New School Year

Well, another summer has come and gone, which means I am about to start my 19th year in teaching.  Over those year I think I have progressed into a pretty good teacher. My goal is to never become stagnant or content, and to always look for ways on improving and challenging myself.  With this in mind I am looking forward to some new challenges this school year.

For the first time in my career, I will be co-teaching a class.  I have little to no expectations about how this will go.  My co-teacher, Mrs. Juhr, is a great teacher in her own right, so together I think we will have a lot to offer the students in that class.

In 2 weeks I will have my first LARGE professional development about Desmos, which I am a super excited about.  Desmos has reinvigorated me as a teacher, not only have I adapted my teaching to include it, but also being part of the Desmos Fellowship has given me a great community to support me as a teacher.  I am excited for this new step in my career, and I am super excited to spread the Desmos word!

Also, I am working on an article for the NJEA Review.  I am a math minded person, so writing has never truly been my strength.  Expressing my ideas and thought to such a large audience is intimidating, I definitely do not envy the editor for the article, but I am excited to share how I use Desmos as a tool in my classroom.

The 2017-18 school year is only a couple of short weeks away.  I am excited for the challenges and the opportunities it will bring me.  More importantly, I am excited to meet and work with a new group of students.  Hopefully I teach them some math, a little bit about life, and help them understand that life is a journey better shared with others.



New additions to my career

The fall of this year has brought some new and exciting this into my career, which has created a spark for me and kept me on my toes.  I have started giving PDs about Desmos, I have written an article for NJEA Review (October addition), and have started co-teaching a class.  For me, change has always be a good thing.  I enjoy the new challenges that come along with change, and change always prevents me from becoming stagnant.

I have to be honest, giving my first PD was pretty intimidating.  First of all, it was for a very large school district (Prince George County Public Schools in Virginia), so not knowing how many teachers were going to choose my session caused a bit of stress.  Second of all, I have always been very critical of PD as a teacher, so I wanted to do a very good job.  I had 3 sessions, and each session I got a little bit more comfortable and go a little less stressed.  At the end of the day, I thought it was very productive, and a lot of the teachers seemed to be excited to incorporate Desmos in their classrooms.

Writing an article definitely was something out of my comfort zone.  I am a very math-minded individual, and writing was never a strength of mine.  Also, writing an article about a mathematical on-line tool presents it own challenges.  But I did my best, I wrote the article and edited it over several sittings, and I am excited to see my ideas in print for and for others to see how I use Desmos as a tool.

My principal presented the idea at the end of last school year for the other 8th grade math teacher and I to co-teach a math class.  Co-teaching is something I have never really experienced in my career.  I have had other teachers in my classroom as basic skills support, or a special education teacher, but I have never had the opportunity to co-teach with another teacher.  This is going to be a challenge because I am use to setting the tone, and leading the class at at all times.  It going to be a new thing for me to have another teacher in control, I am going to have to decide when to interject ideas and will probably have to lose a little control.  It will be a great experience, and I am looking forward to it.

A new school year, some new challenges, and a lot of growth.  I am excited for these new opportunities in my career!!

What did my students learn?

It is quickly coming to the end of the school year, which mean final exam time,(I actually gave mine today).  As my students prepared for their final exam this year, I wondered how much they really learned this year.  As I go through the grade book I see mostly A’s and B’s, and a sprinkling of other grades, but those are on test and quizzes.  I believe a final exam is a useful piece of information to reflect upon how much the students learned during the year, I actually think watching them and helping them review is more insightful than the actual test.  The test and quiz grades tell me they knew the topic well for a short amount of time, but the final exam gives me more insight to whether or not the learned, retained, and can still apply the skill(which is the true goal).

For the most part, I teach a pretty good group of students.  They are very concerned about their grades, and they like to compare their grades and results with one another.  That’s not my main concern….I am more concerned that they enjoy the challenge of solving difficult problems, and want to obtain the skills to conquer these challenges.  When I think about how many of my students have the same goals for themselves that  I have for them, the percentage is very small.  Why????

