Moving Away from the Gifted Math Label

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I’ve been paging through Jo Boaler’s Mathematical Mindsets lately.  I’m finding a few takeaways as I’ve been reading sections over the past few days.  My school has embraced some of the ideas in the book and we’ve been taking small steps each year.  One idea I found interesting relates to gifted students.  Page 94 discusses the “myth of mathematically gifted child.”  I feel like that statement is ripe with controversy as many are for or against the idea.  Most parents, teachers, and students have at some point in their life been told or shown their math identity.  Then that math identity may or may not be adopted and confirmed by the student. That communication can come from a teacher, parent, or somebody else.  Sometimes it comes from a single teacher or constant grades on assessments/assignments. Usually it’s developed early in life and continues with that individual.  People often can’t shake the generalization that they’re “good” or “terrible” at math.  I hear this at parent/teacher conferences, at school meetings and on EduTwitter.  Of course this is a generalization, but I find that this math stigma has lasting consequences.

I believe that the same stigma has the potential to occur with the “gifted” label.   I find that this can happen as early as the elementary level or even before then.  In an effort to address the needs of all students sometimes elementary schools group students by perceived math ability – emphasis on perceived. This often takes students and places them in different math classes during instructional blocks.  Students are moved to these different levels based on standardized test scores, classroom tests, teacher recommendations, or some other data that the team feels is necessary.  The groups can be fluid and change every unit, but sometimes they don’t. In some instances, school also have advanced math classes for students in upper elementary.  These classes might have a gifted label associated with them.   Although they’re labeled “gifted math” the roster doesn’t match the label.  The classroom rosters are often based on a criteria.  Sometimes the criteria is heavily weighted towards one single test-score cutoff, accounting for 40 or more percent.

Many questions come up regarding the actual percentage for students that are identified as gifted.  Most gifted specialists tend to agree that the amount is less than 10%.  Yet, these classes that are labeled as gifted tend to have 1/4 or even 1/3 of the total grade level population.  These classes may be accelerated, but not necessarily be meeting the needs of all the students that are identified.  Moreover, moving students to and from these classes can prove difficult as social/emotional consequences play out.  Often these classes aren’t as fluid and the roster doesn’t change as much since the students are accelerated from day one.

When shopping for school districts I sometimes find that parents are looking for whether schools have gifted classes for their child.  Schools might communicate on their website or through brochures that they have “gifted” classes, but in reality they’re accelerated subject-oriented classes.  Gifted students have academic and social/emotional needs and funding isn’t always available for this need.  It’s up to the local districts to create a system to meet the needs for these students.  I’m assuming positive intentions for the schools and districts in this scenario. In an effort to please the community and potential registrations, districts might used the term gifted to mean that the needs for high-achieveing students will be met.  Also, students that participate in these classes are artificially given the gifted label and they adopt the identity.  For some students they thrive in the class and it’s just what they need.  For others, it’s the opposite. Students struggle and feel contempt for math as they attempt to live up to the label of the class.  Having this happen at the elementary level sets the stage for a student’s math identity into middle school and beyond.

Labeling a class as gifted has consequences.  I want students to be able to create and maintain their own math identities.  Creating engaging math experiences for students with a heavy does of individual reflection can help students decide for themselves how they feel about math.  Regardless of their assigned math identity, I’m hoping my math class provides an appreciation, curiosity, and enthusiasm for mathematics.

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Class Survey Results – 2018

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School officially ended around a week ago and I’m starting to look back at the year.  During the last few days of school I gave students a survey.  I’ve used end-of-the-year surveys before, but this year I wanted to get the students’ perspectives on lesson structure and math interactions.

The reason I went in that direction because I noticed some trends while recording myself teaching. These recording were taking place because video recording were required for a certification that I’m pursuing. I went with the volume approach and decided to record three days a week for the first couple months of school so students would feel more comfortable around the camera.  At first, students would wave, make faces, dab and do all sorts of unrelated math actions around the camera.  That died down once students started to see that the camera wasn’t leaving.

