Education Growth Mindset – So Important for Teachers and Students

I just came back from Kaiserslautern, Germany, where I was working with Department of Defense Education Activities (DoDEA) math teachers as part of the DoDEA/UT Dana Center College and Career Ready Standards Initiative. Our focus this summer, which kicks off the next year of continued support and training, was on helping teachers create a classroom culture of student discourse and a growth mindset that allows students to develop deeper mathematical understanding and become problem-solvers and confident mathematicians. It was a fabulous two days, and the teachers, some who had never explored this idea of ‘growth mindset’, really had some powerful conversations around this idea of providing students productive struggle opportunities and helping them develop this sense that they can solve problems, and they can improve mathematically, and they can learn. It was rather eye opening for many.  How many of us educators have come across those students who give up without even trying because they think they can’t do it? Or they have been so ingrained in the idea that they are ‘bad at math’, so they don’t even try? That’s what this idea is about.

Carol Dweck is a leader is this field of Growth Mindset, and how to motivate and help support this idea of a growth mindset. In fact, the teachers I worked with as part of our workshop, read an article by Dweck that provided some insight into what we as both teachers and parents, inadvertently sometimes do that prevents students/children from having a growth mindset. Something as simple as the way we praise can actually interfere with this growth mindset. More here.

Many of you may be unfamiliar with what a growth mindset is, so I found a great TedTalk from Carol Dweck that explains the idea behind it. As educators, this is something to really think about because we want to develop in our students the willingness to persevere and solve problems that may seem difficult.

 

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.

CHALLENGE

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).

The Last Five Minutes of Class

You teachers out there know that those last five minutes of class – when students are ‘packing up’ even if you are not quite finished with the class activities, or, you’ve finished and they are suppose to be working on their assignments or reviewing – are often  a ‘wasted’ five minutes. In my many years at schools, I saw teachers use that time in various ways – but more often than not, it was simply time to get ready to leave, basically chat time and get your stuff together and wait time. Not productive learning time at all.

It’s easy enough to make these moments into fun, engaging, mathematics problem-solving that students, believe it or not, actually come to enjoy and request. I use to have a few different things that I would pull out – focusing on either logical thinking or number-sense or puzzles. Here are just a couple of things:

  1. I had the 24-game – several different versions.  I(If you have never played this or seen this, you should explore it). So, in those last 5 minutes, I would pull out a card, write the 4 numbers on the board and students would try to reach the target of 24. As an example: 2, 3, 4, 4 and you can add, subtract, multiply or divide using each number one time, to make 24. I often had candy for anyone who could come up with a strategy.
  2. If you don’t have actual cards, you can create your own version of ‘reach the target’.  So, pick 4 random numbers using a calculator, and give students a target number to try to reach (so 24). Or, choose 2, 3, or 4 random numbers with a calculator (or have students give you numbers) and ask students to use all the operations and come up with the smallest outcome and/or the largest outcome.  This is a lot of fun – you get some interesting problems and students have to explain their answers and defend their solutions.
  3. Give the students a logic puzzle.  I actually purchased several logic books, and so would read one out to the students or draw/show the picture on the screen and they could work in pairs/small groups to try to come up with a solution. Great critical thinking and collaboration going on here – and if we couldn’t get the solution before the bell rang, we would take it up the next day with most of them working on it overnight. Here are some good resources for logic puzzles:
  4. Read a story.  Yep. Even with my high school students, I would read stories.  Math related of course. You would be amazed at how they actually enjoyed listening, and of course, once the ‘story’ was finished (which might take a couple days depending on our actual time at the end of each class) we’d discuss the ‘math’. Some of my favorite books:

Students loved the challenge of these last 5 minutes (sometimes it would be more). It was a very competitive yet non-threatening time where they could test their math skills or thinking skills, work together, and have fun with numbers and logic. That time was no longer wasted – it became a time students actually looked forward to and often requested.

