Tag Archives: Growth Mindset

Our First Day Message

What message do your students leave class with on the first day? How do you craft the first day learning episodes to promote that message?

Our students walked into the room with two Which One Doesn’t Belong scenarios.

Which led to a discussion about working on our math flexibility throughout the year.

We wondered what one word students would use to describe their feelings about math.

Algebra 1:

Geometry:

AP Calculus:

(I wasn’t surprised at the negative feelings towards math in Algebra 1 … but I was surprised at some of the responses from geometry and AP Calculus students.)

That led to the Quick Poll that we’ve sent now for a few years from Mindset.

We did a short number talk that I saw on Twitter:

We watched Jo Boaler’s Day 1 Week of Inspirational Math video on mindset and mathematics.

We ran out of time to do our normal opener where students find more than one way to complete a sequence of terms.

We thought about what it looks like when a team is working well together in math class.

TeamWork – Calculus (using Navigator for handhelds)

cohesive         1

everyone is building on each other’s idea 1

synchronization         1

organized discussion            1

clockwork       1

coordinated   1

everyone ends up with the correct answesr and understands   1

everyone ends up understanding the problem    1

communication and listening          1

people help each other, in an oreo 1

everyone gives input            1

everyone talking/ explaining at the same time.    1

clear discussion         1

All ideas and all teammates are listened to.           1

a well-oiled machine.            1

lots of words, pointing, and ideas    1

It looks synchronized            1

Like a well-oiled machine.    1

you are productive and no one gets left out          1

A solid conclusion shared by the entire group is reached based upon the well thought out ideas contributed each individual   1

dividing and conquering      1

efficent           1

We are very focused and productive.         1

lots of high fiving and excitement   1

lots of talking and no one hates each other           1

looks like an oreo      1

Organized discussion            1

explaining thought processes to each other          1

success           1

helping each other and an oreo      1

TeamWork – Geometry (using Navigator for Networked Computers)

People are building off of other ideas and are able to make an educated descision using everyone’s input.           1

When a team is working well together they may not always agree on the answer or how to get to it; they always work to find the right one no matter how difficult or stressful it may be.            1

When a team works well together they are listening to each other and trying to trying all methods (to solve). Everyone listens as much as they talk.     1

When a team is working well together, there will be a lot of communication and listening to others’ ideas and meathods.          1

The team looks uniform and united, and if you fail, then your team can figure out what to do better next time.   1

People bouncing ideas off of each other and creating new ideas or improving old ones. Even if some people are wrong, people correct them in a kind way and tell them how to correctly solve a problem. All team members are putting in effort and carrying their weight, not just leaving others to do all the work. The team finds multiple ways to solve the problem and chooses the best one.    1

All team members working together and solving problems at the same time individually then comparing answers and learning from different views.  1

When a team is working well together, each individual student listens to one another and actually thinks about each teammate’s idea and sees it as a viable solution. A team is working well together when they get along and are respectful to one another.        1

When a team works well together, they work easily and doesn’t argue when someone has a different answer than the other person. And they get the answer right. They should be able to recieve and give feedback from the other.       1

When a team, in math, is working well together, I think of a deep conversation of different ideas. I see different solutions and ways a proplem could be solved coming from all sides of the table… if you know what I mean. 1

When no one argues and everyone considers others solutions to a problem.  1

It looks very good and fluent when your team is working well together. When you have a team to help bounce ideas off of each other and to help each other reach the goal they need it is very useful. Everybody is going to make mistakes, and when your team knows that and will help you to find what you did wrong, you will have a larger success rate.    1

When your team is working well together, every member is sharing their thoughts and ideas, right or wrong. The team members aren’t embarrassed about getting the wrong answers because they know that their other teammates will help them to understand their mistakes and learn from them. Each member comes up with different ideas when the team works together, so that way every person benefits wih a new way of thinking.     1

The team is able to get more done, and do it quicker.      1

When a team is working well the group closer together and they’re all listening to other team members input and are also giving their own input.  1

