Wednesday, January 3, 2018

Opening Pandora’s Trig Box – Unit Circle Socratic Seminar

This was my most exciting project this semester.  I have implemented both formal and informal Socratic Seminars in the past, but this time I decided to go out on a limb by using it to introduce a new concept.  In fact, I used it to introduce one of the most important concepts in trigonometry – the Unit Circle.

One of my past mentors in college always said I was a “take the bull by the horns” type of person, and that personality in my surely came through on this one.  For weeks before I oscillated between the “are you nuts Tara?” and the “I am so excited about this” thoughts on a daily basis; during the school day sometimes on an hourly basis.

I have taught the Unit Circle at least a couple of times before, but it was always flat, and the beauty of this concept deserved much more.  This time around, I was determined to be as creative and student-driven with it as I could be.  It was a huge risk, I was playing with their trig foundation, but I was committed to giving them an experience learning it that was fun, exploratory, and long lasting.  It worked, it was an amazing experience for me to create this activity and then watch as they put smaller ideas together with oohs and aahs throughout the seminar; to watch them derive and form the single most important concept for use and application in trigonometry.  Did my colleagues raise their eyebrows at me when I talked about what I was going to do – of course!  Just as they had done when I began Socratic Seminars at my old school.   That just fueled my intentions as always!

The Journey to Pandora’s Box

I hyped it up – of course I did, I am a math nut that way.  I kept telling them we would be opening Pandora’s trig box for key concepts that contribute to a very important trig foundation.  They kept arguing that Pandora’s box ended up containing evil.  I got cheesy with it telling them that some evil is necessary and can transition to beauty if you can get past the uncomfortable mystery of it.  Some students had friends in Accelerated Pre-Calculus, one level above honors pre-calculus, and they had already heard about the Unit Circle and that it was painful.  They would ask when we were going to learn it, and I told them they were going to discover it and develop it themselves.  They looked at me in shock, I told them I wanted them to find the beauty and patterns in it, so their experience was not painful.  I told them to trust me, and that they did.

The ideas were swimming around in my head, I knew I wanted them to take parts and put them together like a puzzle.  I started developing the activities I would give them to draw out their knowledge and start making connections.  The following are pictures and explanations of each.

“Angle Order” – This is where I integrated the ideas behind Clothesline math, but without the string.  They way in which they received the assignment made it too hard to get a string with cards going – you will see as this story develops.  Still, I had them order radian measure from least to greatest in and around the 0˚, 90˚, 180˚, and 360˚ values, which were the only angles they knew the radian measures to at this point without conversion.  I did not tell them to place the radian angles they already knew, the intent was for them to use that as a basis on their own.  I would later find out that many did just that, and that certainly was evident in the Socratic discussion. 

“Radian Reference Angles” – This had 2 intentions, to bring back the idea of reference angles and give more practice with them, and then also to allow students a visual follow-up to the order of radian angles around the unit circle.  I could not even hazard a proper estimate of how many times the term “reference angle” was used in Socratic discussion when it had been a less than popular topic when introduced before radians and the unit circle.

A Scattering of Previous Ideas – These 4 cards contained ideas that would enhance work with reference angles, and “terminal points” was an early on concept that I had not given much air time to in the days leading up to the seminar.  It was the concept they needed for the coordinate values on the circle, but that was for them to put together.   They did just that during the seminar, but probably not with the prep assignment when prompted.  That was OK, that was just what I wanted them to do – define it in their own words, and then apply it to break away into unit circle values.

Which One Does Not Belong? – I could not resist!  There is a beautiful visual pattern that develops as the Unit Circle develops, and I wanted that to be somewhere in their minds before the seminar without knowing why it was in their minds.  That was the discussion point right before the seminar formally started – there were many different choices among them for which one did not belong to the subject matter at hand, and they were all arguing their points.  This is the entire nature of what “Which One Does Not Belong” is intended for.  There are no wrong answers rather an answer that may “fit” better in a specific situation or parameter.  This was one of the most fun pieces I put into the mix!

“What is the Connection Here?” – We had reviewed their past right triangle trigonometry in the week before the seminar.  We had also talked about quadrants and the positivity and negativity of x and y in the coordinate plane as well as axes coordinate points.  They had not seen the circle on the plane yet in our discussions, and I had not used a hypotenuse of 1 intentionally in the right triangle trig review.  We had discussed and used Pythagorean theorem both in exact and approximate values, used the trig ratios of sine, cosine, and tangent only in exact values, but not with hypotenuse 1.  I saved that for this connection; I wanted to see if they could start to integrate the idea of hypotenuse of 1 can connect into circle of radius 1.

Picking their Brains:   “Points to Ponder” -  This was a guide sheet to go along with the other activities I developed and prompt thought and connections of those ideas.  I reinforced A LOT when they were given this activity that I wanted them to explore with their thoughts and own individual answers and that at this stage of the game, there were no wrong answers; only their own understanding was required and also sacred.

The files for the above activities can be downloaded here:  Pandora's Trig Box Activities

The Implementation of and Opening Pandora’s Box.

First of all, I wanted their pre-seminar assignment of my activities to be different than they had ever experienced in math.  I also wanted it to be distributed in a way that reflected the suspense of the Pandora concept.  For a few weeks, I had my eye on the treasure box in one of our workroom suites that was covered in old-world maps.  I did not have to convince the secretary in that suite very much to let me borrow it – she said I could have it.  Although I told her I would return it, it still sits in my room by my desk because the whole project was a true treasure in our classroom, and I am not ready to let go of it yet!

The two weeks before the seminar, I began prepping the activities.  I copied them onto color copy paper, and double copied many of them onto on side to make the papers they would work with smaller pieces of paper.  I then folded each activity individually in different ways, the “Which One Does Not Belong” activity was in the form of a scroll, and a couple of the activities were folded into the ways we used to fold notes that we passed back in forth in junior high back in my day.  The funny thing with that was they thought it was some sort of exquisite origami paper folding art rather than what I knew it to be.  Perhaps it was, the generational gap between me and them in the age of cell phones for communication kept me from realizing that they would not see it the same way as my memories did.  Such a cool and unexpected element of the experience!