As you are nearing the winter break, there is probably a bit more time to spare or a bit more time needed to keep students attention.  Use that time in an engaging way that allows for some critical thinking, collaboration and a game-like atmosphere that challenges students and keeps those last five minutes productive.

Math and The Electoral College

With the election looming, and yet another Presidential Debate this evening (anyone else dreading it?) and more polls than you can shake a stick at, it seems appropriate to think about the math behind the Electoral College. I admit to really not understanding this whole system – and I know I am not alone. With the rampant conspiracy theories about the November 8 election, and a ‘rigged election’ and cries to eliminate the Electoral College and go to a popular vote only, it had me diving into “what does the Electoral College mean, why do we vote this way, and is it fair?” I think this is a GREAT conversation and critical thinking activity to have with students, especially in classes like statistics where you can actually study and do ‘mock votes’ and see what the outcomes are with or without the Electoral College.

A quick summary of what the Electoral College is – and please note, I still am a little iffy about whether I truly get it. In 1787 the delegates of the Constitutional Congress made the decision to do this indirect way of voting for the President of the USA. It was a compromise between those who wanted a) individual citizens to vote for President (1 person, 1 vote, majority wins); b) letting State legislators choose the President; or c) letting congress choose the next President. The idea was to create a method where the best candidate was chosen. Individuals in a state vote for President – the winner in that state gets all the states electoral votes (though some split the electoral votes now), and the electors (who are elected by voters),  put in the final vote for President. The person who gets the majority of Electoral Votes (270 or more) wins. Still confused? How is this fair?  Bear with me….I am hoping I can figure that out myself!

If you look at the image above, which outlines the number of Electoral votes per state, you can see a huge difference – some states have an enormous number of Electoral Votes, and some very few. As you can see – size might matter (CA, TX, FL), but not always – VA is relatively small and yet has 13 Electoral Votes compared to say Montana, a larger state with only 3 Electoral Votes. So – how is the number of Electoral Votes determined? Hawaii gets 4 vs the very large state of Alaska only 3. So – it must have something to do with population numbers, which in fact is the case. The number of Electoral Votes is the number of state representatives in Congress (both Senate and House of Representatives), which are based on the population of the state. Every state will have at least 3 Electoral Votes (2 Senators, 1 Congressman). Obviously you now see why winning states like CA, TX, FL, PA, and NY are so crucial because of their large populations and large number of Electoral Votes.

I have been reading a lot and searching for good websites that might be helpful for teachers wanting to figure this out with their students. There are several sites that talk about the Electoral College and what it is – I didn’t find these too helpful from a teaching perspective, but they may be of interest to some of you from a historical, “why do we do this” perspective.

  1. Nice interactive map – http://www.270towin.com/
  2. Article about the ‘fair or unfair’ aspect of Electoral College and the funding – not sure it answers the questions but makes you think: https://blogs.scientificamerican.com/guest-blog/the-funky-math-of-the-electoral-college/
  3. This is a nice site with lots of historical perspective and answers to questions, like does my vote count? http://www.learnnc.org/lp/media/lessons/davidwalbert7232004-02/electoralcollege.html
  4. This article makes a case for the Electoral College system being fair: http://www.politico.com/story/2012/12/keep-electoral-college-for-fair-presidential-votes-084651

Here are some sites I found that would be helpful for doing some simulations and having interesting conversations with students. Many of these are interactive, with the ability to create election results (or simulated) to get a better understanding of how the Electoral College system works, and hopefully make a determination about whether it is fair or not.