It looks productive and focused. We are all concentrating on the problem that the team has to solved.      1

It looks like we all know what we are doing. It looks like we have more ideas and know more ways to solve our problem. It makes us look as if we understand the problem more and in most cases we probably do, when we work together well.     1

You are makeadvancements and improve one another and also agree upon an answer.       1

When the team is working well together it helps other people of the team to increase their knowledge because each person may see things in a different way.            1

Everyone is not arguing. People are using teamwork and getting the right answer while teaching others on the team how to do it differently.            1

Everyone is learning and helping each other when they may not know the answer to something or need help figuring out how to do something. No one makes fun of anyone if they get a wrong answer because we all need to learn and grow.    1

Somebody will suggest something and people will get excited or say “”yes!””. Then another person will suggest something and everybody will enjoy making progress. People that originally disagreed will change their minds because of something another person explained. They will keep working together until the project is finished.      1

The team is working well when they all have corresponding ideas that come together to get a problem correct.   1

When a team is working well together the team everything flows and everyone is participating. Everyone is helping, ideas are exchanged, and people are learning. Everyone is set on one goal and everyone is headed to achive that goal.           1

It is when everyone in that team is listening to and coming up with ideas. The whole group is cooperating and completing the task given. That is when a group is working well together.     1

Everyone understands the objective and is comprehending well. They understand why and how the team got the answer. No one is confused and everyone feels like they are making a contribution to the work     1

We talked about Popham’s four levels of formative assessment.

Our goal is for all students to reach the learning goals and not just for the “smartest” and “fastest” to do so. Which means that we will have to help each other. Which also gets into Wiliam’s Five Key Strategies for formative assessment, in particular, activating students as learning resources for one another.

The bell rang before I could have my students reflect on what they learned and what they will do in geometry this year, so I sent them a Google form to complete outside of class.

Algebra 1 students answered a Quick Poll before leaving about what they learned.

today, I learned that anyone can learn math

This year i am going to improve in math   1

About my teachers to be better at math.   1

I have learned If I practice I can become better.

In math this year, I am going to practice more.     1

I have learned that I have three very cool teacher that will make math fun this year and I also learned that math isnt everybodys fav but evryone a math person

In math this year i am going to get better at it      1

You can’t be a math person everyone is good at math it you pratice, so i am going to pratice.           1

I have learned that all three of my math teachers went to NWRHS and in math class this year i will not get bored in class         1

i have learned to think outside of the box. i am going to learn to thinkoutside the box          1

that we have three teachers.

try to work out everything better. 1

that math will be exciting this year and every one is good at math       1

That everyone is good in math in some way. In math this year, I am going to have an A.       1

I have learned that my teachers are cool

in math im going to inprove.            1

I have learned how to think outter box .

I am going to try to do better than the year before in math.       1

I have learned this year to be more excited to more about math.

In math this year, I am going to try my hardest.   1

That I have 3 math teachers. Also math wont be so bad. 1

pay attention 1

nothing and this year I’m going to start fresh       1

I have learned about my classmates and teachers.

In math this year, I am going to try harder.           1

I learned my other classmate’s names and how to do Four 4’s.

In this year of Math I plan on working harder and to advance in my knowledge of Math.     1

I have learned that you need to thing hard to get some of the questions right.

In math this year, I am going to make my math skills better and i want to work math fast.   1

I learned that everyone can do math. I math this year, I will work really hard and do the best I can.          1

I have learned how everybody can do math even if you are not a math person and your brain grow if you work it out. In math this year i am going to try to learn more and get a better grade in math.   1

I have learned in this class period to hold a more open mindset towards math and the many different answers to a mathmatical situation. Different methods can be accepted, and not every person will see math in the same light. I am going to learn to find an excitement in the subject of math this year, hopefully.           1

i have learned peoples names in my class in math this year, i am going to make good grades           1

I have learned that anybody can learn algebra and be good at it. This year I’m going to payattention and do my best at algebra.         1

I have learned that everyone is smart at math, people just need to embrace it.

