Monday, March 4, 2019

Using Puzzles to Create Persevering Problem Solvers




Helping our students to grow through productive struggle is often a challenge for us.  One way to consider as you work to build your students' problem solving skills is through the use of puzzles.  Here are some ideas for you to consider:

Yes--it can be as simple as having a jigsaw puzzle in the back of your classroom.  The visual acuity needed to solve jigsaw puzzles is important for students to build, and who doesn't love to finish a jigsaw puzzle?  Oftentimes, students do not have this opportunity at home, so having one set up in your classroom could help them to develop a new skill or hobby.

Besides jigsaw puzzles, tangram puzzles and pattern block puzzles also help students to build visual and geometric skills.  Allowing students time to explore with tangrams and pattern blocks is important, too, and it allows them to find the creativity in math as well as in themselves.  You can find other resources to help with tangrams in this post as well.

Kenken puzzles are an awesome tool to help build logic, fact fluency and number sense in all students.  The website also has an education portion, and you can sign up to have new sets of these puzzles sent to you weekly.  These puzzles are one of my favorites, but you do need to take a little time being sure your students understand how to do them and reminding them to explain how they know where numbers go in the puzzle.  Too often, students will guess where numbers go.  This method will work for a short time, but as the puzzles become more difficult, guessing will not lead to success.   While Kenkens have some similarities to Sudoku, I think they are better in the classroom because of the decomposition of numbers that is involved.  Many students are familiar with Sudokus, and they are a great type of logic puzzle that can be easily found. More information about Kenkens can be found here.

The website Math Pickle also has a large puzzle bank for you to choose from.  This site offers students the opportunity to play with their work in a way that allows them to better develop math concepts.

These booklets from the Julia Robinson Mathematics Festival also allow students an opportunity to persevere through problem solving in  a fun way.  Although developed for a building-wide math night, many of the puzzles could be used in the classroom.

Let students decide how they want to do their puzzles.  Sometimes students prefer to solve them alone.  Others need to talk it over and think it through with a classmate.  Neither way is wrong.  Let students build their puzzle-solving skills in the way that feels best to them!

Math is fun.  It is puzzles.  It is visual. It is cooperative.  Sometimes, we get so caught up in teaching a curriculum or a standard, that we forget these important pieces of math.  There are so many good puzzles and problems out there for students; this is not even the tip off of the iceberg.  In what ways can you work to incorporate some of these ideas/resources into your classroom.  How can you help your students to not only become more persevering, but to ENJOY doing math?  

Friday, February 1, 2019

Another Resource for Better Communication with Parents




As we work towards shifting our instruction from deliverers of knowledge to facilitators of learning, it is important that we keep parents informed about what students should know during the current grade level.  I recently came across this site  by GreatSchools.org that has videos for parents that are aligned to grade level expectations for students.

What I like about this site is that the video clips primarily focus on conceptual understanding rather than rote memory skills.  They reinforce the message that we should be sending parents:  Student understanding is the key to future math success.

Please, share this site with your parents!  Whether you just send a general email sharing the whole site or choose one specific video that aligns with a current concept, I think our parents will appreciate your efforts to help them make sense of the rapidly changing classrooms they find.

These videos would also be good to share at the beginning of the year or at conference time.  I hope you and your parents find them helpful!

Sunday, January 6, 2019

Goals for the New Year

What goals do you have in mind for your mathematical teaching for the remaining half of the school year?  What can you do to help not only your children grow, but also yourself?  Here are some things you might consider trying in 2019, as well as some resources to help you get started. Pick one or two to get started.

1. Making Number Talks and other Mathematical Routines part of your instruction

2.  Trying one of Jo Boaler's Week of Inspirational Math

3.  Using 3 Act Tasks to build student engagement and understanding

4.  Using Visibly Random Grouping when putting students to work on tasks

5.  Allowing more collaboration and talking among students. Learning should be social.

6.  Using more Concrete and Representational models during instruction, and encouraging students to use and understand them as well

7. Eliminating pages of rote practice problems and instead finding rich problems that make students collaborate and problem-solve together

8. Participating in a Twitter chat. #mathconceptions is on Mondays at 8:30 for a 1/2 hour, and #elemmathchat is on Thursdays at 8 for an hour. Great professional developmennt

9. Working on building a better understanding of DOK for you and your students

10. Using explorations as a way for students to make sense of the math in their own way before being "instructed" in the way things "should be done."

Good luck!  Let me know if I can help!

Thursday, November 29, 2018

Countdown to the Holidays!

You know how I love nrich.maths.org for rich problems to solve.  Well--today I saw that they have an advent calendar for elementary students.  Each day has a rich task that accompanies it.  The problems are not holiday based; only the design of the calendar is.

