Category Archives: Math ideas, lesson, activities for every classroom!

The posts in this category are math ideas that can be used in any math classroom.

Connecting/Integrating Curriculum

Somehow in the past few years, education has moved away from integrating all the content areas focusing instead on teaching each subject in isolation.  So many elementary schools that I visit have a dedicated math time followed by an ELA block, etc.  Jr. High and High schools do the same thing, so that most children go through their days and years seeing no commonality among the areas of  learning that we, as educators, deem important.   I know that this new trend is most likely due to the dependence on testing as a means of funding.  Most states only test math and ELA, so in response to low test scores, we have to focus on teaching to the skills required for the test.  However, by doing this, we are missing out on true learning.  We DO need to integrate the contents that we teach, but we just need to keep a critical eye on whether they stay rigorous.  Whereas ocean’s week in the past lead to an amazing 3-D hallway display did nothing to further our children’s knowledge about oceans, ecosystems, adaptation, or cause-effect.   If you do try to connect your four content areas (Math, Science, Social Studies, and ELA), just make sure you don’t fall into creating crayola curriculum (colorful, but with no real learning attached).

As a secondary teacher myself, I was fortunate to work with a team of teachers that took integrating all of the disciplines seriously.  We worked hard to understand each others standards and made sure to design the learning to maximize interdisciplinary connections.  Elementary teachers are lucky that they can work to connect all contents throughout the day and not have to depend on other teachers to keep the connections alive.  Whatever teaching situation you live in, I highly encourage you to look at ways to bring the four content areas (and any more, if you can) together!  One great way to do this is to start the year off with a coordinating theme.  My sister (an amazing History teacher) and I designed some lessons using our book, Help Wanted at Mount Vernon, as an anchor text.  There is a lesson for math in which you focus on learning the 8 mathematical practices, a lesson for ELA where you examine the rules and norms of your school/classroom using word choice and primary documents, a lesson for Science in which students learn inquiry, observation, and inference skills in order to apply them to engineering, and a history lesson that teaches historical thinking skills for secondary students and primary students.

If you are an elementary teacher, you could read the book once and then use each lesson as a leaping off point to connect the content areas (problem-solving, creative thinking, and inquiry).  If you are a secondary teacher and part of a team of content teachers, then you could arrange to read the book at one time (say during advisory or 1st period), and then throughout the day when you see each group of students, you can just focus on your part of the lesson.  However, the main focus in all of the classrooms is still problem-solving, creative thinking, and inquiry – a common theme to tie it all together!  Whether you are working with a team or by yourself, you can use the essential question – Why is it important to problem-solve, think creatively, and question?   All content areas can use this driving question all year no matter what unit or content you are teaching!

Why do we test the way that we do?

I think that I have been watching too much John Oliver lately, because I find myself questioning the very foundation of everything education holds near and dear.  If you don’t know who John Oliver is, or haven’t seen an episode of Last Week Tonight, I highly recommend that you check out his segment on standardized testing: https://www.youtube.com/watch?v=J6lyURyVz7k.  I love that his show has segments that dig deeply into controversial subjects and forces you to question public beliefs (with a humorous lens).  **Don’t watch John Oliver when children are around – he uses adult only language and content at times.**  Quite frankly, I like to be challenged, and I believe that we should always reflect on our systems to see if we are doing things because they work or just because we have “always done it that way.”

Along those lines, I am challenging why we assess students the way that we do in education.  For instance, why is it that we teach students a brand new concept and then expect them to master it immediately?  Oh sure, we give them some practice, and maybe a few nights of homework, a class discussion, and possibly an investigation, but then we expect them to have it down.  I mean, seriously, where in the world is that realistic?  Oh, you want to be a doctor, OK, day 1, here is a heart in a cadaver, day 2, perform open heart surgery.  Or what about sports?  Do we expect a 5 year old at their first baseball practice to throw from center field to home plate?  However, we expect to show a 5 year old words for the first time and then give them a reading test.  The worst part of that test is that how we judge not only that child for years to come, but also the teacher.  This seems like crazy logic to me!

Quite a few years ago, I had this epiphany while teaching a sophomore Geometry class.  Like the two years before, I taught chapter 1, then gave the chapter 1 test, moved to chapter 2, gave the chapter 2 test, and so on.  Right after Christmas break, when students were organizing their notebooks, a student mused while looking over his dismal score of a 62% on his chapter 1 test, “Why did I miss all of these questions?  These are so easy!  Was I sick that day?”  So, I thought to myself, well of course you know it now, because Geometry builds on itself and we have been using that stuff from chapter 1 over and over.  Is that student a ‘D’ student?  Really?  Instead, I changed the whole testing process.  At the end of a chapter, I gave a practice test that the students scored themselves.  I asked for feedback on what questions were missed and why and took those results forward into the upcoming instruction. However, I didn’t give a formal test. If it was a concept I knew we would do a lot, then I just refocused the students when it showed up, or I added review while connecting to new ideas.  Rather than teach chapter 1 and then test on it, I taught chapters 1, 2, and 3 then tested over chapter 1.  Shockingly, the scores were amazing!  Then I went even further to have a chapter 1 & 2 application project that students worked on and were given feedback on well before the chapter 1 test.  The test scores got even higher.  The only bummer was the very end of the year – because I couldn’t follow them into summer, but I tried to compact some things so that there were more application projects in the last few weeks to really practice the material.  It would have been a perfect system if I could let that last test go and move it to the next year, but, that was a pipe dream…

