Mathematical Mindsets: A Collaborative Book Study 6

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This chapter provides research that supports the need for teachers to provide rich math activities for all students regardless of race, gender, or “math aptitude.” It’s also important that we don’t separate math students into gifted and not.

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This next quote summarizes my thoughts exactly…

“The labeling of students as gifted hurts not only the students who are deemed as having no gifts but also the students who are given the gifted label, as it sets them on a fixed mindset pathway, making them vulnerable and less likely to take risks.” (Boaler, p. 94, 2016)

Hard work, persistence and a growth mindset are better judges of math success than speed and the ability to turn in homework.

My Big Takeaway

Provide rich math activities for all! All students are capable of doing higher level math.

Three Four Tips for me when working with my students

1.  Avoid math groups that make it obvious that there are “levels” in my classroom

While small groups are crucial to teaching, the groups can be diverse and flexible so students don’t feel that they are in the “smart” group or in the “low” group.

2.  Make math learning a positive learning experience

Girls especially need the message that they are capable of doing excellent math thinking.

3.  While this is not an issue at my school, it can be repeated – get rid of advanced math and gifted programs

These programs send out the wrong message.

4. Oh and I have one more, no homework!

Students who might benefit the most don’t have ideal situations to complete and gain from it. Also homework causes unnecessary stress, less valuable time with family, and often doesn’t help students to understand math and will sometimes have the opposite effect because the homework can be uninspiring.

Thanks for reading and lets revolutionize math learning!


Mathematical Mindsets: A Collaborative Book Study 5

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This chapter turns the theoretical into practical, by providing concrete examples of making rich math tasks. Traditional math classroom teachers show the methods for solving math first and then the students would solve similar problems over and over. To make math engaging and exciting for students, the reverse needs to happen: give students problems and challenges and then see if they can develop methods. In this chapter, various examples and case studies are presented, as well as six guiding questions for teachers to develop these tasks.

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The one that made an impact on me, is “Can you add a visual component?” We forget that math is a visual process of seeing patterns and manipulating spaces. Most teachers, when presented with the requirement of teaching type of triangles (right, obtuse, acute, equilateral/angular, scalene, isosceles) will rely on showing examples, labeling each kind, and then having the students follow up with a worksheet or two. Unfortunately students might not learn that a triangle can have multiple characteristics, and might not have the opportunity to think “Can a triangle have two obtuse angles?” An example task that I have created helps make this triangle requirement more engaging.

  1. Provide construction paper, scissors, rulers to each student.
  2. Form groups of about 2-4.
  3. Using the ruler, fill up the whole paper with only triangles. Each triangle should be bigger than their fist.
  4. Cut out the triangles.IMG_0266
  5. Have the students sort the triangles. (Most students will sort by color and size.)
  6. Challenge them to sort another way.
  7. Challenge them to sort still another way. Every triangle has to be sorted, no triangle can be left out. Keep challenging them.

At the end, each group displays their favorite sorting, and then the rest of the groups get an opportunity to view them, with each group presenting how they sorted them.

We discuss each of the ways and they use words like straight angles, or two long sides, or all sides the same or all sides different. We see that a triangle can be sorted multiple ways and we make two categories of sides and angles. They use their words to describe each of the types and then I tell them “What great mathematicians you all are” and “Here are the terms that previous mathematicians used”. Then I tell them the actual terms and we match them up. They are now hooked and totally listening. At this point they want to “capture” this moment, so I let them make posters, brochures, etc, with the triangles they cut out.

My Big Takeaway

Try to reverse the traditional teaching method.

Three Tips for me to remember when planning math

1.  Add more visual opportunities for my students to explore math

2.  Provide opportunities for students to work as a group and present their findings to each other

3.  Don’t worry! Take the time to create rich tasks, make it a priority!

Thanks for reading and lets revolutionize math learning!

Start the Math School Year with some Fun! (Chance to win a $10 TPT gift card)

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Math needs to be fun! And it should be also be engaging and challenging and rewarding and inspiring and motivating and  _______ . But unfortunately too many adults and students don’t think so and would probably have different descriptors. Teachers need to lead the revolution of making math great again ;)! And it certainly can be.