Why do we as a teachers, schools, school districts, and a society still grade our students with percentages and letter grades? Or even letter grades?  It seems almost archaic!  I remember someone once asking me the question, “What do you call the person who graduates LAST from medical school?……DOCTOR.”  Sort of a profound question, but it makes me think about how we should grade students, and what our objective is when we grade them.  I know there is a trend to Standards Based Grades, in my limited amount of research about the topic it seems to make more sense than what I am currently doing.  I guess I would tend to even go a step further and based on their skills and understanding of the standards put students into 3 categories:

  1.  High achievement
  2. Moderate achievement
  3. Partial achievement

Even these are somewhat ambiguous and not the greatest way of grading students, but I feel with “grades” like these we could shift the emphasis.  When I had students who were more concerned will getting challenged and conquering difficult task rather than getting 100% on every test and quiz, I think I could create a students who was more prepared for high school, college, and life in general.  Math was created to solve problems, but I think using math to grade our students is a PROBLEM.



Reflections of 16-17 School Year

This school year is quickly winding down.  As an 8th grade teacher at NCS, where 8th graders are the oldest in the school, there are lots of things to look forward to.  Sometimes before we look to the future, it important to look to the past and see how you have grown.

This year has been a very pivotal year in my career, I have had some decision this year that have changed my teaching style, and I have had great opportunities come my way.  They have sayings that life is “all about taking chances!”, or “you have to take advantages when they come your way.”  These two cliches could be the summary of my year professionally.

The “chance” I took this year was going to a classroom with HW “optional.”  I did only a moderate amount of research about the idea, but I also knew that with 80 minutes of class daily, I was afforded an opportunity a lot of people wouldn’t have.  This was probably one of the best decisions I have made in my career.  I think my students have had a more enjoyable experience in my class, and not having to check HW daily eliminated a lot of stress for me.  It was a “chance” and I am very happy I took it.

The “opportunity” from this year was being invited to be part of the first Desmos Fellowship.  Before the trip Desmos was just a cool tool I used in my classroom.  Going to San Fran to meet the Desmos Team, and more importantly meet and work with the other Fellows has really inspired me to be a better math teacher.  I now look deeper into my lessons and try to create discourse in the classroom.  Also, I have started booking and applying for opportunities to present Desmos to school for professional development.

As the summer quickly approaches I am wondering about what “chances” I might take professionally next school year, and I am also optimistic about what other “opportunities” might come my way.  I can’t believe I have completed my 18th year of teaching.  I remember when I was in high school, my mom told me that “every year of your life will go a little faster than the previous”.  She was right!  This year flew by!  Excited for the summer, and to see what the next school year has to bring!

How Twitter has made me a better teacher!

A couple of years ago if you asked me what I thought about social media sites like Twitter, I would have mentioned how they are nice to keep in touch with old friends.  Or maybe even something like, I think my students are on them too much.  This year has really change my mind about how to use social media….especially twitter.

For many years I had a Facebook account, and used it to keep in touch with friends and extended family and see pics of their families.  Then about this time last year I started to notice how people’s post were getting on my nerves.  Either they were forcing their view upon me, or just over sharing.  I know that Twitter had a character restriction, which seemed interesting because it would logistically limit peoples ranting.  So I started using my Twitter account more and Facebook less.  At first I was following some friends and some sport players and people connected with sports, but my principal at the time Glenn Robbins (@Glennr1809) was using it for professional reasons.  We had an Edcamp style PD one day, where Glenn spoke about how to use Twitter professionally.  I attended and started using Twitter for professional reasons too.

Of course one of first follows I had for professional reason was Desmos (@desmos).  This had become my new favorite tool in the classroom.  In the spring last year Desmos posted on Twitter that they were going to offer a Fellowship at their HQ in San Fran.  I was intrigued so I filled out the application and was chosen.  Besides the free trip so San Fran, this Fellowship gave my career a spark that I didn’t realize I needed.  The training we receive was awesome, but the professional connections I have made from that trip have given me a reason to think about my professional path, and how I want to improve.  The Fellowship has given me a support team that helps we design better activities and lessons for my students.  In addition is has given me reason to explore topics that I would never would have, because I teach Algebra 1.  Some of those topics are polar coordinatesparametrics, and locus of points  .  Exploring these topics have made me explore mathematics to a level I haven’t since my college years.