In math this year, I am going to become smarter in math.          1

I have learned… that you can get differnet answers just by using 4 4s, also I learned how everyone is well in Math, it’s just kids with more experience are more better in it.

In math this year, I am going to.. learn more about math and hopefully actually start to like it.        1

i have learned everybody is good at math and i am going to try my best to make good grades         1

Everyone can learn about math very well, and no one is a math person. I am goin to learn about everything that i can and try my best at it.I am also gonna try and figure out problems the best of my ability.   1

I have learned that the more you practice and work your brain the more it grows.

In math this year, I am going to practice and work my brain so I can learn and get better.   1

Today I have learned that practicing something, even if you don’t fully understand it, still helps. This year I am going to try my hardest to achieve high grades in math.           1

I have learned today in class, everytime you have to find something out there can always be more than one way to it.

In math this year, I am going to try and learn new things that I didnt understand last year.            1

Today I learned that no matter how much i get frustrated that i will always have someone to leaN ON THIS CLASS TO HELP ME WITH MY SITUATION … In math thjis year imgoing to succeed in all things all I do my grades will also be also better.           1

i have learned that anyone can be good at math with good practice.

in math this year im going to learn different things and hopefully get better at math.           1

practice math everyday and that it’s okay to make mistakes because we learn from them.   1

that we can learn things easier by practice so in math this year, i am going to practice if i have troubles until i fully understand it.       1

I have learned that the brain can grow with what you learn.

In math this year, I am going to study more.         1

I have learned that your brain is always changing and to get better at something you have to keep practicing.

In math this year, I am going to practice what I’ve learned in order to get better at it.           1

I have learned that your brain can grow just by learning new things.

I’m going to practice more on math because, if you practice more on something you can get better at it.    1

That math doesnt always have t0 be boring, it cab be reall        1

i am going to try my best to past     1

I have learned that everyone is capable of being in the highest math class there is. There is no such thing as a “”math person””. In math this year, I am going to try my hardest to maintain the highest grade I can, and pay attention in class in order to make good grades.   1

practice and do my best to make a good grade even thooe me and math REALLY dont like eachother. but im going to try to do my best            1

IF you practice you can get better at it       1

I learned that anyone can do math well and in math this year, I am going to try.        1

that your brian can grow the more you practice something , this year i am going to pay more attention.    1

I have learned that anybody can be good at math, you just have to work for it.

In this year of math, I am going to pay more attention than I did last year so I can get better and so I can get good grades.        1

I have learned if I keep practicing and going to different levels I will become better.

This year, I am going to study and practice math on different levels so, I will become better at math.         1

We didn’t really have a lesson, but I have learned about how the brain works with how good you are at something. In math this year, I am going to have no tardys, have straight A’s, and not disrespect the teacher in any manner.    1

that i dont have to dread coming to math. i can grow and learn from it. im going to try to make all a’s        1

You can get better at something if you practice at it.

I am going to try harder. And give up if I don’t understand it.   1

I have learned that as long as I continue to practice math or algebra I will slowly get better at it.

In math this year, I am going to attept to be more optemistic about the work and try harder to get better grades.           1

be able to be good in math by the end of the year. and that i will be able to succeced in anything that i do by just practicing.    1

I learned that when you have a difficult time with a question that your brain is growing at the same time.           1

We went from math is “complicated, hard, frustrating, …” to “I can do this” in 95 minutes. I believe our students left hearing our first day message:

Everyone can learn math.

Our brains are growing when we struggle to solve a problem.

There isn’t just one way to solve a problem.

Learning more than one way to solve a problem grows our mathematical flexibility.

Working with a team is an important part of how we learn mathematics.

And so the journey continues as a new school year begins …

Posted by on August 17, 2015 in Student Reflection

The Last Day of Class

Another school year has finished (two months ago), and a new one is about to begin.

Our teachers did a lot to promote growth mindset this last year.