Here are some ideas for starting the math school year off with some fun:
Capture the summer memories

Take polls and make class graphs to display around the classroom. Here are some ideas:

  • Summer movies
  • Pokemon Go levels or characters caught
  • Vacation destinations: beach, camping, relatives, etc.
  • Books read over the summer
  • Favorite summer foods (I love watermelon!)

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Make a math game center

Make a game center full of board games and puzzles and don’t just have them for special occasions or for finishing work early, it should be a part of your regular math routine. You can even allow families to check them out over the weekend. Here are some of my favorite board games that aren’t too mathy (and don’t take too long to play):

  • Mastermind
  • Monopoly (this takes too long for a class session though)
  • Checkers/Chess
  • Connect Four
  • Tangrams
  • Rush Hour
  • Sumoku
  • Battleship
  • Rummikub
  • Mancala
  • Tangrams
  • Sets
  • or any game that counts like Chutes and Ladders and Candy Land.

I made this game for my 4-5th graders. The answers to the game cards are the answers the students give before they play the game, like how many pets do you have and what time do you wake up in the morning. It’s simple to set up, just needs to be printed, add a die and you are ready to go!

1I also have this collection of math games that focus more on logic than math skills, so it’s great for all ages and levels. I have a set ready for families to check out too! It’s a best seller in my TPT store, so grab it while it’s on sale!

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Don’t start with a test

Nothing says math is hard, like giving your students a test the first week of school, to see what they retained over the summer. I know, I know you need to know what “level” your students are. But wait. Play games with them, make people patterns (striped shirt, shorts, striped shirt, shorts), observe their thinking, have a pattern party, start with a whole class rich math experience, like what does a million look like? I did this the first weeks of school, after reading “How much is a million?” and “How big is a million?” and “Millions of Cats.”

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We thought of different strategies of figuring out a million pieces of rice: by weight, surface area, counting groups of hundred, etc. It was a great way for me to see “levels” without testing and stressing.

For my 4-5th graders, we started by collecting recycling materials, like milk cartons, cans, and cereal boxes to design a desktop organizer. It’s a great way to get them thinking about geometry shapes. Geometry will be our theme for the year.

Alternatively, you can also give them a Math Attitude survey. Find out more on how to make your student’s beliefs visible, from my friend at Math Coach’s Corner.

I hope you have a great start to your school year and check back here often for more math tips to make math fun!

Thanks for reading! – Evil Math Wizard

Don’t forget to enter for a $10 TPT gift card! FYI – Three ways to enter: leave a comment on this blog post, follow my TPT store, or get free math tips by entering your email address in the box in the upper right corner.

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Mathematical Mindsets: A Collaborative Book Study 4

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I’m fortunate enough to have attended a progressive school where playing and problem solving with math was more important than being fast and accurate. This philosophy helped me through all aspects of my career. I became a teacher later in life after over ten years in software product management (big dollar pay for solving problems!) I volunteered in my daughter’s first grade class and knew that I could help students love math. So I transitioned to a teacher. Fortunately I know that understanding math concepts is key to loving math. Today (school started last week), a former student came into my class and I invited her to talk to my class about the “math struggle” that they will all feel is much more rewarding when you work through it, than if your parents give you the shortcut! She told of a story when she went home and her mom told her the shortcut to dividing decimals and when she returned to school I asked her how the shortcut worked. She spent over a week figuring it out, and she did!
This chapter includes various examples with research, that shows the importance of students understanding concepts before formulas.

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Also a key concept that really resonated with me, is that in order for students to properly file away a small nugget of information in their hippocampus, the information needs to come from a huge brain explosion. Meaning the brain needs to explore, play, expand, and try a variety of ideas before the new knowledge can be compressed. To often, teachers try to teach the quick and easy math routine, but with out the concepts, the information nugget doesn’t find a “hook” in the brain to attach to.

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My Big Takeaway

To enjoy learning math, students need to explore, play, and think deeply about concepts.

