How the Desmos Guide to Building Lessons Changed How I Teach

If you know anything about me, you know that I am a Desmos junky.  A couple of years ago I had the privileged of being chosen for the first Cohort of Desmos Fellows, and that has truly changed how I teach.  One of the most important things I took away from my visit to Desmos HQ was the idea of understanding how Desmos designs their activities.  If you are a Desmos user and haven’t read their The Desmos Guide to Building Great (digital) Lessons, you really should.  It will give you some great insight into how to implement the activities that Desmos has designed with your classes, and also make you rethink how you design custom activities using Desmos.  The following are a couple of highlights for me:

  1.   Incorporate a variety of verbs and nouns – have you ever done a worksheet where you had to solve 30 equations?  Why?  Wouldn’t it be more useful to estimate a solution, or compare your results with another student.  The monotony of doing the same routine many times does not have great results.  Also, as we change the math verb, there is the indirect consequence of changing the nouns that go with it.
  2. Create activities that are easy to start and hard to finish – this has a lot of effects for me as a teacher.  When I design custom activities I usually think on this and also the idea of “asking for informal analysis before formal analysis” at the same time.  I want the activity to start off by giving every student a chance to start off with confidence in activity to get them “hooked”, but I also want the activity to progress in such a way that we make a “leap” by the end of the activity so students understand how they grew during the activity and they can see what they learned.
  3. Connect representations – this has been a point of emphasis in my teaching the last couple of years.  It is extremely important for students to make the connection between an equation, a table of values representing solutions to that equation, and the graph of the equation.  Before being chosen as a Desmos Fellow, I did a really poor job of making these connection, but now it is something I am constantly reinforcing with my students.  Also, this is something I think that separate Desmos from other platforms.  The ability to see how changing an equation immediately changes a graph, or how.

Desmos continues to be my favorite tool in the math classroom for many reasons.  The graphing calculator is the most effective and intuitive one that I have found.  Also, the activity site has activities that have allowed me to have high level math conversation, that I previously wanted but could not create.  Desmos helps me create discourse in the math classroom, which has lead to more success and understanding for my students.


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.



A couple of days ago I made a simple tweet about how we should not be using PEMDAS anymore.

It was not meant to pass any blame, but rather just let teachers know that we should not be teaching students “tricks” that are misleading.  The tweet was motivated by an event in my Algebra 1 class that day.  I was doing the Four 4’s activity, and we were analyzing some incorrect answers.  We were discussing why they were incorrect, and I asked how many steps there were in the order of operations, and of course, I was told by many students that there were 6 steps.  Guess that was my main motivation for my tweet.

I was SHOCKED at the number of responses I got to this tweet.  It seems like many teachers are also frustrated like me.  Here are some responses that hit home.







I wondered:

  • Who started this whole PEMDAS thing?
  • Did it actually help students with the understanding?
  • Who is still using it?
  • Why do people continue to use it?
  • Is there a better option?

I would like to start off with a quick and easy change that I saw recommended.  Moving away from a six letter term, to a 4 letter term would make a little more of a connection.  Cathy Yenca (@mathycathy) shared a link that used GEMA:

  1.  G – grouping
  2.  E – exponents
  3.  M – multiplication and division
  4.  A – addition and subtraction

If you need a “cute” phrase to go along with it:


Do I think using GEMA could make a difference?  Yes!  Do I think it is the solution?  No!  Ultimately it is left up to us, the educators, to create an understanding for our students that they can build upon and refine as they progress through mathematics during their education.

Now, the tough question, how do we ensure that people stop using PEMDAS and creating this confusion?  Marian (@DingleTeach) mentioned that by 5th grade her students are already familiar with PEMDAS.  How do we, as a mathematics community, communicate to others that they are causing harm, and that a change needs to be made?  We are not blaming anyone, regardless of who is causing this issue.  I assume they are doing so with the best intentions.  I would love to send an alert out to all educators/parents and anyone else that may be assisting our students in learning math and say “STOP using PEMDAS!!”  But how does that happen?

I was amazed at how many people reacted to my tweet.  Maybe if we all take it upon ourselves to open the lines of communication with others in our schools, community, and social media, we can make this little change in mathematics education that seems to be affecting many of our students and our instruction.  Lets not just complain, or pass the blame, but rather make a plan to make a change.

