How I’m assessing during hybrid learning

First of all….I’m exhausted!!! My school is doing hybrid, split-session schedule. We teach for 3 hours(AM students), have an hour break for lunch and prep, then teach for 3 hours (PM students). I have never been so tired in my career as an educator. This is tough!!!! So many educators have it worse than me, and I just want to say to all teachers that you are doing an AMAZING JOB.

Now to the topic at hand, how I am assessing during hybrid learning. Let me first say that I am not proud of how I am assessing, or of my assessments in general. If it were my choice, I would not assess at all during this challenging time in education. Most if not all of use have lost instructional time with our students, who already have gaps from the spring. To me, the most logical thing to cut out this year would have been formal assessments. For some reason, our school is still grading ‘normally’ where we give a number grade that gets converted to a traditional letter grade.

To avoid handing out paper and collecting paper, it seems like the only way to assess this year is digitally. I thought about how, and like most things math for me Desmos was the solution. I used Desmos in the spring to assess when we were all digital, and it worked well enough. I committed time and energy, and harasses the AMAZING Jay Chow from the team at Desmos, to use computation layer (CL) to auto-grade and give feedback to my students. It was a huge time commitment, it had a steep learning curve, I messed up some CL, but I made it work. It was in NO WAY perfect, but it was a solution.

Fast forward to this fall, and I still had the dilemma of how to assess. I still chose Desmos. Why? I’m comfortable with it, and since I use it a lot as a learning tool in the classroom my students are also comfortable with it. We are all short on time and are getting pulled in 20 directions, and it is even more challenging to make connections with students. I decided to not use CL this fall to auto-check and give feedback, but rather to use the feedback feature Desmos has offered to its users. Now during my assessments I look like Jim Carrey in “Bruce Almighty” during the granting wishes scene.

To be honest…..I HATE that I have to use Desmos to assess. I love designing Desmos activities that make students think, that create conversations, that give students an opportunity to be right and wrong and see the beauty in both. Unfortunately, for me right now, this is the best and easiest solution. I look forward to the day I can have full classes F2F and we can being doing Desmos activities and have great discussions. I also look forward to the day I DON’T have use use Desmos to assess.

Just wanted to share this with my fellow math teachers. Many of us are making decisions we are not proud of out of necessity during these challenging times. Please don’t judge me, and please don’t judge others for their decisions!

As always, reach out to me if I can ever help or if you just want to chat. Teachers need other teachers right now!!!

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!

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.

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 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.

 

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 Desmos.com 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

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.  So I began my journey with Desmos.

When I first began using Desmos, I was really excited about the amount of time it saved me 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, teacher.desmos.com.  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 looked 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 have a great support team 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 (demos.com and teacher.desmos.com) 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.