Three Tips to help my students think deeply about math

1.  Add math play to my daily math routine

I can create a math center full of puzzles, Tangrams, blocks, that students can just play with. I think this will work for all grades!

2.  Memorizing math facts aren’t important to be successful at math

I will make understanding the concepts the important step so that facts and fluency make sense.

3.  Provide math processing time

I need to provide a time for students to think, explain, and reflect on their math knowledge.

Thanks for reading and lets revolutionize math learning!

– Evil Math Wizard

Mathematical Mindsets: A Collaborative Book Study 3

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I teach primarily math to 2-5th graders.  A 2nd grade teacher visited my classroom while I was having a “pattern party.” She said to me “We don’t get to teach patterns anymore because of Common Core.” In my head I said, “Wait, what?” But she further explained that there are not any common core standards that explicitly teach patterns so the “curriculum” management team didn’t schedule them into their district curriculum map. Scary, right?

This brief conversation popped immediately in my head as I read this chapter about the Creativity and Beauty in Mathematics. Exploring patterns, playing with patterns, creating patterns, and identifying patterns are essential for strong math minds.coreI love teaching math, and I want my students to love math as much as I do. So I try to make math fun and engaging for them. So I start the school year (2 & 3 grade) with patterns (no numbers involved).  We make people patterns, shape patterns, we go on walks looking for patterns, and I emphasis the importance of patterns. Then we take turns explaining to everyone the patterns we noticed. It’s important to communicate and explain our thinking.

As explained in this chapter, the importance of thinking, problem-solving, and teamwork are crucial skills to Fortune 500 companies (Boeler, 2015, p. 28-29). And these skills can be achieved if we worry less about calculating (step 3 below) and more about the other important stages of math.

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My Big Takeaway

Learning math is more than calculating – finding problems, solving them with collaboration, and communicating the results.

Three Tips To Help My Students Make Real-World Connections to Math

1. Make Team Math Projects

I need to take the time and creatively think about how I can include more team math projects. I think most math topics can be taught that way, though it does take more effort on my part. I created a project for perimeters, with teams creating a bids for installing fencing around pools at an apartment complex. My students love doing it!

2. Math Class Should be More Thinking and Less Calculating

Instead of posing problems to calculate, I should spend time with my students just thinking of problems, without even calculating, but rather figuring how to solve them and what strategies to use. That way there would be no emphasis on getting an answer.

3. Discuss Math In Everyday Topics

Politics and the Olympics are rich with engaging math discussions. For example, this article on the mathematical break-down of permutations to explain the likelihood that Melania Trump plagiarized Michelle Obama’s speech would be a great discussion. But instead of sharing the mathematician’s process, I could discuss “Is there a way we could figure out if she plagiarized the speech?” And we would explore different strategies and theories, though we wouldn’t necessarily be able to come up with a definitive answer, the discussion would be fun!

I love how this book is logically explaining how math is so important and beautiful too! Onto the next chapter!

Click here for more insights on this chapter:

Related Topics:

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Mathematical Mindsets: A Collaborative Book Study 2

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This second chapter is eye-opening, especially for our current culture of rewards and prizes for flawless though usually easy effort.  Our culture believes that mistakes are bad and reflect the effort. Though as a teacher, I know that a student who spent hours on an assignment with many mistakes, learned more than another student who spent minutes with few mistakes. 
My Big Takeaway
Wrestling with mistakes grows the brain the most!
Three tips to help encourage students to MAKE MISTAKES!

1. Don’t be afraid to make mistakes.
Mistakes make the brain grow and spark! Mistakes should be renamed to “brain sparks.”

2. Develop a culture that celebrates mistakes!
I think I should maybe make a “My Favorite Mistake” bulletin board, with my students filling out a form that explains the mistake they made and what they learned and did about it. And they attach this form to their work and then post it on this bulletin board.

3. Have a Mistake of the Day problem.
Using students work with mistakes (I can also make up some work), we would discuss the misconceptions and talk about solutions and changes.

Math is about learning and growing. I need to celebrate mistakes! Can’t wait for some concrete examples in the next chapters of the book. Click on the link below to view other teachers’ insights on this chapter.