After reviewing many different recordings (this took what seemed like forever), I started to notice trends related to how I was designing and implementing lessons and tasks.  This was a humbling experience.

I noticed that students were doing more independent work that I’d like to admit. There’s nothing wrong with independent work, but I wanted students to engage in math conversations with one another more frequently.  My lessons weren’t generally designed to have these math conversations occur regularly.  I used quite a bit of whole-group math conversations to spur mathematical thinking.  Although that seemed to be a good use of time, I noticed that not everyone was engaged.  There were students that hung out in the background and didn’t engage unless called upon.  I found through this experience that I was spending too much time on certain instructional elements and not enough on others.  I want the time that students spend in my classroom to be valuable and useful.  So I decided to start varying my strategies more often.  Short story: lesson design and pacing is undervalued.

So I made a few changes related to how often students work together.  The class created norms associated with how students should be working with one another.  I decided to increase that amount of “collaboration” so that each class had more of the time dedicated to working with other students.  I used visible-grouping strategies so students could see that groups were randomly chosen and all ideas are valued.  During this partner/group time students were completing math tasks, short-term assignments, long-term projects, Scholastic magazines, Desmos, Nearpod, and Kahoot! activities.   I noticed that students were having better math conversations at a more frequent pace.  While students were in groups I walked around and asked questions to help ignite or guide the discussion.  This slight shift seemed to play dividends as the year progressed.  Students became more confident with their math communication skills and the quality of those conversations increased over time.

Here are the survey results that came out during the first week of June.

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Not quite sure about the 2s and 3s.  I reviewed what the term “appropriate” meant and how it applied to their personal learning before students answered the question.   I think that some students prefer to work independently, while others thrive during group work.  I have to take this into consideration while reviewing these results.  Also, some students might be rating the actual work that is being done during these two scenarios.

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I was pleasantly surprised to see these results.  I tried to focus on giving students multiple ways to show their mathematical thinking.  Looking back, I used whole-group and independent math routines, projects, journal pages, individual tasks, math reflection journals, and  math class discussions throughout the year.  I was hoping to give students multiple opportunities to learn about math.  I believe students enjoyed some of the structures more than others, but having a variety of them gave them opportunities to see math from different perspectives.

The last survey question is below.

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This has been an issue that I’ve been tackling for years.  There are not simple answers for this. Students often view math as a speed game.  The quicker they are, the better.  I believe students see and are experiencing mixed messages when it comes to their math journey.  Fortunately, I get to loop with students and they get the message that math is a journey and there’ll be challenges and wins along the way.  Now what they do with that message differs.  When students perceive math as a journey, they develop a deeper understanding of the concepts that are introduced in class.  There’s also less anxiety related to speed and algorithms.  I’m going to keep this in mind while planning out what messages are being sent to students and the community next year.

An Elementary Desmos Journey

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During the past few months I’ve had a chance to explore Desmos.  I started seeing the platform on Twitter a while back through different educational chats.  It was prevalent in #msmathchat as well as in the EduTwitter math world.  I saw it across my screen, but didn’t really dig into how it could be used until NCTM.  During that time I attended a session titled “Which Comes First:  The Equation or the Functions?  Come Stack Cups and Use Demos to Find Out!” The session was presented by the University of California staff.

The session started out by having the participants sit in groups with a stack of styrofoam cups.  We were asked the question below.

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My table took the cups and started stacking them. They found the measurement of one of the cups and decided to use millimeters to be more accurate.  We came to a consensus and decided to extend the pattern and graph our pattern.  The presenters then asked us to head to a Desmos url where we could plug in our numbers.  The audience filled out this step-by-step sheet for the next 20-30 minutes.  Being a newbie to Desmos, I appreciated how the sheet guided us through the different components of Desmos and how it graphs the line as the numbers change.  The sheet also includes teacher directions that I found useful as I replicated this exact lesson a couple weeks after NCTM.