Another benefit of being on Twitter is that I have been created my own professional support group, from basically throughout the country.  I have made social media connection with math teachers, math coaches, and administrators.  These relationship have led to great dialogues about techniques and and educational philosophies.   Following them on twitter also led me to following some of their blogs, which given even more room for discussion.  I like the give and take and support that we can offer one another.  Twitter has basically offered me PD whenever I want it!

Calling Twitter social media is a little misleading for me.  For me Twitter does offer social media for me, a nice way to connect with some people I want to from sports; but more importantly it offers me professional connections and relationships to help me grow professionally.  If you are a teacher, and don’t have a Twitter account, you should really consider it!

Why Struggling in Math is Good!

In today’s society we can find answers at our finger tips.  With smartphone, tablets, laptops, WiFi, and other tools at our finger tips, we can quickly find out thing we need to know quickly.  This has created a society and a group of students that are not comfortable with struggling, at least in the sense of finding information.  Who remembers going to the library, using the card catalog to find a book to do research, then having to know the Dewey decimal system to find where the book was, then going into the stacks with a bunch of note cards and writing down the important information.  Today’s students can accomplish this feat in seconds using technology, they have become spoiled!

They want the same type of quick resolution in math, but when they can’t google a math problem or use Photomath to do it for them, they get frustrated.  Struggling to solve a math problem is a necessary evil in becoming a good mathematician!  It is the struggle that makes us recall all the tools that we have to solve problems.  One of my favorite things to do as a math teacher is to discuss with students the different ways of solving the same problem.  These are some of the best discussions in a math classroom, I love asking students why they chose a specific technique or a specific order in doing a problem.  It gets them verbalizing and thinking about mathematics in a different way.

When students are really stuck on a math problem I love to ask them to give me some type of  informal analysis of what is going on in the problem.  This can sometimes start us down the right path to the solution.  We have to teach students that informal analysis like sketching, making conjectures, and estimating is necessary when we first observe a problem.  Once we complete the informal analysis we can develop a plan how to transition from informal to formal, and create a need for certain computational skills and processes.  This is just part of what I enjoy about the design thinking behind most Desmos Activities (click here for more).

I also think it is important for students to be wrong in mathematics.  I don’t mean that they added wrong, or missed a negative sign, I mean did a problem completely wrong.  We learn from our mistakes, and in mathematics I think this is a great learning tool.  When we can have a dialogue and observe others solving a problem, especially one which we got wrong, we see a different perspective.  As I progressed through high school, college, and even now as a teacher; I have learned the importance of doing something wrong, and trying to avoid that from happening again.  NOBODY IS PERFECT!!  It frustrates me when students are upset about getting a 97% on a test, but they don’t want to ask why they got something wrong.  numerical percentage grade for me are a waste, and a hindrance.  When students stop being afraid of being wrong and losing points, that’s when we can learn.

This week we are giving the PARCC test in my school.  I am administering the test to my Algebra 1 students.   People have mentioned that the PARCC is too hard, and not fair.  Let me tell you what I have notice:

  • My students worked really hard!  Harder then I saw them work all year
  • My students struggled, going back and forth between the questions
  • My students had some great mathematical conversation when they were done the test
  • My students used a ton of different skills to solve the problem
  • My students weren’t afraid to be wrong and tried almost every problem
  • My students enjoyed being challenged!!!

Adversity is not a bad thing, we learn from it.  My students took a really challenging standardized test this week, and hopefully they learned from it.  I hope they learned that everything in life is not easy.  I hope they learned how smart they really are.  I hope they learned never to give up.  I hope they learn that struggling is a good thing!!

