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.