Rethinking Summer School – Equity & Promoting Student Learning

Summer school – I know that it conjures up bad thoughts in most of our minds. Having to go to summer school usually means you failed a course or a grade and you have to make it up.  But – do only the ‘failures’ or the ‘bad kids’ need to go to summer school? Is that what summer school is for? This is what most of us think of when we consider summer school, when in reality, summer school should be a place where all students could go to keep on track, get ahead, or learn some new things. Research shows that the 3-month summer break is often a huge learning set-back for many students, particularly minority students and students living in poverty, causing a widening of the achievement gap, in part because these students are often denied opportunities for summer ‘enrichment’ courses or camps. Summer school options are usually focused on remediation and failures, and not very enticing for students to attend voluntarily, and so we have most students taking a 3 month break from any learning. But what if we approached summer school differently? What if it weren’t a punishment, but rather a place where students were motivated by other students or college student mentors and were engaged in new and interesting topics that kept them learning?

I found this really motivating TedTalk by Karim Abouelnaga, who from his own experiences with school, decided to try to change the way we rethink summer school. It’s not too late, even for this year, for those of you educators out there getting ready for this years summer school to consider making some changes that would make summer school a learning opportunity for all students.

Thinking Ahead – Planning for Next Year’s Classroom Culture

I was in Austin all last week training for UT Dana Center (@UTdanacenter) International Fellows
(#UTDCIFF) and Department of Education Activities (@DoDEA) College and Career Ready Initiative teacher workshops happening this summer. A major focus for the week was on classroom culture and how important this is to mathematical learning and student discourse. Everyone at this training was either a current math teacher, a supervisor, mentor, coach, professional development provider, etc., so naturally, as part of the conversation, the following questions/concerns arose:

  1. What is classroom culture and why does it matter?
  2. How do you get students to talk to each other and engage in productive learning?
  3. How do you respond to teachers who say things like, “well, this would never work with my students” or “I can’t get my students to talk about math when we are in groups”…

You get the picture, and I am sure you have either thought these things or heard these from teachers you work with.

The short answer – it takes planning, training, and consistency. If a teacher thinks that they can just put students into groups, give them a problem, and they are going to immediately start talking and working together, they are very quickly in for a big surprise. Especially that first time, and especially if you have never done these types of collaborative learning with your students. Which brings us back to classroom culture.  What is it and why does it matter?

There are many definitions out there of classroom culture. I will give you my perspective. Classroom culture is a classroom environment where students feel safe making mistakes, they are comfortable sharing their thinking process with other students and with the teacher, and all ideas are entertained and acknowledged. Everyone’s voice is heard, everyone gets a chance to participate, and there is respectful conversations and debate about the work being done.  This matters because then students are given permission to persevere in problem solving situations where they may not know the answer, or may have a different approach then someone else or may have a question about something another student or the teacher has shared. It ties into those mathematical practices (#1 & #3, just to name a couple):

  • Make sense of problems and persevere in solving them
  • Construct viable arguments and critique the reasoning of others

But, this type of engagement, discourse and collaboration with and among students doesn’t just happen. Here are what I consider the three basic elements:

1. Planning

Planning entails thinking about the structures you want to use with students (so pairs, small groups, whole class) and the types of discussions and work you want to students to engage in. There is more to it than this, but some things to think about are

  • What task are students working on and what is the goal (a worksheet of 40 problems is NOT going to promote student discussion). Provide a rich task that fosters critical thinking, questioning, problem-solving.
  • How do you want students to engage? Are they talking in pairs first and then sharing with the small group? Does each pair/group need to show some product (i.e. their work, their thinking, the end result).
  • How will you bring the whole class together at the end? Will each group share out? Will you hang work and have a ‘gallery walk’ and come together to share?
  • How will you know that students have learned or reached the goal? What should students be able to do?

You need to think of these things ahead of time, most importantly because without an engaging, rich, though provoking problem, the conversations students have won’t be productive (and can lead to all the issues mentioned previously).