Over time, I gave that practice of “letting the test wait” up.  I cashed it in for taking a pre-test, scoring it yourself, then taking the “real” test.  I then allowed students to re-take tests on the material until mastery was shown.  I’m not even sure why I changed back to the archaic system of learn, test, learn, test.  It probably had to do with district made finals and benchmarks – or assessments being out of my control.  Our system just promotes failure, not true learning.  We ask children to take academic risks, but then punish them for actually doing it.  Everything has to be right now.  Learn this now, master this now, because we have to hurry, hurry, hurry.  For what exactly??  And we wonder why so many students don’t like school…

How can you teach creativity?

As I look at the NAGC standards, they often refer to teaching creativity to our gifted youth, which makes me wonder – can you teach creativity?  If you can, how do you assess it?  Is there a way to define creativity?  Well, as it turns out the long respected work of E. Paul Torrance delves into that very topic.  He even has a test for creativity that used to be given in many schools before every one went nuts over No Child Left Behind.  He defined four (4) areas in which creativity can be measured, explored, and basically taught.  Fluency, originality, elaboration, and flexibility are the four areas in which creativity can be viewed as tangible.  There is even a circle test that you can give people and have them score themselves in the four areas.  Unfortunately, you need to be a licensed psychologist to assess the numbers, but I like to give the test as a great introduction to the four areas of creativity, their definitions, and how to start dialogue on the subject.   My favorite book on creativity that was introduced to me by Sue Gonyou (an educator that I deeply respect) is A Whack on the Side of the Head by Roger von Oech.  I find myself constantly reading and re-reading the book and getting fabulous ideas and a whole lot of laughs to boot.  When I taught creativity to my group of teachers of gifted students, I assigned them to read a section of the book and then design a lesson off of one of the ideas.  The lessons were to be appropriate in any classroom from grades 3-5; however, the teachers designed lessons that could be used for most grade levels.  Some lessons take 5 minutes while others last multiple days.  Creativity is usually prevalent in gifted individuals; however, by Torrance’s definitions anyone can learn to be creative.   All of the lessons have a form of assessment attached (mostly to be used for self-assessment).  In order to create these rubrics, the teachers drew ideas from Dr. Richard Cash’s work in Differentiation for Gifted Learners.  I have posted the ideas on my website; they are titled starting with the words ‘creativity lesson.’

Teaching Mathematical Modeling

As I was preparing a unit on expressions (translating, evaluating, and simplifying), I decided to branch out and include a real-world “problem” to entice students to see the benefit of writing equations and expressions.  I ended up creating a video detailing a pretty involved scenario in which students would need to sift through possible constants and variables.  At the end of the video, I asked the question – How can you model a possible solution to this problem?   Because my 5th grade son’s teacher is such a great sport, she offered to test the lesson in her classroom and we certainly found some interesting results.  Upon being asked to generate a model for the problem, all the students started drawing these elaborate schematics and asked if they could create them in 3-D.  It became very evident that students aren’t quite comprehending the numerous meanings of math models.  Looking over Henry Pollak’s discussions on math modeling for the common core, I decided to make a follow-up video helping students see that mathematical modeling can take many different forms.   Here is the link to the original video:  https://www.youtube.com/watch?v=nXBL79tlBg4.  I would love for teachers to try showing this video to their students and see if their misconceptions for math modeling are the same.  The youtube link for the math modeling video is https://www.youtube.com/watch?v=Iew9nppByKs&feature=youtu.be.

Welcome to my blog!

My name is Holly Young and I am a mathematician, math teacher, and math trainer.  I just recently left the classroom and decided to go out on my own to create resources for math teachers.  By and large, math teachers have the raw deal in teaching, especially in secondary schools.  The onus falls on the shoulders of the math teacher to lead every day, every minute of every lesson.  We don’t have scores of amazing National Geographic videos or Discovery websites that further our curriculum.  If we have to be out of the classroom for a day, then we usually lose a whole day of instruction.  It is my goal, therefore, to create useful media that math teachers can access and help forward student learning.  I have lessons available for multiple grades and topics at www.makingmathematicians.com and I will continue to add more lessons and useable media.  This is a journey for me, so I will be constantly improving and creating new resources.  If you have suggestions of what resources you would like to see on my website (or blog), please feel free to let me know.

This first file that I am posting came to me as a sudden inspiration while training teachers on creating essential understandings (questions) in the classroom.  As I was asking teachers to write an essential understanding that encompassed multiple grade levels along the same CCSS strand, I kept asking them, “What is the essence of this strand, and why do we need to learn it?”  The result of that exercise came to me in a flash when I asked myself, “Why do we study the main topics in mathematics?”   Math_poster