The second part of the session went in a different direction.

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Basically, we were asked to find out the option that would give us the most money during the next 14 months.  My table filled out this sheet and used this Desmos template to find a solution.  There was a lot of trial-and-error during this time and some perseverance, but it was a worthwhile journey.  Listening to others at my table was enlightening.  Hearing how other teachers, mostly at the middle and high school levels, gave me a different perspective.  Being able to find patterns and develop algebraic reasoning was at the forefront.  Using Desmos to create or check our predictions was helpful.  Moreover, I was able to learn more about the Desmos platform and how it could be used in my classroom.

Near the end of the session I started gathering all the links to save for later.  I started to think about how this could be used in my own classroom.  I began by using a few different tasks with my sixth grade standards.  The inequality activities were very helpful as I was becoming more familiar with the logistics of using Desmos in the classroom.  Desmos isn’t a math tool that’s used frequently in elementary schools.  The calculator included can be intimidating for elementary students as well the teachers.  Although, when my class first started using the platform my students were totally interested in wondering what all the symbols meant on the calculator.

During NCTM I was fortunate enough to come across Annie’s post on how to use Desmos in the elementary classroom.  I reviewed all of Annie’s examples and decided to graduate and move on to creating my own.  I started with copying a couple card sorts for a kindergarten and first grade group that I see four times a week.  The sort included having students put together base-ten blocks, written names, standard form, and expanded form statements.  The lesson went well and I had to intensely model how to login and ended up using a QR code for students to access the url on an iPad.

I then started getting used to how to create better questions using “what do you notice” or “what do you wonder” types of prompts.  About three weeks ago my third grade students needed to review polygons and relationships.  I decided to put together an original activity.

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I ended up making the shapes in Illustrator and inserted them into the activity.   I used this task with a third grade group of students that were working on fourth grade standards.  Students worked in pairs as I didn’t have enough Chromebooks and iPads for everyone that day.  I used the pacing function and made sure all the students were on the first slide.  I love that Desmos includes that function as many of my students want to speed through an activity.  Stopping with “pause” to review all the different responses was also helpful.  This helped encourage a class discussion.

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At first I used the “anonymize” option, but soon found that students wanted to be identified.  Students used a similar prompt with a trapezoid and triangle.  I then went over a few different vocabulary terms before heading to the next slide.

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Students checked off the criteria that matched the shape.  I then displayed the correct solution and this led to additional questions and conversations.  When creating this I decided to look back at some of the most engaging Demos activities that I’ve used.  Most of them ended with some type of card sort.  I decided to do the same.

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I decided to have a “doesn’t have a match” column to increase students thinking.  It took a while for students to complete this as certain criteria worked with only one shape while other statements didn’t match any.  When I first created this I noticed that some of the statements that were created matched multiple shapes.  Ooops.  It was fixed before I gave it to my third graders, but that could’ve caused a few issues.  After around 10 minutes we review the answers as a class.

Screen Shot 2018-06-06 at 8.21.45 AM.pngStudents self-checked their work to see how accurate they were.  Some students didn’t actually match the statements completely.  They brought the statement to the column, but didn’t attach them.  I should’ve explained how to do this before completing the activity.  This happened with around three students.   The next time we completed an Desmos activity those students were fine and attached the statements.  There’s a small learning curve with these types of activities and this was one of those moments.

My next step is to learn how about the computation layer and possibly how to use it more effectively with my K-3 students.  I think it’d be great to be able to rotate or drag a shape on a coordinate grid.  Students could then use a digital protractor to measure the internal and external angles.   I’m also looking at how to use polygraphs more effectively next year.  My students had a blast using them during the last week of school. Maybe I’ll learn about that during the summer.  I’m looking forward to using this more with my elementary students next school year.