I placed each folded activity into a sandwich bag, and I then placed all the bags (90 in all) into the treasure chest I scored from the copy room.  Was that a lot of work-yes it was.  Was it worth it – a million times over when watching their reactions to it.  I brought the treasure chest to school, and the seminar was scheduled for Monday, October 16th, so I gave them their seminar prep-work homework in sandwich bags on the Friday before.

Seminar prep - homework bags for students and tucking them into Pandora's Trig Box:

I hyped this up too – I let each class pick the person who would open Pandora’s box.  Those students played into it well creeping up to the box and taking a bag.  Then all students were curious as to what in the world was in each bag, so mayhem to get their own bag ensued.  It was a lot of fun watching them open their bags and unfold the activities and start talking about the things they were going to have to do.  The “Which One Does Not Belong” activity was the instant hit.  I encouraged them strongly to work on that part individually first and come together Monday with their thoughts.  I guarantee they had never received a “bag of homework” in math before, and they were intrigued.   My kids are great, and I knew this was a solid truth this day when the main question they asked in amazement was “didn’t this take you forever to do?” or “how long did this take you to do?”.   I told them that yes it had taken a lot of time, but it was every bit worth it to me for them to learn what was ahead and I meant that with all my heart.  This was also they day I would realize in reflection later that we formed a strong, trusting bond as students and teacher.

Students opening Pandora's Trig Box and finding the clues for the seminar prep work:

The Unit Circle Seminar

The day of the seminar arrived.  I had assigned roles to all students; they did not know before that day if they would be in the discussion circle, the writeboard writer's circle, or the observe and record circle.  Because they participate in Socratic Seminars in their ELA and Social Studies courses, they knew what each role entailed, and I also provided a 10-minute Q & A session on the structure of a math Socratic the previous Friday before opening Pandora’s Box.   I assigned students into roles based of data that I had collected from the previous quiz, and characteristics in my students that I had discovered thus far into the year. 

Classroom set -up for seminar:

Data from Previous Quiz:  I gave a Likert Scale response question on the previous quiz (not for points on the quiz), which asked them to rate from 1 – 5 any previous knowledge they had of the unit circle.  The leaders of the discussion group were chosen from those reporting a 5 rating on the question, and the discussion and writing groups were chosen in a mixture of a few 3-4 ratings and more 1-2 ratings.  I wanted some knowledge to be in each group to keep discussion transitioning, but I also wanted a fair number of students who were in pure discovery and connection mode.

Student Characteristics:   I put students who were shyer in the writer’s circle, so they could still contribute their ideas and knowledge via whiteboard, and so they would not be so stressed by the pressure of speaking in the spotlight of the discussion group.  As with any classroom, there are very eager and verbal students that like to answer all the questions if they could, and for this activity, they were assigned the role of observe and record.  It is true that the leader of the discussion group has the role of managing the discussion to avoid participants monopolizing the discussion, but I did not want to place that stress on them the first time we had a seminar in our classroom.  It is not that I do not value the eager students’ knowledge, but I knew that they would share their knowledge in their ,  and know how to effectively transcribe the contributions of others.

Resources used during the seminar were as follows:
  • A projected image of a Unit Circle Template on the whiteboard   
  • Each student had a paper copy of the template to reference at their desks and their bag of seminar-prep homework; nothing else was allowed on their desks.
  • The discussion group (inner circle) and whiteboard writing group (2nd-ring circle) were not allowed pencils that could stifle group discussion.
  • The third ring circle was comprised of students assigned to observe and record the contributions of the discussion group.  Each member of this circle was given a blank unit circle template, allowed to use pencils or pens, and was assigned one member of the discussion group to follow.
  • My role was to record the contributions of the whiteboard writing circle, and provide prompts if needed.

A more detailed explanation of each of the roles in the seminar along with the evaluation tools I used can be found on a previous blog I wrote:   Socratic Seminars in the Math Classroom - Why Not?


As I stated in the beginning of this blog, I was so nervous to try this and knew there was a risk of it not serving the purpose intended.  I opened the seminar by projecting a blank unit circle template onto the white board and saying  “There are 64 Important Facts to Know Within this Image, You May Now Begin the Journey to Finding Them!”

My fears were quickly alleviated within the first few minutes of the first seminar and transformed into amazement.  The interpretations of the prep-work I gave them came flowing out of them as they worked to put all the elements of the unit circle together.  There were two students assigned to scribe the information onto a unit circle template, and they found challenge if keeping up with scribing the flow of ideas coming out of discussion.  There was so much use and proficientcy of vocabulary that I did not realize they had in their discussions.  Below are a few of my favorite quotes from students:

  •  “What are we supposed to fill in for the coordinate points?  Oh wait, are those the terminal points?”
  • “I think we get the terminal points by referencing the angles to form triangles and find the sides”
  • “I thought ordering the angles in radians was easy  because I know that sixths are smaller than fourths and fourths are smaller than thirds.”  (This was my all-time favorite contribution – evidence of pure number talk!)
  • “I think this one does not belong because it has pi only in the circle, and everything else we learned before with degrees”
  • “Does this mean the x-value is always the adjacent side and the y-value is always the opposite side?”
  • “How does tangent tie into this – is it x over y?”
  •  “Oh wait – it is this one that does not belong here because it is more complex and what we had to figure out”

I know there are many more, but I just cannot remember them all, nor could I get them all down on paper as I observed and recorded the process.   The worry I had about executing this topic in a Socratic Seminar was quickly canceled out by the amazing discovery and connection of previous ideas they had and collective efforts they displayed in putting together the puzzle that is the Unit Circle.  Each of the three periods of students had their own way of bringing the development of the Unit Circle to completion.   One of the classes experienced more roadblocks than others needing more prompting from me, but my prompts were only in the form of further questions.  In the end, this class overcame the roadblocks and got everything tied together minus the idea of tangent values.  Though they did not take it as far as the other two classes, the ability to push through the challenge and uncomfortable spots gives them a different type of strength with just as much value. 
Here is a quick video recording of the start of one of the seminars.  The teacher I am mentoring recorded the whole thing, but it gets cut down in the link-up:

Seminar Video:

The message I wish to share in all of this is to run with ideas you are truly passionate about no matter how risky they may seem; the passion will carry you through it and help you to make it work.  Do not worry about raised eyebrows and those who question rather, tell them you will let them know.  If you truly believe in it, you will develop an unforgettable experience for your students with sustainable learning that you will then be able to share with others!