Many of us sent our students a poll with statements from Carol Dweck’s book, Mindset, on the first day of class

and again on the last day of class.

You can see some change in the way that students responded.

I have wondered whether talking about mindset and promoting growth mindset makes a difference in what and how students learn. I know plenty of teachers are skeptical. I’m convinced that it matters.

Many students participated in Jo Boaler’s How to Learn Math: For Students online course through Stanford University. I heard students talking about making mistakes, their brain growing, and synapses firing on many occasions throughout the year.

What has convinced me more than student responses throughout the class, though, are the voluntary reflections that my students have offered. I received a handwritten letter at the beginning of May from a former student who no longer attends our school. An excerpt follows:

“When you taught my geometry class last year you polled us at the beginning and the end of the year to see if our opinions on innate/static intelligence vs. one’s ability to improve intelligence had changed. I just want to say that though I was doubtful at the time, this idea of an evolving and increasing intelligence through questioning and learning through wrong answers has stuck with me and served me well. I was once pretty insecure in my academic abilities: yes, I made good grades without much trouble, but there’s always someone faster or more confident or more eloquent, and so much of my identity was wrapped up in being a ‘smart’ kid that I was often afraid to speak up and make mistakes. Now, though my grades and academic integrity are still very important to me, I don’t see successes and failures quite so black and white. Rather, I try to see it all as a learning moment, and I thank you for introducing me to some of the ideas of growth mindsets and ‘GRIT’.” – CM

This thoughtful reflection a year after the class ended is coupled with a thoughtful reflection from another student who wrote as the class ended last year. You can see his reflection in this post.

We will start another school year on August 6 … our students are going to hear the message not only that they can be successful in mathematics but that we, their teachers, want them to be successful in mathematics … our students are going to be greeted with open-ended problems that are accessible to all (many of which will come from youcubed’s Week of Inspirational Math) – problems that allow them to realize from the beginning that we don’t all think the same way and that making our thinking visible to others is a good and important learning opportunity for all … our students are going to set norms for how the class will learn together throughout the year … our students are going to hear from Carol Dweck on the power of “Yet” and they might even hear from Sesame Street, too.

What message will your students hear on the first day of class? What will they say about your class when asked how they think classes are going to go this year?

I look forward to school starting again, as the journey continues …

Posted by on July 25, 2015 in Student Reflection

Tags: ,

Growth Mindset & GRIT & SMP1

If we want our students to be mathematically proficient, and if we want mathematically proficient students to make sense of problems and persevere in solving them, how will we help them when they don’t? or won’t? or feel like they can’t?

Jill Gough and I have been working on leveled learning progressions for the Standards for Mathematical Practice. Here is the visual for SMP1.

I wonder how much making sense of problems and persevering in solving them has to do with the work of Carol Dweck on Mindset and Angela Duckworth on GRIT. I had the opportunity to hear Angela Duckworth speak at the AP Annual Conference a few years ago.

One of the ways that our students can earn Problem Solving Points in our course is to determine how much GRIT they have:

Angela Duckworth says that the key to success is GRIT. Watch her TED Talk. Then determine how much GRIT you have. Then email your instructor a reflection with a response to at least one of the following prompts:

I like …, I wish …, I wonder …, I will …

We have enjoyed reading our student reflections on GRIT.

I like this idea and I do believe in it. I believe a lot of people don’t really understand how extremely important it is though. I think a lot of people would watch the video and think “oh cool grit whatever” and not realize that that’s more than likely is what will get you hired coming out of college and that it will probably take you farther in life than anything else. I wish more people understood that. I wonder if GRIT is something you can turn off and turn on, like we know it can change but can you just decide you want to be gritty for this one thing and be gritty.