Exploring Scale Factor

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My fifth grade students explored scale factor and dilations this week.  This was their last week of school and it was a great topic to study as they head off to middle school next year.  Some of the geometry that they’ll see in middle school involves this specific topic. The class started early in the week with a brief Kahoot! on similar figures and enlargements as well as reductions.  This was a bit challenging as some of the shapes were rotating and students had to identify a particular side.  After discussing words like dilation, scale, and factor, I gave students a multi-day project.  This project actually stems from one of Allison’s Tweets that I read earlier in the week.

At first glance the image in her Tweet made me laugh.  My second thought was … wait… this might work in my classroom. You know how a Tweet can spark additional ideas?  Yes.  That happened here.  I asked Allison about the project and she provided additional details about the pre-image.  So I put together a direction sheet and rubric.  I decided to have students use a 5 cm x 7 cm grid.  The class then discussed how enlarging the image would change the horizontal and vertical dimensions.  I decided to not have them reduce images since the pre-image was already so small to begin with.  We did discuss how me might need a magnifying class though.

Students went through their Math Magazine.  They looked for an image inside the magazine that they found interesting.  Some students found something immediately, while others took some time.  Students then traced over the 5 cm by 7cm card, used a straightedge to create grid lines, and then finally cut out the sheet.  Students then pick their scale factor page.  Just about everyone picked the 15 cm by 21 cm grid.

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Note to self:  In the future I need to have students randomly  (maybe with dice) pick a different scale factor page.  

Students were then off to work in creating the image.  Some students asked questions about whether they needed to enlarge everything on the image.  Yes.  Interesting … some students thought it was just the picture that was enlarged and not the text.  Everything in the gird was increased by the same factor.  Once that was covered students made steady gains for the next 20 minutes.  They started with pencil and then shaded in the rest with color.  Students were proud of what they accomplished during the first session and many wanted to finish them up at home.

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Students finished up their scale factor projects on Friday.  Since it was the last day of school I sent them home.  I gave each student a survey (this might be another post) before leaving and it was interesting that many commented about how they enjoyed learning about scale factor and ending the unit with a project like this.  Maybe it’s because it was the first thing in their mind, but I thought this type of project was worth the time and will help students moving forward as they discuss similar figures next year.

I’d like to find more time over the summer to create more memorable math activities similar to this. Kids can then hold onto these experiences past the last day of school and look back on them as they make connections next school year.

Math Group Tasks

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My students have around two and a half weeks of school left.  Standardized testing has finished up and I’m planning out the end of May.  Each one of my math classes will be taking one more unit assessment before the end of May.  My fourth grade class has been exploring measurement conversions, computation, and graphing.  For the past week my students have been participating in group work where they’re given a task, anchor chart paper, (sometimes I split one sheet in half or quarters) and Expo markers.  Students work together to create a plan, create visual models, and report out the results.  Below is the structure that I’ve been following.

First, the teacher reviews the task with the entire class.  Students ask questions and clarification is given.  The tasks are often open-ended and require additional thought and reasoning beyond a yes/no answer.  Usually students need to construct a plan and present the best option.

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The teacher reviews the expectations.  Often I have the students show the steps needed to solve the problem, create a visual model, create a number model, and present their solution to the class.

Students are then placed in groups randomly.  I’ve been using the randomizer script this year to create groups.  Using a visible random grouping strategy seems to help here.

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Students are assigned specific parts of the room to start the task.  Students are given some anchor chart paper and a bunch of markers.  Markers are used to put together a thorough response that’ll be shared with the class.  I set the Google countdown timer for 20-30 minutes and display it on the board.

I tend to listen to the discussion in each group and ask questions when needed.  I also try not to talk as much during this time.  Students create some type of rough draft on notebook paper before creating their chart.  When finished, the charts have visual models, number models, and are often messy.  I have no problem with that.  Math is and can be messy.  Students often scratch out number models that didn’t work or change units when needed.  They assign each other roles and determine the sequence for their presentation.  The presentations are no more than five minutes and includes a verbal explanation of how they found a solution.