TMC 2017 – Reflections

For me, I went straight into pre-planning the day after Twitter Math Camp 2017.  Though I started writing this piece about a week after school started, I am just now finding the kind of rest and relaxation to give it proper air time and reflection.   I would have liked a few days or so to digest all the awesome ideas I got at TMC17 before returning to school, but the energy I had from it was a huge plus for enthusiasm going into a new school year.   Now four months later, I am embracing the chance to talk about my conference experience in an applied way.

Looking Back to the Conference Itself with a Quick Glance/Reflection

This was my first year attending Twitter Math Camp, and a lucky thing was that I live in the Atlanta area, so I did not have to travel out of state to go.  I did however, avoid the Atlanta commute by staying at the TMC17 designated hotel.  The benefit of that far outweighed just saving commute time – it allowed for so much more opportunity to meet new people, socialize, and enjoy meals and evening activities with new friends.

I had put in a proposal to do a morning session on Socratic Seminars.  I only had 2 people come to the session on Thursday, so I went ahead and closed it because just needed a few more than that for it to be meaningful, and I did not want them to miss out on something else that could be really influential to their craft by staying.  The good thing that did come out of Friday morning after I closed the session was meeting and talking with Daniel Forrester, who was the point person from Holy Innocents for TMC17.   I did share my materials with him and talk about the Socratic seminars and how they worked.  We are both teaching Pre-calculus this year, so we extended our visit to swapping ideas for that course.  We also exchanged contact email for sharing throughout the year.  He is an amazing person and I am sure an awesome teacher.  Had I not needed technical help for my session, and then not had my session, this conversation never would have ensued- one of many great things!

I was able to meet some great people and go to some amazing afternoon sessions including Glenn Waddell’s session on math concepts that carry through K-12 math courses and how to enhance them at every level, Chase Orton’s session on calculus concepts for early ages, Anna Vance’s “Make it Stick” session, and I was lucky enough to get in on an added “Clothesline Math” session by Chris Shore.  All of this great stuff was in addition to the fantastic keynote speakers each day and the “Favorite Things” talks at lunch each day.

How TMC17 Enhanced My Classroom Fall Semester 2017

One great thing that happened at TMC17 was seeing my student teacher supervisor Christopher Danielson again.  I had ordered his turtle and pentagonal tiles, and he was kind enough to bring them to the conference for me rather than ship them out.  It gave us a chance to catch up and he shared with me his latest passion of working with “Math on a Stick” at the Minnesota state fair as well as his hopes to expand on it however he can.  Christopher has always been a passionate educator and champion for conceptual understanding, and I love that he has taken this to the “ground up” approach with #tmwyk and tactile ways of letting people of all ages engage in “Math Play”.    The tiles he delivered were the first step I took in creating a math play table in my classroom.   The kids absolutely love it, and I have added to it as the semester progressed.   My husband was not sure how this would work in a high school classroom, but I was proud to report back with pictures of football players “at play” on the table.  He was flabbergasted, but intrigued.  He became a believer in it as he progressed through his curriculum and training for a second career math teaching degree.  He wants to teach geometry, so I know when the time comes, I will have to make sure he does not start stealing my tiles for his classroom!  Though it was my play table, my husband was yet another pre-service teacher influenced by the ideas and skills, and knowledge of Christopher Danielson
Below are some pictures of the play table this semester:  Thanks Christopher!

I absolutely loved Glenn Waddell Jr’s session:  “Bridging Elementary Skills & Concepts to High School & Beyond”.  In this session, he highlighted fraction work/exposure from early elementary on through the bridging ideas of intermediate and middle school concepts of common factors and multiples that lead to fractions in the form of rational expressions in high school algebra.  This year I am teaching Honors Pre-Calculus, and in the beginning of the year our pre-requisite work involved review of the operations of rational expressions.  I took extra time and used Glenn’s approach and bridging of elementary, intermediate, and middle grades concepts to build for a deeper understanding of rational expression work for review.  Since the application of these operations would manifest itself in operations for verifying trig identities later in the semester, I knew it was a now or never thing to get the conceptual understanding as solidified as possible.  Wow did it work well!  I have never seen students at this level master this concept so well and with such depth; especially the addition/subtraction work rational expressions.  Further, their strength in mastery of that operation carried through very well during trig identity proofs 3 months later.   His ideas and work with connecting concepts across the grades is a winning addition to our craft-Thank you Glenn!

Our classroom play table in various stages this semester:

Elissa Miller shared a classroom management practice she uses for a “My Favorites” presentation.  I believe she calls it “Two Nice Things”.   The ideas is that she uses this when kids say unkind things to their peers in her classroom.  For every unkind thing a student says towards another, she then expects them to share two nice things about that student.  This really resonated with me as a great way to turn negative comraderie into a positive act in a classroom.  I started this immediately into the semester, and it worked so well.  Double-edged sword is this:  I stopped having to do this early on in the fall, which was great in that it meant students were more respectful of each other, but I did like giving them the experience to think about the balance of positive and negative feedback as it is an important life-skill and such a necessary one to our craft.  Thanks Elissa!

Anna Vance’s “Make it Stick” session was solidifying for me.  I had read the book and loved it, but the ideas of spacing, lagging, and spiraling were still seemed like such a blended concept to me rather than separate intentions.  Her session helped me to develop them as separate entities in my mind and figure out which ones I had implemented and what I wanted to add in the future.  Last year I started to spiral homework, but it fell by the way side early.  This year I decided to continue work with this concept first and got further with it this semester, but the cramming in the end due to missed weather days off set the attempt in the end.  I will continue with spiraling of concepts next semester, but in a way that probably mirrors more of the spacing concept.  I want to keep students working on concepts that need strengthening and reinforcing as they venture toward Calculus next year.  Even though I have not seen this practice through consistently, I believe it has really helped students in the times that we were able to do this.  Thanks Anna for straightening these concepts out for me!