2. Training

How do you get students to talk about math (or any subject?) How do you get students to work in pairs or small groups and stay focused on a task? How do you get students to listen to each other and to provide critiques without insult (i.e. no ‘that’s stupid’ or “you’re an idiot”). It takes training.  I mean that literally. You have to show and model what it is you expect of them and practice, practice, practice.  Again, there is more to this than what I am listing, but here are some ideas:

  • Start those first few days/weeks of school with non-content related activities that are non-threatening, fun, and where everyone feels comfortable sharing (so talk about ‘the best horror movie’ or argue for/against a ‘beach is the best place to vacation’)
  • Set up group norms – i.e. if someone is talking, everyone else is listening; everyone makes mistakes, and that’s okay, you can support them and provide alternatives, but never insult them; everyone must contribute one idea; everyone’s idea should be heard; you can disagree but must provide a reason why; etc.
  • Show them how to get into small groups (so physically moving desks back and forth – it’s fun to do this a timed game); show them and practice how to talk with elbow partners, or face-partners, or the people next to them.  Practice sharing talk-time (a time works here).
  • Show them and practice group ‘roles’ – i.e. timer, recorder, controller, group spokesperson, etc. Switch roles up.
  • Practice different ways of calling on students (so they know they are all responsible at any time) – so person in the group/pair with the shortest hair, or the darkest colored shirt, or blue eyes….really anything works.

There are obviously lots more ways to set up these collaborative processes, but the idea behind training is that there are some expectations for talking, sharing, and working together, and if we practice these and adhere to these, then our time learning is going to be more positive and productive. Practice, practice, practice.  Which leads to consistency.

3. Consistency

I know teachers here this all the time – if you set boundaries for your classroom, you need to be consistent or students will not follow them (heck, this is true for parents as well!). Again – those first few days and weeks of school are where you set these boundaries up and start practicing with students and modeling both behaviors and actions. More importantly, follow through on any consequences. For classroom culture, this means if you have an expectation that students listen when others are talking, whether that be student or teacher, then be consistent.  If you are talking and they are not listening, stop – call it out – and then talk again. Same thing for students talking. Acknowledge when something is not adhering to expectations and call it out and then refer back to your expectations. Students very quickly learn what is expected, and if they realize that you are going to consistently hold them to these expectations, such as listening, allowing for mistakes, everyone’s ideas matter, etc., then they are going to feel comfortable speaking up and sharing their questions and their solutions/ideas. It becomes a classroom where learning is up front and center and ‘we are in this together’ becomes the norm.


I plan to do some more specific posts about classroom culture and provide some resources connected to planning and training. For now, I brought this idea of classroom culture up at the end of a school year because as teachers, you are about to embark on a summer of rest and relaxation. For most teachers I know, it is also a time where we do some personal learning and planning for next year. I would like to challenge all of you to really think about how you want your classroom culture to be next year. You need to start on day one of school creating this classroom culture, so spend some time this summer planning for that. What structures do you feel you could incorporate (i.e. pair work, small groups, etc.) and learn about those structures. What are rich tasks and go find some that would work for the content you teach. What do you want students doing when they are learning together? Go find some tips and ideas for how to create those collaborative discussions and problem-solving environments.

Only YOU can change the classroom culture in your own classroom – so think about what you want that to look like and sound like, and spend some of your summer learning and finding ways to foster this culture in your classroom when school starts in September (or August).

Annual ASSM, NCSM, and NCTM – A Week of Math Ed Leadership & Collaboration


Just returning from a week of fun in San Antonio where the annual math leadership and teacher conferences were held. Casio was a proud sponsor of a few events and at NCTM we had such a blast showing off our new graphing calculators (both approved by College Board for use on the PSAT, SAT, & AP exams), the CG-50 Prizm and the CG-500 Prizm CAS (3D graphing anyone?!) Not to mention the added bonus of blowing TI out of the water! (Side note: I will be doing specific posts for each of these in the next couple of weeks showing off some of the new and exciting features).

Thought it would be fun to highlight some of the moments we had sharing math education and technology with the dedicated math leaders and teachers we met throughout the week.


For the second year, we were honored to sponsor the opening session of ASSM (Association of State Supervisors of Mathematics). Mike Reiners, one of our amazing math teacher leaders and Casio user from Minnesota, provided some technology talking points after the main speaker and then everyone enjoyed some good food and conversation.

DSCF3005At NCSM (National Council of Supervisors of Mathematics) we were able to connect with many math leaders at our exhibit booth. We had a great time sharing our new calculators at our Showcase workshop and everyone walked away with a brand new CG-50 prizm to explore


Benjamin Banneker Association Reception at NCTM

It was a privilege to sponsor the BBA Reception at NCTM for the 2nd year in a row. What a great group of math educators who work so hard to ensure equity for all students. We were excited to continue our scholarship for a deserving student to support their future education endeavors.