Twitter account for Desmos Algebra 1

So…….I had an idea, partially a little bit selfish on my part.  Create a place where Algebra 1 (and possibly 8th math and Algebra 2) teachers can share ideas on how they use DESMOS to ENERGIZE their class.  In addition, it could also be used as a place for math teachers to share graphs, activities, and ideas in a more “intimate” setting.  If any of the following things interest you, I recommend that you follow @AlgebraDesmos on Twitter:

  • You would like to grow your PLN to include some amazing Algebra 1 teachers.
  • You love sharing how you use Desmos in your classroom.
  • You would like to see how others use Desmos in their classroom
  • You have question about a Desmos tool specific to Algebra 1
  • You would like to have others offer ideas about your Desmos Algebra 1 activities
  • You only heard Desmos…..and that was enough

I chose to start this during the spring with the intentions that the numbers of followers could grow and we would have a nice group when the new school year started.  If the account grows would love to lead some chats too.  Please join me in celebrating the beauty of mathematics, Algebra 1, and Desmos!

My thoughts on standardized testing

Standardized testing can be a truly polarizing topic in the world of education.  There are some that think the data we get from the results is a valuable resource for guiding instruction and other think it is a waste of time and adds unneeded stress to our students lives and wastes valuable instructional time.  As an educator, I can truly see both sides of the discussion, so I guess I will take a moment to express my thoughts.

I think standardized testing is an important part of our education system.  Whether we are talking about playing an instrument, working out at the gym, playing sports, saving money, or basically anything else in life; it is always important to measure our growth to see if we are accomplishing our goals.  I feel like measuring growth of individual students, schools, and even individual teachers is important.

I do have several issue with our current methods of standardized testing.  I don’t think we need mandatory state-wide testing to occur as frequently as it does.  I live in NJ, and testing happens in grades 3-8 and also HS.  That is too much!!  In my opinion it would be sufficient to have statewide testing 3 times during a students path: once in elementary, once in middle school, and once in high school.  In between those, I believe individual school district could have bench mark assessments to measure growth.  I also have issues with how and what we are testing.  During class I am supposed to have my students work together and collaborate, many classroom are set up with students to work together, but standardized testing happens and they have to sit in rows and be quiet.

Don’t even get me started on the tools students are permitted to use or given on these test.  My Algebra 1 students are provided an embedded graphing calculator on their standardized test, similar to the one I used 20+ years ago in my math class (with the big pixels and all).  If we want to measure if they are ready for college and the real world, we need to be giving them tools they will be using when they get there.

As we evaluate standardized testing moving forward, we really need to consider many things.  Change needs to happen!!!  We need to incorporate administrators, teachers, parents, and students and give them all a voice to make the change.  NJ has promised to move away from PARCC, which is nice, but maybe we need to rethink standardized testing as a whole before we make a new plan.

PARCC’s Choice of Graphing Calculator

I am a teacher in the state of NJ, where we currently give the PARCC exam (although our new governor says we are going to move away from it.  In this post I am going to refrain from my opinions of the actual test, but I will quickly mention that I understand both sides of the debate about the test.  Regardless of my thought, it is a test my students have to take, and although I don’t “teach to the test”, I do try to give my students tools they need to succeed in their math classes in the future and also on any standardized test they may cross during the educational journey.

The majority of my students are in Algebra 1, therefore they take the Algebra 1 PARCC exam.  In NJ passing this exam is a graduation requirement,  which adds another level of stress and importance to the exam.  During the exam the students have an embedded graphing calculator available to them, and this is where my objection occurs.  The graphing calculator offered to them is a TI – 84 plus silver edition .  This is calculator is very similar to the graphing calculator I used in high school and college over 20 years ago….still featuring all those amazing pixels!!  Why would PARCC choose this calculator????  There are several online graphing calculators that are far superior to the one offered on the PARCC, my favorite being Desmos.  Desmos is a much more intuitive tool to use, has much better resolution, has more features, and also has accessibility features for students who need them.

Below is the graph of the same equation in both Desmos and using the TI calculator provided on PARCC.  First of all, which one is more visually appealing?  Also, I would like to point out that on Desmos you can see both the equation and the graph on the screen, TI it is 2 separate screens.  In addition the tools and interactions with the equations and graphs are far more intuitive with Desmos.  There are many other benefits to using the Desmos calculator….too many to mention in this forum.