Clothesline math presented by Chris Shore is an incredible concept – the proof is concrete in that there was demand for a second session of it at TMC17 AND the room was packed to the gills!  I integrated this concept into my fall Unit Circle Socratic Seminar, which will be a separate blog to follow this one.  I did not actually use the string, but the concept of it was there and played an important role in the development of radian use on the unit circle for the students.  There is so much great work that can be done with number sense across all grade levels involving this strategy, and I would love for our new Algebra 1 team to learn this method, but time and lack of funding for professional development got in the way for first semester.  I am hoping we can find the time to show our new team this at some point this semester.  Thank you Chris!

Ideas from TMC17 that I Plan to Drive My Second Semester Instruction

I attended the Desmos session on the Wednesday before the conference began.  At this session, there were break-out sessions developed for the afternoon.  I attended Chase Orton’s session on calculus concepts for early ages.  In this session, he talked about the concept of area in early grades extend into non-vertex edge images/curves in an estimation sense; further, to use concrete area calculation to drive the estimation.  I had never thought of connecting this idea so early and in parallel to usual area concepts and calculations.  As I look to second semester with my Honors Pre-Calculus class and think to our algebraic units this coming semester in preparation for Calculus, this will be a concept I embrace when looking at graphs of functions.  We have the time to do it as I have just “functions” penciled into the calendar, so what a great way to enhance the study of the curves of functions they know and lose redundancy that is typical in this practice.  Thanks Chase – I cannot wait!

Lastly, I went to a session on standards-based grading given by Tony Riehl and Jennifer Brackney:  “Standards-Based Grading in a Traditional Setting”.  This was so informative for me on the ideas of implementation of this practice as our district is and has always been a traditional grading district.  A beginning contradiction to that, our district has started piloting standards-based grading practices in a few of the elementary schools with intent to expand into all grades at some point.   I had always come across standards-based grading on a 4-point scale when exploring it, but I really liked the presenters’ 10-point system that they developed to bridge the transition from traditional to standards-based grading.  This semester, I am looking to utilize the information and resources they provided in working on my data collection and analysis skills; I need work in that area.  Our department chair is already implementing the practice of posting our standards on our tests this semester, so it seems like a natural pairing.  This will be a big challenge for me, but I am committed to at least developing it along with her request.  I really like the objectiveness that it brings to the table of evaluation of student skills, and I am hoping I can find enough success with it to share in further development of our Algebra 1 and Geometry initiative for next year.  Thank you Tony an Jennifer for providing this valuable information for traditional-based classrooms to involve themselves in a more growth-orientated mindset!

In closing, there is so much more I experienced at TMC17, but I would be writing for days and days; I wanted to highlight the experiences that have and will receive real-time application this year.  Though I wish my session at TMC17 would have come to fruition, I realize it was pre-mature of me to try to speak at a first Twitter Math Camp being a newcomer.  I wish I had allowed myself the opportunity to be a participant at one of the other morning sessions given how much I drew out of the shorter afternoon sessions.  Those sessions have driven my instruction thus far this year and fuel my excitement for more implementation for 2nd semester as I sit here and write 2 days before going back to semester 2 pre-planning.    I am hoping I will get the chance to experience a thorough and in-depth morning session as well as more afternoons sessions in Cleveland as I do plan to enter the registration lottery in February.  With holiday festivities over for all of us and a new semester in the dead of winter ensues, 

I am hoping the timing of my reflection of TMC17 can help boost the yearly excitement we all feel for TMC this time of year because the professional development and relationships we form at TMC are priceless!  

Saturday, August 19, 2017

Classroom Management:  
Be Pro-Active and Positive, and the Classroom Manages Itself!!!

I struggled with classroom management the first couple of years of teaching, which were really two first years for me.  I started my career in urban Minneapolis, and then I moved to suburban Atlanta.  Two completely different worlds in every way, so just as I started to get down a rhythm for the urban environment, that had to be deleted for my new teaching job.  In suburban Atlanta, I learned quickly that parent communication was one the non-negotiables in teaching, and that was the first thing that I tackled my third year of teaching.  What I did taught me that more than necessary, it was very powerful to building relationships in the community of families that passed through my classroom.  This was the first big step in my classroom management experiments and learning, and I will elaborate further on it later.

Though I have not really had a lot of issues with classroom management in the years past the start of my career, I feel that many methods I tried and used lacked so much purpose and meaning.  In reflection, I feel most of it was driven by re-action to past problems rather than pro-active measures.  Though I had become pro-active with parent communication, the pro-active switch on everything else was stalled.  The pro-active parent communication helped behind the scenes of my classroom early in my teaching career, and it kept amount of communication less frequent and more positive.  When I began to implement more pro-active and positive measures in the main stage of my classroom with students in later years, I never really gave classroom management much thought anymore – it managed itself.

I would like to share a few things I have adopted in my classroom, most of them in recent years, that have helped immensely with making my classroom run smoothly.  My definition of smoothly includes efficient use of time and resources, safe, positive learning environment, constructive encouragement and reinforcement of student success, and most importantly of all, strong communication and relationship building with students and parents.  Notice I put students before parents in the previous sentence.  I have learned that heavy focus on pro-active strategies with students drives strong relationships with parents.   While I want to share successful strategies, I also believe it is important to acknowledge what did not work in the past and why it drove change.  I will incorporate both in what I share.

Getting to Know Students Early and Continuously

In the past couple of years, I have started the year with Sara Van Der Werf’s Name Tents the first week of school.  These are such a great way to start getting to know your students.   More importantly, it lets the students know that their thoughts, likes, fears, experiences, etc. are welcomed and valued in your classroom.  It gives them a sense of belonging and a place to have a silent dialogue with their teacher without having to ask questions or share something in front of their peers.  When students feel like they belong, they tend to engage with more ease.

Name Tents:  

There were so many years that I had students fill out a student information sheet and never had time to read them.  I did borrow a student information sheet from one of my colleagues that I really liked and gave it to them this year to return to me.  The difference now is that the pressure is off for me to read it right away because the Name Tents jump-started the “get to know you” process in the first days of school.  I still intend to read the sheets and have set a date to do so while driving down to the coast for Labor Day Weekend as it will give me something fun to do while on a long car ride.   I can then enhance instruction and daily conversations with them by productively using that information they gave me.  I will also be acquainted enough with them to really digest the information they provided.