I like that Angela Duckworth and Princeton (and you too, Mrs. Wilson) are speaking out and beginning to normalize this idea that intelligence is a fixed point, that we can’t change, is all wrong. Yes, it’s true we are not all rocket scientists- but should the people with less of an initial gift for learning have any less of an education? I’ve felt that in our school and our society there are a lot of limitations, including how high you rank in standardized tests, that influence how much you are pushed and expected to succeed. However, I don’t think that people who rank lower in testing scores should be shoved aside and given just the bare minimum. If the fear of failure was not so prevalent in the school system, maybe kids would believe that they can succeed after the initial failed attempt; that not just the ‘smart’ kids will be the ones to succeed.

I wish that someone had told me about this sooner, and that we were setting the goal at something more like GRIT, not just if you get the answer faster or easier than someone else. I’ve been in the smart track my whole life so I might sound out of line, but even I know that I won’t be a mathematician or the one to find a cure for cancer. No matter how hard I try, there is reality to remember, and though I’ve had encouraging parents and many very helpful teachers, I’ve still had the idea of my failure put into place. Can I wipe away that misconception that I was hardwired with a certain capacity for greatness? Even if I do, I feel that I just wasn’t born with a lot of determination. I’m sad to say my GRIT score was only 2.7 or so.

I wonder if this idea will die away or flourish in the new minds of the next generation. Before I came to your class, I’d always had teachers who would seem to forgive our wrong answers, but never one who said that, if used in the right way, it could actually help improve our overall smartness. I wonder how I could improve my measly 2.7 GRIT to something stronger. I wonder if I’ll ever find a motive to push me through, something to fuel my resilience.

I will work on not giving up; what better time to muddle through than high school? Opportunity to dump homework and just watch netflix abounds, but I will make a conscious effort to improve my GRIT and become a more responsible, diligent person.

I will definitely try harder in school and in other commitments after watching this video. The grit survey site gave me a grit score of 3.88. It also stated that I have more grit than 70% of the US population. Wow! I am shocked that 70% of the US has a grit score lower than 3.88. I am not fully satisfied with that score, so I will try harder to increase my grit score.

I took the grit survey and my result was 3.25. That makes me grittier than more than 40% of the United States of America. I will work hard to persevere on any project I begin. When I do projects, it always feels like I work so hard when I start, but as I get closer to being finished with it, I don’t work as hard as I could. I need to work on having patience to see something completed. I will also work to not get so discouraged when I get something wrong or when I don’t understand something. Once I start to do some of these things, I will become more successful and grittier.

I like how Angela Duckworth developed a grit questionnaire and how she admitted that she didn’t know how to instill grit in kids. I also liked how she ended with “In other words, we need to be gritty about getting our kids grittier.”

I also took the grit survey, and got a 3.5 out of 5, which is apparently better than 50% of the US population. I don’t if I should be happy that my 70% is better than nearly 160 million people or sad for the same reason.

Does it help for us to make our students and children aware of growth vs. fixed mindsets? Does it help for us to purposefully use growth mindset and GRIT language with our students? And whether or not research shows that it helps, can’t it not hurt if we want all of the learners in our care to make sense of problems and persevere in solving them?

The First Day of School

What do you do on the first day of school?

Our teachers did a lot to promote growth mindset, learning math using the math practices, and norms for teamwork.

More of us asked students with which statement(s) they agree, from Carol Dweck’s Mindset. We were pleasantly surprised at how many of our students have a growth mindset towards mathematics (statements 3 and 4).

We will continue to work on promoting mindset and making our classrooms a place where errors are welcome – where making mistakes and correcting those mistakes is evidence that students are learning. Some teachers showed one of Jo’s videos about mindset and mistakes. We are also encouraging students to sign up for Jo Boaler’s course through Stanford, How to Learn Math: For Students.

Several of us asked students what it looks like when your team is working well together.

There is no yelling or fighting.

Everyone contributes; we help each other.

Create a variety of ideas and listen to all ideas. We build off of one another’s ideas.

Constructive Criticism− if someone gets the answer wrong, don’t lower their self-esteem by saying stuff like “”Ha. you got it wrong!””.

Agree to disagree respectfully.

Expand knowledge, learn life skills, and be open minded.

