activity and pass out to students with little/no knowledge of what students will expect / questions they will ask.  The book also gives a list of possible student misconceptions to watch for.

If your students are not used to this layout of lesson – it may take a little more time to get them through it.  Once students got a feel for it, the last stations went more smoothly and quickly.

I hope to hear more from others who are using station style lessons. @tbanks06 also shared some experiences with stations for #myfavfriday and said its the best $40 you’ll spend this year!  Shop around – I found all 3 of my station books for under $85 total.

Got to give a little shout out to HoppeNinjaMath – welcome her to math teacher blogging!

Station Activities for Algebra I

I began working on creating cards for the activities needed in this book:.  I typed the “index cards” needed for several of the lessons.  Feel free to borrow/tweak and use in your classroom – and share – please, just don’t sell “my cards.”  You can find the card sets I completed here.

I am now teaching Algebra 2 and Geometry, so the Algebra I project is not going to get completed anytime soon.  Sorry.

Literacy Strategies for Improving Mathematics Instruction

Wrapped up our twitter book chat this week over

#lit4math – Literacy Strategies for Improving Mathematics Instruction by Joan M. Kenney, Euthecia Hancewic, Loretta Heuer .

You can read (here) how I am not a fan of writing and words.  Literacy – communication – its all the same, in my opinion;  You can read, write, speak – but its all to share/get information, right?  I do realize the importance of providing students with strategies that will help them succeed, to give them opportunities to write and talk about their thinking can be a key component in their learning to help expand their understanding of certain concepts.  I look at this chance to learn about literacy in math as a way I can learn with my students – to be open that words are my weakness – but by facing my fear – something I struggle with – I can help them realize words are not the enemy either.  I am able to help them learn this “new language” called math and share ways of conquering it !

Though this book did not end as strongly and wow! as it began, it was worth my time.  Chapter 1 really pulled me in, causing me to think about my classroom, questioning some of my strategies and left me craving more!  It showed me how students – who are not as math-minded – can struggle because they view concepts differently.  Chapters 2 and 3 – gave me tools / suggestions of ways I could provide students with opportunities to share – ways I could become more aware of their thinking – and prepare for their struggles.  Through our chats, I was able reflect how I could improve things I am currently doing – but also looking at new ways of viewing mathematical text and ideas (literacy really isn’t a 4-letter word).

The remainder of the book, well, I was diasppointed – but would still recommend at least a skim – because there are some key ideas – but mostly, some great articles/research mentioned you may wish to take a look at as well.

I’ve linked to catalog from Storify of our Twitter Chats – again, some good thoughts – good articles and links.  Also, take a look here, Teaching Statistics Blog offers some reflection with posts from reading the book in 2010.

June 11 – Chapter 1 Mathematics as a Language

June 14 – Chapter 2 Reading in the Mathematics Classroom

June 18 – Chapter 3 Writing in the Mathematics Classrom

June 21 – Chapter 4 Graphic Representation in the Mathematics Classroom

June 25 – Chapter 5 Discourse in Mathematics Classroom

June 28 – Chapter 6 Creating Mathematical Metis

All in all – it really boils down to becoming aware of those struggles students will encounter and being ready to help them bridge past that struggle.  Notice I didn’t say be the bridge – productive struggle is a good thing.  We must give them opportunities to read, write and share – expanding their understanding by listening to other learners.  When they write about their thinking – cognitive demand is much higher.  We must listen to their conversations – not always answering their questions, but providing them with questions that will move their thinking deeper.  When they talk, discuss, even argue over a solution – they have greater opportunities to build connections as opposed to a sit-n-get teacher centered classroom.

My summary:

 ‏@pamjwilson to get students actively engaged, the tchr must 1st be actively engaged- listen, question, be less helpful ‪#lit4math‬

What is Volume? A Literacy Question…

Driving down the road yesterday, my 8yo was looking at the cover of a dvd and asked “Mom, what does ‘Volume 3’ mean?”

As usual, I asked, “What do you think Volume 3 means?”

“Well, I guess it the means the sound is set on Volume 3.”

Hmm.  We went on to discuss different meanings and determined this one was because the dvd was part of a larger set.

 

These past few weeks, I’ve been thinking a lot about writing and communicating in math class.  Even with our first chat on Twitter #lit4math over Literacy Strategies to Improve Mathematical Instruction (Kenney, et al) – I was reminded there were many words students struggled with due to multiple meanings; however, this question from my 8yo really drove the point home.

Let’s see…volume – in this situation it meant part of a larger set;  my 8yo reminded me, its the level of sound we turn up or down to hear better; but in my mind all I think of is how much a container/object can hold, well, because I’m the math teacher.

This conversation reminded me of the ELL student in #lit4math who thought “whole numbers” were numbers which contained “holes” when written, for example 6, 8, 9, 10.  Since 6 had one hole, 6 would be odd; likewise, 8 has 2 holes, so it would be even.  We can learn so much about students thoughts and understanding, if we will just take the time to talk/communicate with them about their learning, misconceptions and ideas.

So, back to Volume…

Merriam-Webster :  noun

series of printed sheets bound typically in book form; series of issues of a periodical; a scroll; the amount of space occupied by a three-dimensional object as measured in cubic units; cubic capacity; a considerable quantity; degree of loudness or intensity of a sound

Middle English, from Anglo-French, from Latin, volume roll, scroll from volvere to roll

I began my search for the history of Volume with a resource shared during our first book #lit4math chat jeff560.tripod.com/mathword… is an excellent site for learning about the origins of math words. Dave Radcliffe

By the way, he also reminded me that entomology was the study of insects, and I was likely looking for etymology (Thanks Dave!)

 

I found nothing on volume in a quick search of this resource, so I moved on to searching online for etymology of volume – do I settle that it has to do with the size of a book or scroll? Hmm.

Still I am not satisfied.  It looks as if providing quality literacy strategies will be an on-going event, learning with students as I go… taking time to develop understanding and address “new-to-students” meanings of words and concepts…in an effort to impact their learning.

Research shared in Marzano and Pickering’s Building Academic Vocabulary (BAV) makes a strong argument for having a systematic approach to teaching academic terms.  BAV states this is “one of the most crucial services teachers can provide, particularly for students who do not come from academically advantaged backgrounds.”

More than ever, I realize how important it is to take the time to plan and develop strategies for literacy in order to provide the highest quality and most effective learning experiences my students deserve.

I look forward to learning and sharing more as the summer progresses on this topic.