You might just refer to it as a holiday countdown calendar, but no matter what you call it, it should lead to some good student thinking!



Monday, November 26, 2018

3 Act Tasks: Have you tried them yet?



3 Act Tasks offer our students such an engaging opportunity to make sense of math! However, as teachers, sometimes we are afraid to try something new not knowing where it might take us and scared that something bad might happen.  I just heard an analogy recently about this being like being at the top of a rollercoaster:

via ytCropper


And, while it might have twists and turns and dropoffs, not to mention bugs in the face, it also brings an excitement and thrill that we rarely find doing a traditional math lesson. We need to think about putting ourselves in that precarious position at the top of the rollercoaster; it's what we ask our students to do on a regular basis so that they can grow.  We should try it, too!

3 Act Tasks are real-world problem-solving scenarios which require students to make sense of what to do.  During Act 1, they use the reading skills of visualizing, predicting, and inferring in a math context.  They figure out what they need to know to solve the problem. In Act 2, students work to solve the math question in a way that makes sense to them. They discuss their thinking with a friend and compare their answer to their estimate.  Act 3 is exciting because that is when they find out if they were on the right track!  


While they are working during Act 2, you are monitoring (and asking questions that help them understand--not helping too much).  You are monitoring to see the methods that students used in order to solve the problem.  During Act 3, it is your job to have students share ways that they solved the problem.  These should be sequenced so that you can show connections between different methods. Be clear on what your math target for the lesson was and be sure that your models and discussion help that math target to be evident to everyone.  You synthesize the learning at the end of the lesson.


3 Acts are very visual and often use videos to help students better understand the situation. They follow more of the format of "you do, we do, I do" rather than the traditional layout of "I do, we do, you do."


Typically, a 3 Act Task in K-2  about 20-30 minutes.  In 3-5, a task usually takes about 4o minutes.  As students get stronger and more comfortable, the time needed for a 3 Act might decrease.


I am happy to come and model a 3 Act Task for you and your class, but I know that many of you can do them without my support.  You just need to put yourself on the rollercoaster!


At the top of this blog, you will find a tab labeled 3 Act Tasks.  This will take you to a large number of standards-aligned tasks that I have organized using SMART Notebook (and sometimes Google slides).  They are by a variety of mathematicians; I just put all of the pieces together into one format.  You can also find more great tasks by clicking here or here or even by Googling 3 Act Tasks.


As always, share with me your questions, struggles, or successes and let me know how I can help!

Monday, November 19, 2018

Would You Rather? -- Holiday Edition



If you are looking for some problem solving to get your students thinking and proving themselves while mixing in some holiday cheer, maybe these Would You Rather problems will work for you!

Would You Rathers are something that students are very familiar with, and these just include a mathematical twist.  Students can choose whichever option they want, but they need to have a mathematical explanation of why that is what they chose or didn't choose.  They can be used with students of all ages and offer great opportunities for collaboration.

If you like these, you can find more like them at this site, but I am betting you can come up with some good ones of your own!

Holiday Would You Rather 1

Holiday Would You Rather 2

Holiday Would You Rather 3

Holiday Would You Rather 4

Holiday Would You Rather 5

Thursday, November 15, 2018

A Stepping Stone to a More Student-Driven Workshop

If you are still looking for ways to make your math workshop more about collaboration and problem-solving rather than about independent work and computation, a Week of Inspirational Math by Jo Boaler/Youcubed might just be the ticket!  If you have done any of these lessons before, you know how awesome they can be!  Well--she has recently posted her WIM #4!  That's right--4 weeks of math explorations and engaging lessons that you can use to build your mathematicians.

These engaging lessons are organized by grade level strands and are grouped into a week's worth of lessons.  They are great to use a week at a time, but you certainly could use them independently if you needed to.  They embody the paradigm shift in math education with a focus on growth mindset, visual math, patterns, and collaboration.

Besides that, each lesson will really engage your students for at least math period.  (Oftentimes, students keep working on the problem after class...) Each lesson begins with a video that you can show if you wish.  It helps to build the growth mindset in your students and presents them with mathematical thinking that helps them to see math is all around them.  After the video, there is a lesson (with full lesson-plan) that you can have students work on in small groups and share out with the class.  You can learn so much about your students as you circulate the room listening to their thinking, and they will learn so much about themselves as mathematicians!

With the craziness of the holidays, you might find a few days where some WIM activities are just the ticket, and they might cause you to begin rethinking your workshop!  They might be a good way to spend your math time during those days right before holiday break, but they might also be an awesome way to set the tone for 2019!

I have blogged about WIM before, but I can't tell you enough how much they can invigorate and change your classroom, your student's thinking, and your own thinking!  Time well spent!