Monday, June 18, 2018

Dice Chats

Another way to bring conversations alive in your classroom is with "Dice Chats"!!  These are similar to Dan Finkel's Unit Chats.

Simply show these images and ask your students "How many do you see?"

The students could:
  • Count the total dots
  • Number of dice
  • Number of colors
  • Number of dots on a certain dice
  • Number of dots on a certain part of the pattern

I would provide students white boards (or have them at non permanent table tops) and have them write down how they know.

After 2 or 3 minutes, simply start the conversations and reply to every answer "How do you know?".

Remember, during this time try to ask more questions than give answers.

Here is a slideshow showing different possible pictures.

Wednesday, May 16, 2018

Differentiating Assessment

“The primary purpose of assessment is to improve student learning” -Anne Davies, PHD.
The above quote sums up why I challenged my assessment practices. In 2013, as a High School Math teacher, here is the model I used:
  • Teach concept 
  • Various quizzes during the learning journey.
  • Summative unit exam.
  • Repeat 
After 8 years of teaching in this model, I realized there was an issue...students who entered my class with passion towards mathematics, were leaving the class beaten down, sometimes dropping out, and ultimately not having the desire to learn more math.

Originally, I thought this was normal!! When I went to high school, math classes always ended with less students than it started with. As a student, I remember daily expectations of having to do the odd (or even) numbered questions on page X, multiple worksheets, and having to prepare for weekly quizzes or tests. This was my normality. This was the machine I wanted to perpetuate when I entered teaching.


Because this worked for me. I am intrinsically motivated by mathematics, and I find prime, fibonacci, and complex numbers inherently interesting...because they are!! However, too many people have not had the chance to struggle, discover, and play with these awesome, and other, mathematical ideas.

In 2013, as an educator, I saw the true assessment style was more about ranking, sorting and grading, not at all about learning. Even furthermore, I was more focused on preparing students for AP, or diploma exams, instead of creating an environment which allowed students to bring their passions and interests in, next to their pencils and paper.

Similar to the comic, my grades were focused on what was easy to test, grade, and report on, instead of what was important.

This had to change. If I was differentiating my instruction, why was I focusing on standardizing my assessment?

In 2013, I made a stand:
I will only assess in a way that increases learning; if my assessment isn’t increasing learning then the assessment needs to change.
In this year, my late friend Joe Bower reminded me “the word ‘assessment’ comes from the latin word ‘Assidere’: to sit beside”; an action that was rarely taken when I was assessing my students.

Here is my journey, and the steps I took, to explore what it mean to provide differentiated assessment.

1. Manageable outcomes:
In consultation with University professors, colleagues, and teachers across the province, I looked at every course outcome through the “Rock, Sand, Water” analogy: If you plan for the rocks first, then sand and then water, it will all fit, however if you simply plan a course to cover all outcomes equally, all the outcomes will rarely fit.

During this process I combined parts of one outcome with another, broke up some outcomes into smaller chunks, and then I created a list of “Rock, Sand and Water” objectives:

  • Rock outcomes (outcomes that pass the endurance, leverage and readiness test) - Expect ALL students to master. 
  • Sand outcomes - Expect MOST students to master. 
  • Water outcomes - Expect SOME of my students to master. 
I then ensured that these decisions reflected in my long range outcomes, course outlines, and daily plans. I planned my courses in a way to ensure that the essential learning outcomes were weaved throughout the entire year, while less essential outcomes were covered through the lens of a higher leverage outcome. Of course, I still taught all the outcomes, but I decided to only report on the essential ones, regardless of how difficult it might be to do so.

2. Change the tests
After having a smaller list of outcomes to report on, I decided to ensure my summative assessments matched this philosophy. Instead of giving tests grouped by question type, I grouped questions based on outcome. Any assessment that covered more than 1 outcome would be given back to students with more than 1 grade. Each grade represented the learning of the student on a specific outcome; no longer did I average 2 or 3 outcomes into one mark and call it “Unit X Test”. I then changed the categories on the online reporting program to “outcomes” instead of “Quizzes, tests, homework, etc”. Every mark, on a specific outcome, was reported in the corresponding “outcome” category.

3. Ensure learning is the focus on every assessment
During this time, my summative assessments where 1 part multiple choice, 1 part numerical response and 1 part written. Simply sorted by outcomes not by question type.