Another method I use to build relationships with my students is during homework check time.  A few years ago I realized that homework return was slipping, and the whole process of checking and recording on my own grade sheet seemed so useless and lacked anything positive or productive. Determined not to give up on assigning work, I came up with the idea of giving them check sheets to carry with them, which I explain more in depth below.   If nothing at all, I will never give this up because it provides me the opportunity to still interact daily with them.  I can ask them how they are doing, how was the game last night if they are in a sport, how is the play going if they are in theater, how was that biology test that you were crazy studying for yesterday, etc.  It is a daily way to continue to learn more about them and let them know that they are individual in my classroom rather than just part of a group.  Below is a photo of my check sheets:

Building a Positive Environment Through Language, Acknowledgement, and Recognition.

Try Not to Use the Word Fail- Working on use of productive language is something that I have increased commitment to every year in my classroom.  The earliest memory I have was of incorporating the commitment to never use the word “fail” in my classroom; about 7 years ago.  This was a word that I had stopped using in communication with parents as well because I was tired of hearing it from a couple of my son’s teachers on the occasion when they emailed me.  It just felt like such an inflammatory word, and as a parent, I realized that after I saw that “if then statement” with the word “fail” at the end and not much else included in the conversation, I did not feel good about the communication taking place.

Anyway, it was not that I took the reality of failure away from dialogue with students and parents, I just simply switched the words to “may not be able to pass”.   It acknowledges the situation if it arises, but in a way where communication can stay non-volatile and still give hope and chance for change.  The first year I incorporated this into dialogue with students was when I had my first math support class.  I had the students 2 hours a day, so I knew them well and talked with them a lot each day.  At the end of the year I had them do reflections of their experiences in my class.  One of my students wrote that one of the best things about me as a teacher was that I never told them they would fail and that really helped her to keep going even when she struggled.  Such a powerful moment when I read that – the fact of the matter is that I acknowledged that reality with them near every assessment when going over problems, but in the way of “be careful of details, and not showing work because I may not be able to give credit for what you do know, and you may not be able to pass the test, which I do not want to see happen”.    Changing the face of one single word has driven incredible change in student motivation and relationship building for me, and I have never used that word since.

On acknowledgement of student work:  In early years, I hung student work in my classroom when possible, and sometimes hung up yellow stars for certain learning situations when students performed well.  The most recent appearance of performance based stars was with my Algebra 1 support students a couple of years ago when assessing on factoring methods.   While the students who earned stars thrived on it, I never realized what it meant to those who were not able to.  While out of the classroom last year and tutoring, I was working with an AB Calculus student.  She was struggling a lot, mostly because she was not ready for the course, but our district did not allow for any other options at that point for her to take other than below level math.  Anyway, the same types of stars were up in her classroom for test success, and she was so upset about performing below the level of earning a star.  My heart broke for her when she told me that she believed she would never be able to get a star.  I knew as a teacher that no teacher ever sets out to harm by doing this.  it is meant to be a motivator, but it was not until that moment that I realized how demoralizing it can be.  I vowed then to be different in my intentions with this process.  This year, I bought some “star student” cards from Schoolbox, and there are many already up on my board (I forgot to take a picture yesterday before leaving).  Right now some students earned a card for gaining strength in factoring skills, and I intend to give cards for things like increased success, making mistakes that contribute to learning, and other contributions that are not grade-related.   This is a far better way than my previous method to acknowledge all levels of student success as it is different for everyone, and all of it is key to our classroom.

This is what the star student card looks like:  I not only put their name on it, but I also write why they earned it.

On School Driven Recognition – Our school gives teachers 5 “Rich Raider” cards per week to hand out to specific students who have demonstrated citizenship, integrity, hard work, or respect.  We fill them out and give them to students to put in a box in the cafeteria.  Several cards are drawn from this box weekly, and students can earn prizes.  This is another way to show students that their individual contributions in our classroom matter, and they matter in the school scene outside our classroom.  There is nothing better than the excitement in their eyes when I hand them one of these.  A lot of the time they do not realize what they did warrants recognition as the academic world they live in now is so much about quantifying their success in numbers only.  I am happy that my school, and many others in our district do this.

Our school's Rich Raider Tickets - This is the bunch I will hand out next week:)


Interactive Notebooks:  Learning to organize has really made my class run smoother.  Most of this learning curve came after I began to implement Interactive Notebooks into my classroom almost 3 years ago.  There can be a lot of shuffling around with paper and materials, but I fell in love with this classroom strategy almost immediately and vowed to clean up my “disorganization issues” to maintain the practice in my classroom.  This strategy teaches students to organize notes and build a powerful resource of their own to reference daily for homework, group work, and preparing for assessments.

Interactive Notebooks in use this past Friday during a group learning check:

Every day when my students enter my classroom, their note pages for their notebook are on this podium for them to pick up.  If there are activities instead of interactive notes on a particular day, the empty podium communicates with them as well in that we may be using the notebooks versus adding to them.

The "Work Pick-Up Podium" - I also leave them a note for the day.  This particular day was to wish them a "Happy Pythagorean Triple Day"

This table at the front of my room is a one-stop shop for students to organize their notebooks and any other materials.  There are always glue sticks, high lighters, markers, colored pencils, tape, and often scissors on this table for them to use for adding note sheets to their notebooks and/or enhance their notes.  I introduce these notebooks as their way of building their own textbook, so they are free to add to it in any way that helps them.  There is also a stapler and hole punch for homework sheets as I give our copier a break by not hole punching – after all, I want the copier to work when I need it rightJ?

The crate on the table contains folders for every class for make-up work pick-up and extra table of contents for the notebooks or extra homework grade sheets if they need them.  There are also calculators up there for them if they do not have one.  This is their area primarily, and I give them the independence to use and maintain it.  Giving students independence signals to them an upfront trust and belief that they can handle the responsibility.   The supply table helps them to organize their materials in class as well as feel comfortable about the process.  This and the play table make my room just as much their room the hour they are in it, and when students are comfortable, they are more engaged in the learning process.