 

 

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After the alarms sounds students then present their findings to the class.  Part of the criteria is that all students are required to help when presenting to their peers.  Students are then given time to ask questions.  Each group presents and I hang up the charts all over the room.  I then model and review the answer with the students.  By then the class is just about finished and we’re on to the next lesson.

I’m finding that these types of  group activities to be great opportunities for students.  The collaboration and conversations that occur during these events are sometimes undervalued.  Students seem to be empowered to find the solution for themselves.  I provide scaffolding when needed, but I tend to let the students struggle through and find the best solution.  I find students using math vocabulary and critical thinking about the answer as they create number models and visual representations.  I’m hoping to include more of these opportunities in my planning for next school year.

Connecting and Extending Math Strategies

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This post has been marinating for a few weeks. I started thinking about it before NCTM and afterwards found it just as valuable.  In Late April my third grade students were exploring fractions.  This third grade group had experiences putting together and taking apart fractions earlier in the year.  They also used number lines to multiply a unit fraction by a whole number.  Students have slowly and steadily improved their confidence in being able to use fractions when completing application problems.  That’s when I came across a problem that seemed to stretch the fraction strategies that they’ve been using.

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I displayed this problem on the whiteboard.  I gave the students some time to digest the task and asked them what their first step would be.  A few students wanted to dive right in and use repeated addition to find the solution.  They thought this might be the most efficient method and what’s available in their strategy toolbox.   Other students thought that there might be a better strategy.  One students had an idea to possibly use an area model for this problem.  Curious looks came across the classroom as this particular student spoke up a bit more.  She mentioned that using a partial-products strategy could be helpful in a situation like this.  Some students agreed, while others were shaking their heads in disagreement.  For the most part, the class is very familiar with partial-products so the area model wouldn’t be a stretch.  Students also had an understanding that multiplication might be one way to tackle this problem.

I gave students time to discuss in their groups the different ways to solve the problem.  There was a lot of disagreement happening during this time.  I wanted to stop the whole class because of the noise, but the math conversations were actually really good. Students were vocal about using an area model, while some students said that they could find the answer by using a traditional method.  More students seemed confused, as this isn’t really a method that students have used with decimals.  I gave the class time to independently try out their strategy and find a solution.  Students worked on this for around five minutes.  Pictures were drawn, number lines constructed, and repeated addition was in full swing.  Some students had a correct solution, but I didn’t give an affirmation (which is crazy tough not to do).  I asked students to show a number model and most generated (5 * $1.13) + $1.39 = ?  I displayed the different strategies on the document camera.  I then asked the class if it’d be possible to use fractions to find a solution for this?  Just then, a group of students raised their hands.  They said that the 1.13 could be represented by 1 13/100 while 1.39 is equivalent for 1 39/100.  A collective whispering sound came across the classroom.  Then a bunch of hands came up from all over the room.  The class went through this strategy to find a solution.  Our number model changed a bit.

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The class then took the number model and used an area model.

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The students then added the 1  39/100 to the 5 65/100 to get 6  104/100.    Students then said that the answer is 7 and 4 hundredths.  Another students chimed in that the answer can’t just be written as a decimal and that it’s $7.04.  Students were satisfied with this method and asked if they could use it in the future.  I asked them why not?  A couple students said that they didn’t see fractions in the problem.  They saw decimals and that automatically changed the approach to a more “decimal-friendly” computation strategy. A few students replied that they didn’t think they could use it because it wasn’t taught.   Ouch.

After the class I pondered that response and thought about what is explicitly taught and what we expect students to explore and construct on their own.  Do we truly give students opportunities to discover mathematics in a way in which they can bridge strategies?  Not one student verbally called out to using a decimal to fraction conversion for this problem.  This has me wondering how explicit teachers are in empowering students to bridge strategies and concepts.  Are they given that freedom?  For example, are fraction strategies only used when students see fractions?  Is the substitution method only used when students see 1-step equations?   I believe it depends on the situation and background information also plays a role here. Having a deeper conceptual understanding of fractions and decimals might have led students to look at how the last strategy might be helpful.  Also, while an area model might be helpful now, the strategy will most likely change as a student’s math journey progresses.  Multiple strategies are beneficial for any learner, but this lesson has me asking more questions.  It was a terrific lesson and I know students were making connections.  That’s an #EduWin in my book. Next week the third grade class will be investigating angles.