  1. This was my favorite – be sure to check out the “Play Presidential Politics” link, as it has a simulation vote where you can create your own populations for states.  Would be great for students. http://www.sciencebuzz.org/topics/electoral-college-math
  2. Lots of information (some of which I used) in kid-friendly language: http://www.congressforkids.net/Elections_electoralcollege.htm
  3. Nice lesson here – some interaction/lesson plan info as well: http://www.scholastic.com/teachers/article/math-majority-rules
  4. Yummy Math – nice lesson here (using the picture above!) http://www.yummymath.com/2016/electoral-college-vs-the-popular-vote/
  5. From NCTM – a lesson on the “fairness” of the elections – Love Illuminations! https://illuminations.nctm.org/lesson.aspx?id=2825

So – is it fair or not fair? Does your vote count? I am not sure I can give you a definitive answer. It probably depends who you are, who you want to win, and where you live. But, in my readings looking at several charts that compared the ‘weights’ of individual votes toward the outcome (i.e. Does your vote count?), I think my personal opinion is yes, your vote does count, and yes, it is fair.

Notice Alaska, with a smaller population, has a much more weighted vote compared to CA. This may not seem fair – but, Alaska, a huge state with many diverse needs and interests but with a small population, deserves an equal representation in the government, which may not happen in a one-vote majority rule election, if we look at populations sizes of CA or NY, with their enormous populations. This is why the Electoral College was created in the first place – so every state gets a fair share of representation for their interests in the outcome, no matter their populations size, and those ‘states’ with larger populations don’t end up  deciding everything. NY’s interests are vastly different than Alaska’s, after all. A popular vote would be unfair because those larger states, who lean more one way or another, would control the outcome, leaving those states with fewer people, left out of the equation, and their interests not accounted for or lost in the process. My personal conclusion – I am actually for the Electoral College, after all my reading and my still foggy, but much better, understanding of the system.

One final note – look at the overall United States (in chart above) – the total population, the total Electoral votes, and the weight of each individual vote.  It’s 1.

So YES – your vote counts – get out and VOTE!  (And make it an educated vote, based on candidates proposed policies and plans – not based on emotion).

 

Multiple Entry Points and Rich Math Tasks

I was reading this article the other day about how a strength-based approach to learning math (and learning in general) redefines who is “smart” and allows all students to succeed. In her article, Katrina Schwartz has some quotes and reflections from former students who learned math using the complex instruction method, and who were all successful.  They talked about how “math class made them feel safe, heard and able to express their ideas without fear”.  Wow – how often do you hear something like that?!!

Complex instruction is based on the idea that learning is collaborative, where students are learning using rich tasks with multiple entry points and pathways, and each student has a role and accountability. This isimage15 not a post about complex instruction however. What I was thinking about while reading the article was in fact about the Common Core Standards for Mathematical Practice and how they support what the students were expressing in the article – that math class “was a process and it required other people. It wasn’t just you and your work and not talking.”

If you actually read the 8 mathematical practices, you will notice over and over again words like communicate, justify, analyze, plan, make sense, look for entry points, reason, ask questions, make viable arguments, apply.  The practices are all about communicating and talking and finding multiple entry ways to solve problems. And working and talking with others to get there. Like complex instruction, these problems should be rich, where in fact, there are multiple entry points and possible solution pathways. Where each students strengths can support the process and help build the understanding of others. Learning is collaborative, NOT an isolating experience that a worksheet or a lecture so often create.

The Common Core gets a bad rap because so many publishers and testing companies have standardized it – by providing ‘common core problems/strategies’ that are in fact limiting and narrowly focused so they can be graded easily. When I see parents and students and teachers complaining about “common core problems”, I get so angry because what I am actually seeing are ‘forced entry points’ – meaning, rather than allowing all students to approach a problem from their mathematical strength and understanding, they are forced to choose between 1, 2 maybe 3, ways to solve a problem, which may NOT be understandable methods for them.  Therefore, NOT Common Core (or Complex Instruction). As it says in the practices: “Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution”. It does not say mathematically proficient students are given specific entry points to solve a problem.

image16My hope is that with the changes in standardized testing on the horizon under the Every Student Succeeds Act, that math teachers and classrooms can truly begin to focus on students strengths and learning, not preparing for a test. To actually provide learning experiences focused on allowing students to work from their strengths. But it requires a willingness to have a noisy classroom with students talking and collaborating.  It requires  rich mathematical tasks, not standardized worksheets and drill and practice,  that truly provide multiple entry points. This in turn requires teachers who are willing to accept multiple solutions from students rather than the traditional one-way, algorithmic approach we tend to focus on. And it requires support for teachers – in resources, training, time, and expectations.