Homework – In and Out of Class

Giving, Checking, and Grading Homework - Homework is something I will not relinquish in my classroom, but I have acknowledged the fact that I need to work on meaningfulness with it.  This year I am spiraling and lagging homework for them, and I am hoping it will help not only with work in my classroom, but help them to keep skills strong for their future math classes.  Almost every day I check homework, and I use a homework check sheet to do so.  This check sheet contains 6 weeks of homework checks that they keep with them; at the end of every 6 weeks, we have progress reports, so they can better gauge when that is coming.  I collect the grade sheet every 2 weeks and put their homework grades in the system.  Though I have not had a lot of instances of students losing them, I encourage them to take a camera phone picture of them every couple of days just in case; sort of like “backing up files”.  I also strongly encourage them write down the assignment in check box each day in case there is a disagreement of homework grade, they can know what it is and show me.
Second-though I check for completion and work shown, I also key in on a couple of key problems each day as I go around, and I can give them a quick prompt or two for correction if they need it as well as underline or circle parts of their work to look at again; this helps me to know where they are at and what to spiral through more for homework and going over homework at the board.  Lastly, when students start to see missing work, on this check sheet, the will to get back in to the habit emerges very quickly.  I equate it to adults and credit cards.  It is easy to create negative money, but we do not get the daily reminder of what we spend unless we seek it out, and then the monthly bill can be a real shocker!  This way students get the daily reminder instead of the grade book shocker every two weeks.

Prompting Homework Questions and Maximizing Time Allotment -This is something I started working on 2-3 years ago and then let lapse last year because of being ill; the break allowed me to see the difference it made.  One of the things that can make homework ineffective is when students do not ask questions when they need to.  I wondered just how much the peer thing mattered to students when asking homework questions, and I can tell you now it is a BIG issue; bigger than you think.  I started this process with placing 3-4 blank post-it notes on random desks before the start of each period, and the student with the blank post-it note on their desk could put a homework question on the post-it and put it on the board before class started.  If they did not have any questions, they could put it on another desk.  I got so many more homework questions with this process, and it was great feedback for me on student struggles.  The drawback was that there was still not enough anonymity in that students knew where the post-its came from.  This year, I hung a poster up front right next to the supply table for students to post homework questions.  I labeled the top of it with a sign that says “learning Inquiries”  to give further encouragement on mistakes and misunderstandings as a learning process.  Here is what it looked like one day this week:

Basically, the first few minutes of class each day are for students to paste note sheets in their notebook , put their homework and check sheets out for me to look at, post any homework questions on this poster, and start the warm-up work or directions on the board.  During this time, I am checking homework, attendance, etc.  Because everyone is focused on getting their things organized and starting class, no one knows who posted what questions.

Two weeks in students are already in the routine of having their homework out for check.

  When I get to the time for homework questions, I just transfer the post-its to the white board and go through the problems.  I also take this time to address any issues I saw in work I checked while going around the room.  I usually allow time for 3-4 questions, and if I have more, they know I will work them out completely with side notes and post them on my website.  There are days I cannot get to questions, but again, I know which ones are being asked, and they know I will post solutions for them to check.   All learning inquiries on the poster and mistakes in work I see and gather in the first few minutes of class are anonymous and make huge contributions to all students.  This is a priceless way to make homework more purposeful to the students both individually and as a whole class.

Cell-Phones – This is something that I gave a lot of freedom to students with over past years, and probably more than I should have.   This year, I vowed to change that as I realized last year that we now have students growing up and coming to high school who have little or no memory of life without a smart phone.  I mean, it’s been 10 years since the I-Phone first came into the market – where has time gone?   While the older generations certainly enjoy technology too, we also remember life without smart phones and some of us any cell phones at all.  I wanted to make the theme of my mission with this a learning experience – a way for them for at least one hour a day know a life without being plugged in.  Because I did not want them to feel like I immediately mistrusted them with their phones (although I did, but through no fault of theirs as they only do what they know with plugging in), I told them the story of what I learned by unplugging for a few hours a day this past summer with my I-pad.  I told them that I was very attached to my I-pad (and I am), and my husband was very attached to his TV (and he is).  This summer, my husband was having trouble getting his course work done for teacher school (he is doing the second career teacher thing).  I was having trouble separating from my I-pad and the couch (exercise and me are not friends).  We both committed to turning them off for 6 hours each day to get the things done that we needed to.  He got his school stuff done, and I got most of our house cleaned and organized, more books read than usual, and started journaling again.  I was amazed at how much more productive I was – I knew I probably “I-padded” too much, but WOW… 

 Sharing this story with them right off the bat set a tone of purpose for them putting their phones in the pouches on the wall.  It was not a “because I said so and think it is a good idea” sort of thing, it was a “I get it and want to help you” type of thing.  I took the idea that Tony Riehl talked about as a “my favorite” at TMC17, and I talked about cell phones, and my I-pad, as a distraction to learning and work that needs to be done.   

Phone Storage Station with Sign Suggested by Tony Riehl

 As the days continued during the first two weeks, I noticed that some students were just simply tucking their phones away in their backpacks.  I told them that was fine too, but that they needed to stay tucked away.  I have only had to take a phone back to the distraction pouches twice, so I think the overall expectation is set now.  I am circulating often enough in class to reinforce it as well.  As far as the need for students to have technology in their hands some days to enhance learning, our school has one-to-one devices, so we are set for thatJ

Parent Communication – I saved this for last on purpose after talking about it briefly at the beginning of this blog.  If I had been writing this blog 10 years ago, this portion would have been 2-3 times the size of this one as this was my primary form of classroom management early on by control rather than purpose or meaning.  I am still pro-active with parent communication because I enjoy forming a community in my classroom that extends to families of students.  I have sent them a group parent welcome email every year for the past 10 years, but I no longer email them weekly or at the start of every unit.  Part of this is because I have had teacher websites or Edmodo class sites the past 5 or so years, but the other reason is because I have begun focus much more on building working relationships with students. 

The benefits of a group parent email are that it establishes a line of communication that is positive early on.  This way, if problems arise during the school year, the first time a parent hears from me is not when there is an issue.  It is a pro-active way to partner with parents and collaborate when needed for the success of the student.   I let the parents know my website as that is where all calendars, syllabuses, and homework resources are.  After that, I maybe check in and send an email once or twice a semester to give updates. 