Desmos Sliders…not the little sandwiches

To me, one of the most underrated tools on are the sliders.  Sliders give the ability to make things move, including a function. (Check this link out to learn more about SLIDERS)   There a couple of reasons I think sliders are so important and useful:

  1. Students love to see things move!  Usually the first time I use Desmos in graph I show students a really cool graph I made a couple of years ago.  It has a bunch of moving parts and really gets the students to “buy-in” to using Desmos.  Check out  MY GRAPH.
  2. I don’t have to tell students what the parts of an equation mean anymore.  By putting sliders in for the different parts of an equation, students can explore for themselves how each part of a function affects the graph. (see below for examples)
  3. It makes me a more efficient teacher.  It seems like every couple of year we have a change in our standards, inevitably that means more standards to teach in the same amount of time.  Before Desmos and before sliders that meant doing a bunch of graphs using x/y chars and plotting them so students could make the connections.  Now, something that used to take a whole class period takes about 5 minutes.

There are so many reason I hear why people love to use Desmos in their class, but I really don’t hear people talk about he sliders that often.  For me, the sliders are a tool that makes Desmos an invaluable tool in the classroom.

Below are a list of graph I use with the students that have sliders:

Linear Equation – transformation form

Absolute Value Function – vertex form

Quadratic Function – vertex form

Exponential Function – vertex form

Order of Teaching Quadratics?

Almost every year I spend a significant amount of time thinking about the order in which I teach Quadratics in my Algebra 1 class.  I break down the topic of quadratics into 3 specific topics/standards: 1) Multiplying/Factoring    2) Graphing    3) Solving Quadratic Equations.  The order in which I listed them above is also the order in which I presented them this year, but in past years I have started with graphing and then  hopped back and for between the other two.  Last night, while I was laying in bed not being able to fall asleep, I found myself debating this topic to myself.

As I have mentioned before, I teach in a K-8 district and I am the only Algebra 1 teacher.  This make the idea of discussing it with another teacher sort of a challenge.  In the past year or so I have realized that social media is an integral part of how I develop as a teacher.  Thus I am throwing this out to any reader to comment back to me with your ideas, share it will your colleagues, and give me some much needed insight!

Last year I had the honor of being chosen as a Desmos Fellow, which BTW is accepting applications for its 2nd Cohort, and I have posed the same question to them.  I have always been of the philosophy that the best teachers use other teachers as resources….so that is why I am reaching out to you.

Thanks in advance!!!

Struggles of an Algebra 1 Teacher

I have recently had 2 discussions that have been interesting to me, that I would like to share.  The first one was with my class about number sense.  Another was with a concerned parents about me giving students “the steps to solve problems.”  The reason I am grouping both of these together is because they made me reflect upon the idea of why/how do I teach mathematics.

The first discussion was with one of my Algebra classes on a day where we were discussing solving exponential equations.  As we were investigating a problem where the common base was neither of the original bases, I had one student who verbalized how to solve the problem and identified the common base that we should use.  Another students responded, “how did she do that so quickly?”  My response was that the other student had very good number sense, to which the student responded “what the heck is number sense?????”  I explained that number sense is the ability to understand how number work together, and that there is no lesson in any textbook that is titled number sense.  I describe that the development of number sense happens over long periods of time, and that students who do not “abuse” calculators have better number sense.  The curious student then followed up with “how do I get more number sense?”  I didn’t know how to respond….  Is it past the point where this student can develop it.  This students is an “honors” level student, shouldn’t they have number sense?  What can I do as an Algebra 1 teacher to help my students develop number sense?  I do not have the answer to these questions.  If you do, or would like to discuss more about it, please let me know.  It is not often in my class I don’t have the solution to a problem, but to be honest, I am a bit confused about how at the Algebra 1 level I am to BEGIN developing number sense.