We have stimulating conversations.

We make progress.

Teams also work better wearing matching shirts.

Synergy. The whole is greater than the sum of its parts.

We debuted our Learning Mode poster so that we make students more aware of how they should currently be learning – alone, with a partner, with a team, or participating in a whole class discussion. The best moment in my second class was when I looked up and noticed that a student sitting near the front had changed the learning mode for us based on my verbal instructions. The class had already nominated her to be in charge of the poster!

One of our other teachers used video clips from the Big Bang Theory to help students have a better understanding of the Math Practices. You can find them under “Going Deeper with the Big Bang Theory”.

Many of us gave our students a copy of the Math Practices Poster that we have hanging in our rooms.

Another teacher assigned each team a Math Practice and asked them to make some kind of visual representation of the Math Practice. They hung the posters, and then all of the teams viewed the posters and matched the practice to the poster. Another class “judged” all of the posters for each practice at the end of the day and voted on which one will be hung in the teacher’s classroom. Can you tell which practice is represented by each poster?

All of us started with open-ended, low floor high ceiling tasks so that every student had access to starting the task. One student told her teacher that “geometry is going to be fun”. Another student told his teacher that he was so glad they did something during class besides going over policies.

This year’s journey is off to a good start, and I am thankful for the good company of my math department along the way …

Day 180 – Embracing a Growth Mindset for Learning

Another school year has ended, and so I want to report on the first day of the second semester and the last day of class. This report will make more sense if you know about my first day of class.

During the year, we talked a lot about learning from our mistakes. Students also had the opportunity to learn more about GRIT through the following problem solving points opportunity:

Angela Duckworth says that the key to success is GRIT. Watch her TED Talk here. Then determine how much GRIT you have here. Then email your instructor a reflection with a response to at least one of the following prompts:

I like …

I wish …

I wonder …

I will …

A reflection from CM during the fourth quarter follows:

I like that Angela Duckworth and Princeton (and you too, Mrs. Wilson) are speaking out and beginning to normalize this idea that intelligence is a fixed point, that we can’t change, is all wrong. Yes, it’s true we are not all rocket scientists- but should the people with less of an initial gift for learning have any less of an education? I’ve felt that in our school and our society there are a lot of limitations, including how high you rank in standardized tests, that influence how much you are pushed and expected to succeed. However, I don’t think that people who rank lower in testing scores should be shoved aside and given just the bare minimum. If the fear of failure was not so prevalent in the school system, maybe kids would believe that they can succeed after the initial failed attempt; that not just the ‘smart’ kids will be the ones to succeed.

I wish that someone had told me about this sooner, and that we were setting the goal at something more like GRIT, not just if you get the answer faster or easier than someone else. I’ve been in the smart track my whole life so I might sound out of line, but even I know that I won’t be a mathematician or the one to find a cure for cancer. No matter how hard I try, there is reality to remember, and though I’ve had encouraging parents and many very helpful teachers, I’ve still had the idea of my failure put into place. Can I wipe away that misconception that I was hardwired with a certain capacity for greatness? Even if I do, I feel that I just wasn’t born with a lot of determination. I’m sad to say my GRIT score was only 2.7 or so.

I wonder if this idea will die away or flourish in the new minds of the next generation. Before I came to your class, I’d always had teachers who would seem to forgive our wrong answers, but never one who said that, if used in the right way, it could actually help improve our overall smartness. I wonder how I could improve my measly 2.7 GRIT to something stronger. I wonder if I’ll ever find a motive to push me through, something to fuel my resilience.

I will work on not giving up; what better time to muddle through than high school? Opportunity to dump homework and just watch netflix abounds, but I will make a conscious effort to improve my GRIT and become a more responsible, diligent person.

I sent a Quick Poll on the first day of the second semester to find out whether any students had changed their thoughts on intelligence since the first day of school. And then I sent it again on the last day of class. The statements are from the first chapter of Mindset by Carol Dweck. Dweck suggests that those who agree with the first two statements tend towards a fixed mindset regarding their intelligence and those who agree with the last two statements tend towards a growth mindset regarding their intelligence.