NCTM & The Calculator Face-Off Challenge

NCTM was a big endeavor, with game-show stage and podiums, screens, lights, calculator displays. Thanks to the amazing team of Chris and Lionel from Events Special Effects and our own Casio Exhibit gurus John and Jason, the vision was made into a reality and it was a pretty beautiful booth if I do say so myself. Kudos to the team – it’s hard work designing, building and creating everything, but they did an amazing job. Some behind-the-scenes photos:

We had some crazy fun at the booth with hourly game-shows, and T-shirt spotter program where we gave away Kindle-Fire to those spotted in our t-shirts. We had G-shock watch giveaways, calculator prizes for our volunteer contestants and a magician, Mark Paskell, doing some magical give-aways and tricks. (My mind is still blown away by the reproducing bunnies….) 

We loved all the connections and interactions we had with math teachers, showing offthe amazing capabilities of all our calculators, but definitely our newest CG-50 and CG-500 graphing calculators. The look on our game-show participants faces when our CG-50 just blew the TI competitor out of the water was priceless. I know I am excited by the number of converts!

Here is a slide show highlighting some great moments from the games, demonstrations, sharing and talking with math educators, winners of our T-shirt spotter program, and some magic as well. Thanks to all the great math educators who came by and participated! Big shout out to our Casio teacher contestants, Jennifer North Morris, Tom Beatini and Mike Reiners.

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STEM In Action – Science Fair Amazement

I had the honor of being a judge for the Bucks County Science Research Competition (i.e. Science Fair) at Delaware Valley University yesterday. This is a competition for students in grades 6-12 who submit research projects in STEM related fields such as math, physics, engineering, chemistry…just to name a few. This was my first time volunteering as a judge, so I wasn’t quite sure what to expect, but what I found reinforced my belief that students can do amazing things if given the chance.

There were hundreds of displays, where students laid out details of their research projects on 3-paneled poster boards, including images, their research paper, their hypothesis, pictures, graphs, data and some even including the devices they created or used. I was assigned to the Engineering judging team, so my focus was the 22 Engineering projects, which we spent 3 hours reading/reviewing, and then 2 hours interviewing the students themselves. Let me tell you – if these 22 students are examples of future engineers, the world is in good hands! It was very hard to ‘judge’ and the ultimate goal as a judge was to get the students to talk about what they did and why, and provide them with suggestions and questions that make them want to continue their research and explorations. I would say the most impressive part of the day was the interview time we had with each of the students, where they gave us their ‘elevator’ talk about the why, the what and the how of their research. These students were articulate, passionate, and most impressively, able to explain the math, the science, the technology, and the engineering behind their creations and findings.

There were too many impressive projects to be able to list them all, but I will describe a few standouts.

  • One sixth grade girl created a robotic hand that she programmed as well as a ‘human-like’ hand out of gel and straws/string (that she notched joints in so she could move the fingers) and compared the force of the finger compression.
  • A seventh grade girl compared the prepackaged program of a drone to her own programming of a drone to show her commands were more efficient and smooth.
  • An eighth grade boy developed a laser beam cane for the blind to help them ‘hear’ objects in their path.
  • An eighth grade girl, trying to solve the fresh water problem in 3rd-world countries, tested 3 natural  ways to filter water to help provide an affordable way for these countries to use their own resources to filter the water.
  • A junior in high school is in the middle of a 3-year project to design a 1-rotating platform 3D printer that he hopes will be a more efficient 3D printer than those currently out there. And he printed the parts of his new printer from the 3D printer he already made a couple years ago…..(of course?!)
  • A senior girl was using 3D printing to develop prosthetic for lower legs and ankles.
  • Another senior girl created her own biodegradable implants for meniscus tears that she believes would be stronger and more durable than current implants.
  • There was a senior boy who was building a water desalinization machine that uses de-ionization to get the salt out of the water and would be, if he is successful, a cheaper alternative for 3rd-world countries than current machinery
  • Then there was the seventh grade girl, spurred on by her parents and siblings diabetes, who built an artificial pancreas.
  • And finally, the middle school boy who tried to show that ground solar panels were more efficient than roof solar panels, and if nothing else, proved to his parents that their decision to invest in solar panels was a good one.