The other recent discussion was with a concerned parent.  We were discussing what can be done so that the student could have a better understanding and a stronger grasp of materials.  During our conversation the parent ask if I was “giving students the steps to solve the problems.”  When I responded NO, the parent seemed quite perplexed.  They mention how their child NEEDED the steps to solve the problems.  In my opinion it is more important that students understand the RULES of mathematics and understand broad topics that can be applied to many situation, but how do I convey this to a parent.  I quickly grab the textbook and picked two problems that were right next to each other in the textbook and showed the parent how one problem takes 3 steps to solve and the problem next to it takes 5 steps.  Then I explained that there are other ways to solve those problems that were different than they ways I showed them, so how could I give STEPS to these types of problems?  After showing the parent these problems and discussing it a little more they finally saw my perspective.  As a math teacher I want my students to be PROBLEM SOLVERS, not robots that follow a bunch of steps.  I want my students to understand a handful of broad topics that they can apply to many situations to solve problems.  That’s why we learn math….to solve problems!!!

In the past year or so I have spent a lot of time reflecting on my teaching techniques and process.  I am always trying to improve my instruction, and make my students better problem solvers.  What do students need to succeed in Algebra 1 and beyond?  Is their prior education preparing them?  What can I do to make up for some of their lack of skills?  These are some of the question I am always pondering!

The Desmos Effect

A couple of year ago, after having a Smartboard for a couple of years, I went on a hunt for an online graphing calculator to use in my math classes.  I knew that TI would have something I could get a free trial of for 60 days, but I was looking for something better.  After several weeks of searching I narrowed it down to 2 sites, DESMOS and some other site I can’t remember at this time.  To be honest my first choice was the other site, but as I began to use the 2 sites more an more, it just seemed like Desmos was more intuitive.  Do I began my journey with Desmos.

When I first began using Desmos, I was really excited about the amount of time it saved my from graphing all those lines and parabolas that an Algebra I teacher needs to graph.  As time passed on and the site evolved, along with my skills of all tools Desmos has to offer, I started using Desmos in different ways.  One of the first tools I researched and learned how to use was SLIDERS.  To me, this is what sets Desmos appart from all the other online graphing calulators.  Sliders are what allow for movement in Desmos, which I thought was really cool at first because could make PICTURES THAT MOVED.  Although this is a pretty cool way to use sliders, it took me a while to really understand how to use sliders to teach.  Last year I was struggling with teaching graphing the absolute value function.  I had spent a lot of time on the topic and the students still weren’t getting it, then I had a great idea to use sliders.  He is what I showed them using Desmos about THE ABSOLUTE VALUE FUNCTION.  It worked, and worked quickly!

Along the way I found that Desmos had also created a separate site from the calculator for math activities,  This site start off with only a handful of really cool math activities, activities that I would make sure I booked the computer lab weeks ahead of time to make sure I used.  Eventually the created more activities and also gave you the ability to make your own, which I tried with some success.  Over time there were more features added, and they continue to add more features and activities today.  I had become a Desmos junky!

Last spring I noticed on twitter that Desmos was offering a Fellowship, I got really excited.  I look at the application, I was slightly intimidated, and optimistically filled it out.  I had little to no expectations of getting the Fellowship, but gave it a chance.  Then one day I got that e-mail from Shelley, I was chosen.  Excited was an understatement, I was given the opportunity to join the staff of Desmos and a select of chosen people to visit Desmos HQ in San Francisco and learn more about the company.  This Fellowship affected me in so many positive ways.  I now how a great support teach to help with Desmos and any other mathematical questions and explorations I need help with, and it has change my educational philosophy.

Not only has Desmos had a positive influence on me, it also has had a positive influence on my students.  Yesterday I had a student tell me that she was going to be going to Florida and miss class today, and wanted to know what we are doing.  I mentioned that we would be doing a couple of Desmos activities, and she seemed bummed to be missing that.  I told her we could do a Google Hangout during class time if she wanted to, and she took me up on it.  I set a tablet up at her normal classroom sheet, and she got to do the activities along with the class.  Not only did she do the activities, but she had some really insightful responses that added to the class.  If I said we were doing worksheets, would she have wanted to do a Google Hangout???

Thanks Desmos!!!