As far as individual parent emails, I have changed my approach on this as well over past years.  I strive very hard to resolve any issues with behavior or lack of work with students first before contacting parents.  While I believe it is important to inform parents of problems, it should be when a resolution is not being reached after at least a couple of attempt to work with the student.  I think it is important for students to know that they will not automatically get tattled on if they make a mistake, and parents tend to appreciate quality vs. quantity when it comes to communication.   I also make it a point to alleviate inflammatory words from any communication with parents as I mentioned above with the word “fail”.  My experience with less than thoughtful teacher communication sent to me as a parent drove that decision, and it has been a powerful experience to give back to other parents in a positive way.

In closing, I really hope some of the things that I have learned and implemented can help those of you looking for new ideas for your classroom.   While I was able to control my classes early on given the fact that I am a tall and thicker individual with a voice that carries and a commitment to keeping parents in touch with my classroom, it was not effective classroom management.  The biggest lesson I have learned regarding classroom management has been this:  the more you focus on creating pro-active and positive tones in classroom environment, interactions with students, and organizing the instructional strategies you feel work best, the more your classroom will manage itselfJ

Saturday, August 12, 2017

An Outstanding First Day and Week!   2017-2018

School started for us this past week.  I can honestly say this may be the best first week of school I have ever had- I feel so blessed!   My students are so good-natured and hard-working; they remembered more from last year than I ever could have imagined.  I only discovered that at the end of the week as we spent the first part of the week getting to know each other and doing cool math-y activities.

The first two days back I did a couple of Sara Van der Werf’s activities that I had not implemented yet.  The first was the 1-100 number task for group-work skills building.  The students were just as engaged as I had seen in pictures on Twitter from other teachers who have done this activity.  Below is a picture from my senior Calculus students working on it.  If you have not tried this activity yet, you much do so – it is a total winner!  Even if you have started school already, it can still be done before you start any routine group work for the year to help students work together in groups.

I introduced my students to Ken-Ken puzzles this year again but in a different way.  I had seen this idea on Twitter, but I cannot remember who posted it.  Anyway, I started by putting a Ken-Ken puzzle on the projector like this:

I then had the students stand and go find a different partner for this activity.  I had them do what Sara Van der Werf calls a “stand and talk”.  I gave them 2-3 minutes to look at the solved puzzle and talk about things they noticed about the numbers and patterns in the solutions.  We then came back together as a class and people shared what they had talked about.  Together they shared observations such as how the "numbers in bold" operated together to get the number at the top of the box, that no numbers were repeated in rows or columns like Sudoku, and they noticed that only certain digits were used..  Given that, I clicked on the link for a new unsolved 4 x 4 Ken-Ken puzzled that we solved together as a class.  They got through it very quickly and were actively engaged.  That was on Tuesday, and by Friday they endeavored to solve a 5 x 5 puzzle.  They struggled a bit with an extra row and column, and they did not finish it before the bell, but I told them that we would pick up from there next week.  They had tried a new level, and I was proud of their motivation.  Below is the link to the site for Ken-Ken puzzles that I used:

Also on Tuesday after the Ken-Ken puzzle time, we played Sara’s 5 x 5 grid game.   After using some of the period for Ken-Ken puzzles, we played two rounds of this game.  I had the students work in pairs, and for the first round of the game I told them to place the numbers anywhere in the grid they wanted as I drew the cards.  While drawing the cards, I could hear them talking about placing the numbers a certain way; they were trying to figure out what the strategy would be.  After the first round, we discussed what strategies they used; many were trying not to place repeats side by side thinking that was a penalty.  In fact, the strategy is to place as many side by side as possible, but I loved hearing about the strategies they were using.  After I showed them Sara’s blog post of the grids and how they are scored, they got really excited for the next round.  I especially enjoyed talking about the slides she had where they had to figure out which placement of a set of 4 tens would yield more points.  Most student pairs had earned anywhere from 20-50 points in the first round, but after we played the 2nd round, their scores ranged from 140-200 points; what a difference.  It was fun to watch them during the 2nd round as they were intent on working together to get adjacent placement of numbers as much as possible.  I did a 1st and 2nd place winner in each class, and they earned a free homework pass to be used during review work at the beginning of the year.  That way if there is a topic they already feel strong in, it gives them some free time.   Here is a picture after we had just finished round 2, and they were calculating their scores.

Because Sara’s blog was up on the projector during the game, they noticed her and asked about her.  I told them that she was probably one of the best math educators in our country, and I believe that to be true.  I also told them behind the name tents that we were working on too; they thought that was really cool!   By doing this, I established myself as a teacher who is also an active learner from other teachers.  They probably know teachers share materials, but seeing it in action from across the country seemed to interest them a lot.   

Also throughout the whole first week, I did name tents for the second year in a row.  This year I included two days for them to ask me questions; one more random, and one about classroom policies/expectations that they still may be wondering about.  It takes a fair amount of time the first week to respond each day, but it is TOTALLY WORTH IT to do this with your students as a tool for getting to know them and letting them know that they are valued as individuals in your classroom.   The question-answer part of the name tents gives students a more private way of communicating with their teacher without having to comment or ask questions during class.  A few students really shared a lot about their extra-curricular involvements, career goals, and interests beyond the scope of questions, and I really enjoyed reading and dialoguing with them!   One student asked if we were going to do this every week.  Unfortunately, time will not allow for that, but I have decided to utilize the name tents more than last year.  One, I am going to use them to set-up groups throughout the semester rather than write names in marker on desks.  Two, I think we will paste in a second page the first week of second semester and do this again.  That way I can do a check in on the class and what is working for them or not, ask them how their holidays were, and because they are juniors, I can start seeing what they are thinking about for post-secondary options.

Lastly, as mentioned in my last blog, I set up a play table/area in my classroom for puzzle and pattern play.  My teacher friends thought it was cool, but my husband and son thought I was nuts!  They did not think juniors in high school would want to “play with blocks”.  Well, right back at them I can say absolutely they do.  The look on my husband’s face when I showed him this picture was priceless!

So yes, big kids do “play with blocks”, enjoy it, and I love that they enjoy doing this in their down time.  Here are some cool patterns that ended up on the table by the end of school on Friday:

All of the above said activities made for a great first week back.  Though I was tired by Friday as usual, I was also very happy and energized; that is a new and wonderful feeling.   Gone are the days of focusing on syllabuses, pre-tests, and “getting started as soon as possible” on course curriculum.  I had slowly lost those items over the most recent years, but I cringe when I remember years when that is what the first days looked like in my classroom.    It is so much more important to take the time to make math fun and get to know my students, and this is not something I will be willing to ever give up again.   I owe many thanks to the network of colleagues I have in the MTBoS who have taught me to see and try new things.  It allows me to be an active teacher learner and provide my students with great experiences in math.  This week was the biggest example of that yet!