I was blown away by the creativity, the interest, the dedication, and the knowledge these students demonstrated both in their displays, but more importantly in the communicating of their ideas and hopes for future research. A big part of the science fairs is to encourage these students to keep exploring, to keep asking questions, and to continue to pursue these STEM related interests into the future, and hopefully into future STEM-related careers. It was so encouraging to see the number of girls at this event as well.  I left the day inspired and hopeful about the future – these students are already thinking and exploring ways they can improve it and if their projects were any indication, they are well on their way to doing so.

Numeracy – Skills for Life

I just watched this very interesting, and slightly alarming, TedX talk by Alan Smith. It drew my interest because of the title: Why You Should Love Statistics. Statistics is one of those math topics that I really believe all students in high school should take, yet it is often considered secondary in importance to pre-calculus or Algebra 2. My feelings about Statistics is that it is more important for the majority of students (and adults) because statistics are used daily and without an understanding of statistics, it is possible to be continuously deceived or misled. I think our present day political climate is a clear indication of this.  It all comes back to numeracy and understanding numbers and what those numbers, or data, are telling us about the world around us.

Smith begins his talk with some information about numeracy in the UK and then shows some data from the OECD Survey of Adult Skills (PIAACX2012) comparing the numeracy rates from 12 countries, shown below.


There is a clear problem numeracy in several countries.

Smith goes on to talk about statistics and how statistics are about us – “the science of dealing with data about the state, or the community that we live in….it’s about us as a group, not us as individuals”. He goes on to show how the way people perceive statistics is remarkably different than the reality of those statistics. It’s much more interesting to actually listen and watch Smith as he talks and shows results, so here’s the talk:

His basic message is we need to be more excited about numbers and statistics in general because it gives information about us. And if we are excited about numbers, we become more engaged in looking at numbers and data which can only improve our understanding of numeracy rates and more importantly, an understanding of us. Something much needed in this day and age.

Changing Classroom Strategies – It Takes Practice and Commitment

downloadHappy New Year!  I hope everyone had a wonderful holiday season and is ready to start 2017 with a new outlook and determination to make this the best year yet, both personally and professionally.

My New Year’s post from last year, New Year’s Resolutions for the Classroomprovided a list of 5 things I use to do to rejuvenate my classroom each year – things I really tried to emphasize and focus on deliberately to help foster student engagement.  The list is still appropriate, so I am not going to repeat it here – read last year’s post if you are interested. Instead, this year, I wanted to focus on change – which is what a ‘resolution’ is after all.  And by change, I mean long term, sustained change, that becomes habit and routine, which, when we are talking about effective classroom strategies, these are the changes we want to be making in our instructional practices.

Change is hard, as we all know. It’s much easier to keep doing what we have been doing, even if we know it isn’t working.  That unfortunately has been the problem with education for a long time – change that will have lasting, positive impact doesn’t happen overnight, and therefore when results don’t manifest immediately on a test or in a classroom, we think the ‘change’ was a failure and move on to something else. (Hence the reason why education looks remarkably the same as it has for the last 100 years or more). Take the Common Core Standards – a very positive change if done right, but deemed a ‘failure’ when results on standardized tests didn’t dramatically change or show improvement immediately. It’s not the change – it’s that there wasn’t enough time – enough practice – enough support. Real change for the better, in anything you do, takes serious time, commitment, support and practice. And unfortunately, we do NOT give teachers enough of any of those things to really make significant changes in instructional practice.

According to Malcom Gladwell in the book Outliers, it takes 10,000 hours of practice to master a skill. Now, granted, there is some debate about that, but, the point here is it takes a lot of practice to get better at something or to make a change and become good at it. So, let’s say in a math classroom, we want teachers to change their practice and provide better questioning (i.e. critical thinking) practices. Let’s say this is your New Year’s resolution – you are going change how you ask questions of your students so that they are using problem solving and critical thinking versus just regurgitating answers or providing ‘correct’ or ‘incorrect’ solutions. This means that you must first learn what are some good questioning strategies and questions to ask that provoke thinking, and then you have to practice incorporating these into you current practices.  Deliberately incorporate, which is often very difficult, especially in a math class where it’s pretty easy to just ask what the answer is and move on when a student provides it. So – practice. Every day. On this one thing. If we calculate out 10,000 hours, and say you manage to do 2 hours a day of practicing good questioning strategies (that’s probably over-estimating, but we will give you the benefit of the doubt). So that’s 5,000 days.  Which….if we think about a typical school year of 180 days, it’s going to take 27 years to master the skill. Unrealistic, right? (Though…as someone who has been in education for 27 years, I would say my questioning skills are significantly better than they were when I started….but I still don’t think I have mastered it!)