One of the most frustrating aspects of PARCC’s decision on the graphing calculator is the related cost to the schools and the students.  The cost of these TI calculators is around $100, which seems like a high amount considering that over the last 20 years that haven’t improved their technology much.  Not only is Desmos a free website, but is also has a free app available for all devices.  It is amazing to me that schools and students have to spend around $100 for a graphing calculator, when there is a far better tool for free.  If PARCC changed its choice of graphing calculator is could be using a better tool, and could save the schools and students its testing money.

If you or somebody you know works for PARCC, TestNav, or Pearson and would like to discuss this, please reach out to me.  If you are a NJ teacher or administrator let the DOE or PARCC directly know that their choice of graphing calculator is UNACCEPTABLE!


Professional Goals for New Year

Recently I have gotten overwhelmed by the amount of teaching tools that I have heard about on twitter.  I would love to incorporate all of these tools into my classroom, but I first have to investigate them, then have the courage to use them in my classroom.  I try to keep my instructional techniques current and up to date, but with 2 toddlers at home it can be a bit of a challenge getting the time and energy to investigate new techniques.  Go to conferences can also be very expensive, and out school has a limited budget for professional development.  I would love to go to more conferences, and observe other teachers using these techniques; but the time and money to do so is so limited.

The topics I am committing myself to spending more time exploring in the new year are:

  1.   Clothesline Math –
  2.   3 Act Math –
  3.   An exploring and incorporating more Open Middle –

Explore and incorporating these are part of my professional new years resolutions, I think it is important for teachers to always be looking for way to improve their craft!

More time in math

How much time do students spend each day in their mathematics class?  Is it the same across each school, state, or even country.  Do students have the same amount of time in English class (or Language Arts, Reading, or whatever you school calls it)?  If we want to get better at something at life, don’t we usually spend more time working on it?

These questions should lead us down the road to understanding why students need to be spending more time each day in their mathematics class in school.  A couple of years ago my school change from 42 minutes of class each day to now 80+ minutes each day, and I feel like my students have greatly benefited from it.  We hear stats about how the US if falling further and further behind in topics like math and science, but how are we changing instruction.  It seems like we keep pushing higher level material into lower and lower grades, but when are students given time to grasp and understand the key concepts so they can apply them to higher level concepts.  If we want student to understand math better so they can become better problems solvers we need to give them MORE TIME!!

When my school made the change several years ago to 80 minute class periods, it was a very difficult transition for me.   For years I had a routine I used in my class every day, that I rarely veered away from, because I wanted to optimize every second of class.  I did a warm-up, went over the previous nights HW, gave my students notes, I modeled examples, we did guided practice, and started HW.  That was basically how every class went, because I felt that a routine gave me the best chance of using every minute possible so that I could cover the wealth of standards I need to.  I knew I wasn’t being creative, but I felt this was what was necessary to for students to learn all of the standards.

Now my class is completely different!  HW is optional, I place some practice problems with answers in my google classroom if students need it.   I do not follow the same routine every day, which is very freeing.  I now have time to let conversations drift away from the main topic, and create better understanding of how different parts of math work together.  I have time to do DESMOS activities, which are some of my favorite things to do in class.  These activities help create a need for mathematical vocabulary and new mathematical skills, and help me create discourse.  More importantly, more time in class gives me more opportunities to build connections and relationships with my students, which makes them enjoy class more and makes for a better overall learning environment.

More time in class has definitely helped my students, but also increasing the amount of time I have spent being engaged with mathematics has made me a better teacher.  Over a year ago I was selected to be part of the first Desmos Fellowship , which has given me a great boost in my career.  I met some amazing people through this fellowship, and now have a great community of math teachers to lean on when I need help.  It also inspired me to be more active in social media with other teachers, these interaction have lead to some pretty amazing lesson in my classroom (Check out #MTBoS and #ITeachMath on twitter).  Finding this time can be challenging, but giving up Facebook was a good trade off.

If we want our students to succeed to a higher level in math, I think the solution starts with giving them more time in their math classes in school.  In my life experiences, to get better at something you have to make a time commitment to it!

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.