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!!!


My transition to OPTIONAL HW

For a couple of reasons this year I made the transition from giving HW 3+ times a week, to having optional HW.  I noticed the no HW trend in education last year, and did some investigations during the summer and thought that HW optional was the best idea for me.  One of the reasons I wanted to get away from assigning HW in the traditional way was the inequity of how I was giving credit.  My rule has always been to receive full credit EVERY problem had to be ATTEMPTED, if not, no credit was given.  So I had students who tried there hardest and didn’t know how to start problems, which is frustrating but understandable, that received no credit.  I had other students who put down “slop” for a lot of questions, that I was giving full credit to.  I knew it was not fair….but I didn’t know what to do.  In addition I have the luxury of an 80 minute class each school day, which gave me a lot of flexibility in my schedule.  Keeping these things in mind, and wanting to do something new, I took the plunge and went HW optional.

This was probably the best decision I have made in my career as an educator!  Let’s start off with the selfish result, that I now longer have the internal struggle about who to give credit for their HW assignment, since there is no mandatory HW.  When I compared my grades to the past couple of years I noticed little change, class averages are actually a little bit higher.  Students actually started asking important questions during my lesson and while they were doing their practice problems, instead of when we went over the HW the next day.  Students actually asked questions about the optional HW I had listed on my teacher website, I was in shock about this!   As I reflect on the school year as a whole, I have not noticed 1 negative consequence from the change.

The next question you might have is, “What changes did you make?”  I did have to change what I was doing in class a little bit.  The textbook series that I use is Big Ideas Math, which I like for a couple of reasons.  It works well with our 80 minute class period because it starts off each lesson with an activity to activate the students prior knowledge of the topic, and so that students can start to develop their own understanding of a topic.  I did have to cut back a little here, instead of doing all of the activities I picked and chose which ones I thought were the most important.  Something that sort of caught me off guard was I actually gained some time in class because I didn’t have to walk around and check all 20+ students HW assignments, and have all the clerical work that went along with that.  Usually I would have a long warm-up that the students would work on to give me time to do this, now I have 1 or 2 questions warm-up that are very specific to check for understanding.  I have also used Desmos ( and a lot more this year.  If you haven’t used Desmos, you really need to.  It is a tool I have used more and more every year that makes me a better, more efficient teacher.  If you need more info about it please let me know.

Its only half way through the school year, but so far I am excited about the change.  I am very interested to see if the change has an effect on my standardized test score, in NJ we use PARCC.  If you haven’t spent anytime rethinking your HW policy, you really should.


Great teacher moment!

The past couple of weeks have been sort of challenging.  Trying to get back into a good routine in the classroom after our break and my kids have been sick.  This time of year in New Jersey isn’t overly pleasant either, we had snow last week and the days are short.  I was really looking for something to change my attitude and behavior, and luckily a couple of positive things happened.

Yesterday I attended a vertical articulation with the high school that my 8th graders attend (I teach in a K-8 district).  The point of the meeting was to insure we (including the other sending districts) were all on the same page.  In the next couple of weeks I will be doing course recommendation for my 8th graders for their HS classes.  The meeting was very positive, and I got a lot of good feedback about how my students were doing in high school.  It was reassuring knowing that I am doing a good job of preparing my students for high school, and that they are succeeding.

Today, I had one of those great teachers moments.  We started a new chapter today in Algebra 1 about Exponential Equations and Functions.  The first section is about Simplifying Radical Expressions, something the students have little to no prior knowledge of.  I tried to use a Socratic method and ask a lot of questions and let the students lead the lesson, rather than me shoving rules down their throats.  It seemed like the students created a pretty good understanding of the topic, and the lesson was a success.  After class I had a student come up to me and say, “I really liked today’s lesson and I thought it was pretty cool.”  Then another student who overheard the comment, agreed and said it was “FUN.”  Math fun??????  It was one of those moments that makes you smile as a teacher and realize that you are  doing a good job and positively affecting students lives.  THAT’S WHY I TEACH!!!!!

Long term substitute in Math

I had the privilege today of helping my principal help choose a long term sub for the other 8th grade mathematics teacher in my school, who is going out on a maternity leave.   After the interviews my principal still had not decided who the best person was for the job, but it made me start to think…

Regardless of which candidate is chosen, I know it is going to be part of my job to help them acclimate to our school, math program, curriculum, and students.  I do not envy their job for the 16 weeks they will be with us at NCS.  They have to come into a classroom that has an established set of rules and procedures and make it their own.  They have to quickly learn a new curriculum and a new set of students, analyze their strengths and weaknesses and make a decision about what is best to do for all of them.  Although I am optimistic, I am also realistic and realize that this will be an uphill battle for both the teacher and their students.  Finding good math educators is tough, finding teacher who strives in middle school is tough, finding a good math teacher for a middle school long term sub position is challenging to say the least.  This is one of those times when I am happy I am a teacher and not an administrator!




Let me introduce myself, my name is Nickolas Corley.  I am married and have 2 great children (17 months old and almost 3).  I am a passionate golfer, and love to travel, those kids I talked about a second ago have but a little wrench into that.  I am an 8th grade mathematics teacher in Northfield, NJ.  I am trying to make myself a better mathematics teacher.  My professional goals for this year are the following:

  1. Spread the Desmos word – I have been using the website and for many year.  Last year I was choses as a Desmos Fellow, and now I want to make sure as many teachers as possible are using Desmos and using it to its fullest potential.
  2. I want to explore the possibility of changing my grading techniques to standards bases grading, which can eventually lead to the long-term goal of having my class be pass/fail.  I am always frustrated by students trying to achieve a goal of a certain number in my class.  I want to put the emphasis on becoming a better problem solver, and acquiring skills and techniques to help achieve that.
  3. We have an “EdCamp” style period in my school, and I am on a never ending quest to find creative mathematics activities to do with my students.

I don’t know how often I will get to blog, but I thought blogging with be something new for this year.  I recently gave up Facebook, it was too much “Fluff” for me, so I thought with the extra time I could start blogging.

I am always looking for constructive critisim and looking to develop new professional relationships to help me grow.  Feel free to share/collaborate with me.