27 years of practice to master a skill, or make a change that has an impact. Crazy. Let’s think about some changes teachers are asked to incorporate into their classroom, focusing just on math. There are new standards, so they have to change some of the things they have taught, the curriculum they use, the resources they have. There are recommended strategies – i.e. more collaborative learning experiences, incorporate more technology, foster more problem-solving and critical thinking, utilize questioning skills, focus on conceptual understanding not just skills, incorporate modeling….and the list goes on. Some of these are not new or changes for all teachers, but many are. And if each one of these ‘changes’ takes 10,000 hours to master, we definitely have a problem! Teachers are given usually a couple months to make these changes – if they are lucky, a couple of years, but then there are always new changes coming down the road, and there is NEVER enough time to practice any of the changes enough.

Obviously, no teacher is going to be given 27 years to practice something new. My point here – change in strategies imagesis important and necessary, and to change requires consistent practice over the long haul. You may not see the results right away, but don’t give up because it takes TIME and commitment!! Make those New Year’s resolutions to be a better teacher, to do better at questioning, to use technology more, to help your students think critically and to work collaboratively. But realize that it takes practice – lots of it – to make these changes have a real impact on student learning. Devote that time. Focus on one resolution/change at a time and just keep doing it – over and over – till you get better and until it becomes a habit. Practice truly does make perfect (or at least better) and your students will benefit. I don’t think it will take 10,000 hours to see positive results, but it won’t take a day or a week or a month either. It will take your commitment to practicing a little bit every day until it becomes routine and you continue to improve over time.

Keep practicing and Happy New Year! Let 2017 be the year of change!

The STEM Around Us

NCTM Innov8, the new team-based conference that NCTM is sponsoring, is going on right now in St. Louis, Missouri. Our team is there of hqdefaultcourse, supporting math teachers with our technology and a great team-building session based on the Wheel of Fortune and the probabilities of winning (session is Friday, November 18 at 10:45 am in Room 265/266). St. Louis brings to mind the very famous St. Louis Gateway Arch, something math teachers attending will probably be exploring and trying to mathematically represent – is it a parabola? (In fact, it is NOT a parabola, but rather a flattened catenary). (Cool 3D mathematical model here).

This idea of looking at real objects and connecting mathematics to them is something math teachers do often. It makes complete sense, and, as I have been teaching a geometry course for Drexel these last several weeks, I have really deepened my appreciation for this idea of looking at our constructed world to find the mathematical connections and relationships. What I think we tend not to do with students, and what we should do much more of, is go beyond the obvious “shape” explorations and function fitting to explore the STEM connections.

What I mean is after we identify the inherent shapes and/or functions in ‘real-world’ objects, start asking questions that get students thinking about the why behind those shapes. The why questions lead to investigation and research by students into science, technology, engineering, and math applications that would take them much deeper into understanding the world around them. And, I wager, this type of questioning will engage students in learning and applying what they learn in a much more relevant and interesting way.  Giving them purpose for learning. And, as a result, we might have more students going into STEM fields.

Some examples:

2016-11-17_15-32-11    download     images

Why, for example, are most buildings polygon shapes, particularly triangles and rectangles? Why don’t we see more circular or cylindrical shapes for buildings, besides the grain silos or water towers? Is there a reason? This is where engineering would come into play – are certain shapes stronger from an engineering perspective?



Why are science and medical tubes cylindrical? Is their a scientific reason for these shapes/containers? Why not use a prism shape, so then you could set the vials down on a table versus having to store them in special holders so they don’t roll away? Is the shape somehow connected to the way molecules or blood cells behave – i.e. science factors that might determine the tools used.  2791136-image-of-the-motherboard-without-a-pc-processor-closeup

Look at all the different shapes on a computer motherboard – there are cylinders, rectangles, squares, networks of curves/lines of wires, prisms…so many things going on. Students could ask whether certain shapes provide better conductivity? Or heat control? How does the height of a component impact it (notice the different heights of the cylindrical components). I don’t even know the questions to ask here, but this is a great example of where technology comes into play.

I feel that if we allowed students to explore beyond simple things like fitting a function to a curve or identifying shapes in a picture, and really focused on STEM applications and reasons behind the use of those specific shapes, we would be encouraging students creativity, curiosity, and developing research capabilities in order to find solutions. It would be so engaging and really get students interested in those STEM careers, but more importantly, a better understanding of the STEM around them.