Side note:  I finally submitted by components for board certification this week.  It’s a huge relief to send the files off, but now it’s a waiting game as I won’t get the scores back until December.

NCTM Reflection

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NCTM 2018 finished up yesterday.  It was a whirlwind of experiences and it has taken a while, but I feel like I’m caught up on my sleep.  Overall, it was a memorable time in DC and the weather was terrific for the most part.   In this post I’m going to put together a couple brief takeaways during each day.  Emphasis on brief, as there’s so much that happened over the past few days.

My flight arrived late Wednesday afternoon. Later that night I was fortunate enough to attend the NCTM game night.  Check out the tag for a few Tweets.  I was a bit reluctant as I was going solo, but decided to try it out anyways.  Glad I went.  I think teachers need this type of time to meet each other and build community.  I found the games intriguing and the conversations even better. Kudos to the volunteers and designers of the game night. Everyone that I encountered was welcoming and inviting. I love the idea of the Pac-Man (@ericholscher ‘s idea) tables.  This is something I’d like to bring back to my own school’s staff meetings. It was here that I met many people face-to-face that I’ve known and followed online for years.  It was great to connect and engage in conversations that extend beyond Tweets and direct messages.  There are too many to mention in this post, but it was a pleasure to meet so many inspirational people in person.

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Thursday was really the first day of the conference.  My hotel was about five blocks away from the conference and it was a great walk each morning.  Friday was the exception as it was raining.  I went to visit a few different sessions related to integrating math practices and technology tools.  Kudos to the presenters that also included short-links so that I can view the presentations later.  Annie shared her presentation on math tools and strategies.  I went out to the gorgeous city center for lunch.  Came back and learned about integers and the orb strategy from a group of three teachers.  By this time I had a decent understanding of where the rooms were located and how to navigate from one part of the conference to the other.  I dropped by the #MTBOS (I forgot to pack my #mtbos shirt from a few years back) booth multiple times throughout the day.  I was also able to meet my #msmathchat pals Casey and Bryan face to face.  Both are passionate educators and it was awesome to meet them in person.

Friday started off with a lot of rain.  I walked/ran to the conference center.  I attended a session on how to integrate mathematical practices better.  I also was fortunate enough to learn about Bongard problems – a new concept to me.

I didn’t get it as first, but was in rhythm after a couple practice tries.  I’m still looking for ways to integrate this into my math classes.  My presentation was at 11:30 and seemed to go well.  My only wish was that I had an extra 10-15 minutes of time.   I guess time management plays a role here.  Maybe I should apply for a full session in San Diego next year?  You can find the slides here.  During the afternoon I was able to learn more about math practices and attended a middle school Desmos session on equations and paper cups.  It was here that I actually learned how to use Desmos for the first time.  I’ve tinkered a bit with it this year and have used it for lessons, but found application potential at this session.  I closed out the day with a session on a partnership between the University of Delaware and a geometry lesson study.  It was interesting to hear how the university partnered with the local school districts in designing a lesson study.  Afterwards, I went out to meet some friends for dinner.

 

It was a good trip and worth the sub plans.  Excellent to meet many of my pln in person.  These people are truly changing math classrooms for the better.  There are still some people that I wanted to meet, but didn’t get an opportunity to do so.  Time was limited and so were the sessions.  Maybe next time. The people at this conference are inspiring.  Many of the presenters are still in the classroom or working with schools and I’m encouraged to see the work that they’re accomplishing and willing to share with the math community.  I’m looking forward to finishing off the school year strong.

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