One class of students marked the statements as shown below on the first day of class.

The same class marked the statements as shown below halfway through the school year.

And marked the statements as shown below on the last day of the school year.

A few days later, there was a card on my desk from one of my 9th grade boys. I’ve included a picture so that you will really believe it, but I am going to type the text as well.

Dear Mrs. Wilson

In a class of 32, I think moving from 12 students with a fixed mindset to only 3 students with a fixed mindset is an important result of the school year. But I know that it wouldn’t have happened without the tireless work of Jo Boaler, Carol Dweck, and Angela Duckworth to educate educators, parents, and students about how we think about learning.

So here’s to the end of another school year as the journey continues ….

1 Comment

Posted by on May 26, 2014 in Geometry, Student Reflection

Day 1 – Embracing a Growth Mindset for Learning

Another school year has begun, and so I want to report on the first day of class. The report won’t make as much sense without knowing what has been on my summer reading list.

Embedded Formative Assessment – Dylan Wiliam

5 Practices for Orchestrating Productive Mathematics Discussions – Smith & Stein

Mindset – Carol Deck

What’s Math Got to Do with It?: Helping Children to Learn to Love Their Most Hated Subject–and Why It’s Important for America – Jo Boaler

Teach Like a Pirate – Dave Burgess

On top of that, I’ve been taking Jo Boaler’s course on How to Learn Math.

After reading what I have read, I knew that somehow the first day of class had to be different this year.

In the 4th session of Jo Boaler’s course, she talks about a framework for a growth mindset task that they developed at Stanford.

1. Openness

2. Different ways of seeing

3. Multiple entry points

4. Multiple paths / strategies

5. Clear learning goals and opportunities for feedback.

Consider the following task for a geometry student as students are beginning to think about inductive reasoning.

Finish the sequence: 2,3,5,8,12,17,…

A few years ago I changed this task for day 1 of geometry.

Now the directions are to find and explain at least two ways to finish the sequence.

2,3,5…

2,4,8,…

5,3,6,…

So what is the difference between the two tasks?

I want students to realize from the first day of class that there will often be more than one way to answer tasks, that we are not all going to see the same thing, and that being able to explain our thinking is important. Even if we arrive at the same solution, we might use different paths to get there. I also want students to realize that part of being a good student is being a good listener, so that we can really begin to get at constructing viable arguments and critiquing the reasoning of others.

I collected student responses to the sequences using TI-Nspire Navigator.

Our discussion encompassed recursive sequences, prime numbers (and composite), the Riemann Hypothesis, RSA Encryption, powers of 2, memory storage for electronic devices, the Fibonacci sequence, and more.

In light of this task, I passed out the CCSS Math Practices Handout that our department made last year and asked my students to reflect on which practices they had already used in class (they suggested make sense of problems and persevere in solving them, reason abstractly and quantitatively, construct viable arguments and critique the reasoning of others, look for and make use of structure, look for regularity in repeated reasoning).

We talked about using the practices to do math, and I told them that I will want them to reflect on using a practice at least once each quarter using the CCSS MP journal prompts that I had copied on the back of their handout.

Finally, we had a discussion about fixed and growth mindsets. I sent the following poll and asked students with which statements (from the first chapter of Mindset) they agree.

Dweck suggests that those who agree with the first two statements tend towards a fixed mindset regarding their intelligence and those who agree with the last two statements tend towards a growth mindset regarding their intelligence.

One class of students marked the statements as shown below.

I shared some of the research that Dweck cites about growing your brain bigger (creating synapses) when you make and learn from mistakes. I also told my students that I can look back in my own life and see a change from a fixed mindset into a growth mindset. We are certainly not finished having this conversation, but I hope that my students will begin to realize that they can do something to change their intelligence and embrace the work that will require.

So here’s to another school year as the journey continues ….