Read the article by Katrina Schwartz – it also has links to information about Complex Instruction and great feedback from San Francisco Unified School District who has made a concerted effort to teach mathematics this way. Read the Common Core Standards for Mathematical Practice. If you are not already doing so, try to incorporate some of these practices into your math instruction. It’s not what you teach, but HOW you teach, that has an impact on students.  Every student can learn math – it’s up to you to create a culture that helps them believe that.

More than Calculators – Teacher Support & Resources

I received a message the other day from a reader who commented on how much he liked the Prizm, but because 2016-05-13_12-52-22Casio didn’t have any resources to support the learning of the Prizm, he was a little reluctant to try it.  My first reaction was “What?!! We have a TON of resources!!”  My second reaction was to ask myself why might he think this? I was able to answer my own question when I searched for our resources – the issue being they are a bit hidden among all of Casio’s other products, (which, just so you know, is of course in the process of changing as we create a more user-friendly web-page).

In the meantime, I want you to see the great teacher/student resources we have! Let me share with you the resources we have that supports teachers (and students), from complete subject-specific or grade-specific resource books (i.e. complete lessons), so sample lessons and activities (free), to online course for Prizm (free) to webinars (free).  There are teacher-created resources and quick-start guides.  Casio WANTS teachers and students to use their calculators and get the help and support they need to use them appropriately.

  1. Free online activities and sample questions: http://www.casioeducation.com/educators/activities
    • These include grade-level activities and specific Casio Prizm-vs-TI 84 activities
    • Scrolling down the page you will find sports activities for use with five different calculators
    • Keep scrolling to our Quick Start Guides for 6 of our calculators (including Prizm)
    • Keep scrolling to Subject-specific Teacher Resource Guides and Calculator Tips
    • Scroll further to see all our grade-level and subject-level resource books that contain complete lessons
  2. If you look at our products page, under Software & Additional Products, you will be able to scroll through all our grade-specific/subject-specific resource books: http://www.casioeducation.com/products/Calculators_%26_Dictionaries/Software_%26_Additional_Products/ED-WKBK-PRECALC
  3. Here’s a short-link to our Casio Lesson Library (with teacher created activities): http://www.casioeducation.com/lesson_library
  4. Short-link to Guided tours for the Prizm: http://www.casioeducation.com/resource/prizm/features/index.html
  5. 2016-05-13_12-56-04If you are interested in the Prizm, we have a whole webpage dedicated to Prizm activities and support, which includes lessons, videos, and also has the OS updates. http://www.casioeducation.com/prizm 
  6. We have a free online course for the Prizm (self-paced).  If you complete the course, you get the Prizm (fx-CG) emulator software for free. http://www.casioeducation.com/educators/online_training
  7. Free webinars on many math topics (statistics, geometry, algebra, calculus, etc.)(you do have to register your email to view these, but they are free): http://www.casioeducation.com/educators/webinars
  8. Links to manuals for specific calculators: http://www.casioeducation.com/support/manuals
  9. And let’s not forget the videos showing you how-to’s and comparisons! https://www.youtube.com/user/CasioPrizm/videos?view=0&sort=dd&shelf_id=2  and http://www.casioeducation.com/resource/HTML/edu_videoPage.html

As you can see, we have a ton of support for teachers and students wanting to use and learn-to-use Casio calculators to support their instruction and/or math learning. We hope those of you out there excited to start working with Casio calculators start using these supports. We are educators here at Casio and want you to love the calculators as much as we do!!