Mathematical Mindsets: a Collaborative Book Study 1

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As a teacher I really wanted and needed to read this book, but like most teachers I lacked quality time during the school year to really give this book the focus it requires. So I, along with other teachers, are reading this book over the summer and will be blogging about our learning and goals. So let’s get started!
 
This first chapter sets the tone for the book by exploring how our brain is flexible and is capable of more than we previously thought. Our brains can be open to new information and that means that “no one is born knowing math and no one is born lacking the ability to learn math” (Boeler, 2015, p. 5).
My Big Takeaway
It’s so important that teachers and parents used proper words to encourage students to have an open growth mindset and that using phrases like “You’re so smart” while sound positive and good are actually worse than saying nothing at all since students who are “smart” have a hard time exploring ideas and solving problems that are challenging and might not make them look “smart.”
Three tips to help encourage a math mindset for my math students 

1. Math is cool!
And everyone is capable of enjoying and exploring math at a higher level. Students (of all genders, races, and income levels) need to think that math is cool. How as a teacher can I encourage that in my classroom and school?

2. Make math fun!
I vow to make more math projects that encourage exploration, problem-solving, and team work. Especially projects that are real-world, have multiple answers and multiple approaches. My students should get to “play” with math.

3. Help parents help their students.
As part of curriculum night or an math workshop for parents, we will discuss growth mindset and ways they can positively help their students at home and not perpetuate the idea that “I’m bad at math, and so are you.” Math skills are not genetic!

So, math is fun and I enjoy teaching math and it’s my responsibility to share this enthusiasm with my students. I’m looking forward to reading the rest of this book for my insights and action steps!

 

Chapter 1: Why Math Education Needs to Improve

Book blog hop July 2016

Balancing the Equation

By Matthew R. Larson & Timothy D. Kanold

Chapter 1: Why Mathematics Education Needs to Improve

“We are systematically underestimating what our kids can do in math.”  Amanda Ripley, Investigative Journalist and Author of The Smartest Kids in the World

The authors’ purpose of this chapter is to help educators and parents understand how well math education is doing based on national and international scores and why mathematic education needs to improve.

Good News and Bad News about Test Scores

First the good news… According to the National Assessment of Educational Progress (NAEP), math scores have steadily improved since 1990, to an all time high in 2013, with small declines to 2015. The scores in 2015 are still significantly higher than the scores in 1990. While there are a variety of causes for this decline, the authors’ suggest it might be due to the alignment of NAEP with Common Core.

Now the bad news… While scores have significantly improved, less than half of all students are proficient in math. Let’s pause and think about that fact (the authors’ have provided plenty of evidence). Less than half of all students are proficient in math! “Yes, the percentage of students who are proficient has more than tripled for fourth grade and more than doubled for eighth grade over the period of standards-based reform, but it is still less than half.” (Larsen & Kanold, 2016, p. 13). The achievement gap between whites with Latinos and African Americans still remains. Also according to 2015 ACT math scores, less than 50% of US high school graduates were prepared for college-level math. Ouch, not good. Finally, internationally US students math scores and numeracy skills rank below the international average.

Wait there’s more… Probably due to No Child Left Behind (NCLB) most states lowered their standards to show growth, which increased the disparity between the NAEP scores and the states scores. As a result, more students are unprepared and unskilled, and cannot find a place in a knowledge-based US economy (Larsen & Kanold, 2016, p. 20).

In other words, state mathematics proficiency rates based on the old state test expectations inflated students’ true level of mathematical understanding when measured against an international performance standard that defines mathematical literacy in terms of understanding, procedural skill, and the ability to solve problems. This coincides with mathematical skills becoming increasingly valuable in the workplace (Larsen & Kanold, 2016, p. 21).

The authors go on to report that the problem isn’t the new Common Core Standards, but the false sense that our math students are doing fine on state tests that were lowered in order to meet the demands of NCLB. While we might feel good that our students are doing well on these tests, the tests are not a good indicator of what our students should know and be able to do. We need to expect more.