One fun thing that happened that I had not planned on was using Elissa Miller’s classroom strategy of  "Two Nice Things”.  A student in pre-calculus called out another student across the room, and immediately Elissa’s rule popped into my mind, and I said immediately “now you have to say two nice things about him!”   It worked!  The kids were immediately on board and agreeing, and the student followed through!  Also, did not hear that happen again the rest of the week –

So you see – the things we learn from each other are always with us, whether we plan to use them or not.  They are in our minds for any moment we may need themJ

Sunday, August 6, 2017

A New School Year = New Goals!!!!

Tomorrow marks the official start for my school district for the 2017-2018 school year.  I am really excited to be officially in the classroom again returning to the school I was at in the fall of last year.  A lot has changed since leaving the classroom last December:  realizing teaching was still my true love for a career, realizing that the school district I left was in fact the best fit for me and my home, and finally making a commitment to myself to not overload with things that overshadow my passions; easier said than done of course!

My teaching schedule this year includes Honors Pre-calculus and Non-AP Calculus.  I have taught pre-calculus before, but Calculus will be a new challenge for me as a course even though I have tutored it for many years.   What is most energizing to me is that neither course has a standardized test tied to it, and this will be the first time in my career that I have had this opportunity.  I can teach at the pace that is comfortable for learning in my classroom, and we can delve deeper into topics and incite meaningful learning in our classroom.  I am the only one teaching both courses in my school, which is also a bonus – this year it is all about my kids and I and what works best for our classroom.  I intend to embrace this teaching gift with every fiber of passion in my teaching soul!!!

In addition to an awesome teaching schedule, I am returning to a department of colleagues I came to miss a lot last spring as well as many new ones that seem to be very motivated and hard-working.  Our school has a new learning incentive for Algebra 1 and Geometry courses to improve our EOC test scores.  We received extra positions to meet the needs of this program, and now each Algebra 1 and Geometry teacher will have between 15-20 students only to allow for learning needs of all students to be properly met, and students are able to learn as they go/move on when ready after each concept rather than fit into a “one-size fits all” pacing for the year.  It is an incredible opportunity for 9th and 10th grade students and teachers!  So far, I have been asked to lead in the professional development and resourcing involved prior to pre-planning and in contribution to the first week of instruction.  Being a member of MTBOS definitely helped me to provide rich and powerful teaching resources to them.

As school starts tomorrow, here are my goals for this school year:


  • To continue using interactive notebooks in my classroom.  I have used them for the past 2.5 years, and they have provided students with success at all levels.  Honors Pre-calculus students can use them for reference next year in calculus, and Calculus students can revisit the art of organization with note-taking resources as they make their way to college.  Maybe they will take college calculus and use it!
  • I have created not only a play table in my classroom, but a whole play and puzzle area in the back corner of my room; that part of the goal is finished.  I now would like to instill in my students the desire to “play with math” by using pattern and number sense exploration through tactile play and number puzzles.  I want them to see math as fun and magical.
  • I started spiraling homework in the beginning of last year, but it dropped off quickly as I went into survival mode to stay well enough to finish the first semester.  This year I am going to do this again as well as lagging homework.  I was not able to go to Henri Picciotto’s session on lagging homework at TMC17, but I have read the archives of TMC17, and love the benefits to it that he outlined.  I definitely can see how lagging content in the the assignments a student does at home is much more meaningful and productive.  I do not believe in “no homework”, but I do know that my homework assignment habits needed a huge overhaul; just looks like just the right fit.
  • To help our new math teachers in the building as much as possible by providing good professional resources and advice from my experiences both successful or not.  I have been assigned one of them specifically to mentor, and she is a new teacher this year.  She has great energy that I want to foster and enhance with the professional resources and networks I am a part of.  Outside professional organizations have kept me in this profession through the good times and bad.  Even when I went astray from them, they were there for me when I was ready to re-fuel.
  •  To become much more active in MTBOS this year with sharing materials, resources, and fun chats with my fellow mathies across the country.  I want to keep up with regular blogging and #teach180.   I am hoping to join some of my North Carolina peeps for their professional development activities too.  I am hoping we have another Southern MTBOS tweet-up again this October as last year was a lot of fun, and I have a great idea/location OSin mind with another possible mathematical journey beyond that oneJ
  • To get as many colleagues of mine as possible on Twitter and in the MTBOS!
  •  Balance…  Balance, balance, balance.  If my former principal could hear this now – he instilled the importance of this into me, but I only truly realized it after I left.  The past 5 or so years, I loaded my working life with a full-time teaching job and almost full-time tutoring business.  No more of that for me – it killed my passions for teaching in the classroom, it wore my body out, and it robbed me of the joys one needs in their personal life to create that needed life-work balance.  I will still tutor a few students each week, but nowhere near what I have done in the past.  Though it helped us re-position financially, that is not needed now, and the personal cost is not worth it.
  • I still managed to read during all the crazy of the past 5 years, but now I have the time to read even more.  On goodreads, I have set my goal at 50 books in 2017, and I would like to meet that goal or get as close to it as possible.  It has been a busy summer, so I did not get as many read as I had hoped, but I am happy that I am maintaining a mixture of personal books and professional books. 
  • Exercise – it is my nemesis.  I would rather do anything else, but I bought a new bicycle last spring and have barely been on it.  I traveled a lot this summer, but now with the routine of the school year upon me, I would like to work into biking in 3-4 days a week.  

6 professional goals is a lot, but most of them are already in progress and need to just be built upon.  All of them are things I am super passionate about, so it is always easier to work towards those goals.  I predict my biggest challenges of those I have listed will be keeping up with the lagging/spiraling homework, and regular exercise, but I am committed to it.   This is the first blog I have posted in a while, and I have also yet to post my TMC17 reflections, but that is next this week!

As with any “first day of the school year eve”, I find myself a little nervous about tomorrow, but I am super excited and happier both professionally and personally than I have been in years. 

Here’s to a new and awesome 2017-2018!!!