Implications
  • Current math teaching does not work for most students.
  • It’s time to break from the past and increase standards and rigor.
  • Balancing the equation doesn’t just mean balancing the types of math instructional approaches (blending procedural fluency, conceptual understanding, and problem solving), but also means balancing access to great math education to EVERY student, regardless of race or poverty level.
My Call to Action
  • Collect math data for my students and compare them to national data, not state.
  • Find out if there are any performance gaps due to race or poverty levels, or something else.
  • Find out my state’s NAEP scores.
  • Figure out how to communicate the need to raise math expectations.
  • Expect more from my students.

In summary, state tests have lowered our math expectations and students are not prepared for college and careers, especially Latinos and African Americans.

Juan Williams (@TheJuanWilliams), in WSJ 7/5/2016, states “For black and Hispanic students falling behind at an early age, their best hope is for every state, no matter its minority-student poverty rate, to take full responsibility for all students who aren’t making the grade — and get those students help now. That means adopting an attitude of urgency when it comes to saving a child’s education.

Please don’t despair, while the task is difficult, this chapter serves as a call to arms and the rest of the book provides more insights and answers to this serious problem that we can work together and solve.

Here is how the rest of the week will unfold…

Project Based Learning Summer Workshop

If you are teacher reading this, it’s probably summer time, so I hope you are enjoying a much deserved break. I also know that you are busy thinking about next year, cleaning up your room from last year, and possibly going to some teacher conferences.

I recently attended a two-day workshop on true project based learning. Like some of you, I was intimidated by doing projects in my class, but I knew that PBL is a valuable and authentic way for teaching.

The workshop focused on middle and high school teachers demonstrating their class projects – from making water rockets, designing aqueducts and boats. Before you panic on how huge these sound, I also realized that mini-projects are a good way to start. I think the key is to engage the students right away by asking compelling questions that students are eager to answer. These questions are key and should be around a topic that you are comfortable facilitating (or not, if you are up for a big adventure). But for your first project, definitely choose a question that you can do.  Below is a graphic that represents the “gold-standard” to organizing project based design.

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Fresh off this workshop, I’m eager to think of some projects that I want to kick off the first weeks of school. I think it will set the tone for our year as well as engaging my students in teamwork to help them get to know each other.  What should I do?  Don’t know yet, but I do have a couple more weeks to work this through. So keep in touch as I work things out here on my blog.

Here is a good resources for you – What is Project Based Learning?

Thanks for reading, enjoy your summer!

– Evil Math Wizard

PS – I do still need to finish my Fraction Log blogs, it’s on my long summer to do list!

End of Year Class Traditions

I teach a 4/5th grade combo class. My 5th graders are moving on to middle school, so we do a couple of traditions to mark the transition. We don’t do to much, as our middle school is right across the street and comes over for lunch; we are pretty much a K-8 campus.

Classroom Wills

This tradition is when each of my 5th graders make a “will” leaving certain things to the next year’s class. These are not just physical things, like cubbies and classroom hooks, but personality traits, like sense of humor, dedication, and friendliness.  They read them to the class one of the last days.  So they will say “I leave my clean cubby to ______” or “I leave my sense of humor to _________” or “I leave my math skills to _________” It’s fun and good way to recognize each other’s strengths.

“I Remember” Speeches

Over the course of their time at our school, at the start of the year, each student draws a self-portrait. We keep these every year and when they are promoted to middle school, we have a collection of 6 portraits from K-5th grade. During the ceremony, each student shows one at a time, and then says a sentence that goes with each. For example, if they are holding up the Kindergarten portrait, they could say “I remember when we hatched chicken eggs.” They say one memory for each grade. It’s a sweet way to see their progress, especially through the transition of self-portraits, from Kindergarten blobs to fully-formed human bodies.

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Promotion Hats

During the promotion ceremony, the fifth graders were special hats that are made by the Kindergarteners. They are so funny and creative. We don’t give them any ideas, and we provide paper, feathers, stickers, yarn, pipe cleaners, tissue paper, etc. When I get a chance I can put an example in here, but you can probably imagine what they look like!

— Good luck with your final days!

Evil Math Wizard