I quickly realized that when my students answered a multiple choice question wrong (or even when they guessed right) I was clueless as to how to support them from their current understanding to mastery. If I wanted learning to be the primary focus, I could not administer multiple choice exams.

In 2014-2015 I moved to an entire written response assessment strategy grouped by outcomes. Instead of 1 part multiple choice, 1 part numerical response, and 1 part written, I only assessed with questions that forced students to make their understanding visible. It was in this year, I truly started to sit next to my students and provide them written and verbal feedback that pushed their learning forward instead of simply saying “here are the X questions you answered incorrectly and here are the correct answers”. My feedback was focused on learning, not on which questions did they answer wrong.

I was writing grades and comments on everything my students handed in. This was the inherent problem; I was giving both grades and comments.

Every time I handed back an assessment with a mark, I quickly noticed that students focused on their individual grade, their friend’s grade; and how they ranked within their peer group; and most completely ignored the comments. Students were not asking “How do I understand this better?” but instead “How do I get an A (or 90% or excellent)?”

I had invested a lot of my time into giving useful and effective feedback however these comments were being overshadowed by mark. Grades were the commodity of my classroom not learning. This had to change.

4. Challenge the grading system

Simply put, I stopped writing grades, learning levels, or any other ranking system on student work. Instead I only provided feedback and asked questions that pushed learning forward. Even if a student demonstrated “mastery” of an outcome, I would still provide feedback or leave them with a question that pushed them beyond the scope of the outcome.

This was the most profound transformation I have ever experienced in my entire career.

Students truly became engaged in their learning, not their grade (or ranking). As well, I was able to truly push my students forward when they made mistakes. When I looked at the work of my students, I simply focused on 3 essential questions:

  • What does success on the essential learning outcome (rock outcome) look like? 
  • Where is the student now? 
  • How do we close gap? 

This ensured that the feedback I was providing to students was truly “learning focused”. Every written comment was also input into our online reporting system.

This meant that when a parent, or a student, logged into our online reporting tool, they didn’t see grades, but instead comments for any outcome. Instead of seeing “80%” on an outcome, parents (and students) would see what they need to work on to close the gap...without the support of a grade.

Even the conversations I was having with parents were learning focused and not grade focused. Incredible shift! At the beginning of the year, parents were apprehensive of not receiving any marks as feedback, however when parents saw the products their children were bringing home from my courses, parents were quick to become allies of this new model of assessment.

5. Differentiate the assessments
I finally started a “Differentiated Assessment” model. After teaching outcome X, I would have an assessment on the outcome, however, I started to use this time to also assess each students’ understanding on a previous outcome. For example, students who were also being retaught ideas on outcome 2 would have questions around outcome 2 on their sheet, the ones who were working on outcome 3 would see questions around this outcome...truly every single assessment was tiered to the individual student and what he/she has been working on in the previous weeks.

The assessment Jimmy and Jane received on this day, would only match if they were working on identical material with identical errors and misconceptions; which was rarely the case. Even when designing the questions from previous outcomes, the questions were focused around the feedback the learner had received on their last assessment. For example:
  • Jane might be tasked to demonstrate understanding of a specific part of a certain essential outcome, because I saw only a minor learning gap when I previously assessed her on this outcome. 
  • Jimmy, however, might have more questions around the same essential outcome, because when I assessed him previously I saw major learning gaps. 
This is when learning became the focus of every single assessment I gave. I can honestly say that every assessment had learning as the only priority!

Looking back, I have always believed that every child can learn math to the highest levels, but only in the past 3 years did I take a differentiated approach to what happens when they don’t.

Monday, January 29, 2018

Folding Paper Activity

How high will a piece of paper get if you fold it 3 times in half? 7? 10? 20? How long until you get to space??

Check it out digitally with "Folding Paper digitally"  Check out possible uses below

Early grades: Ask the question I did, wonder, try it, wonder more, and then to the site...wonder before you click each time.

Middle grades:  Ask the question I did, wonder, try it, wonder more, see if you can create an actual equation for the height vs times folded..and then to the site...wonder before you click each time.  Ask then, how big would the original sheet have to be to be able to stand on the stack after X folds?

High Grades:  Ask the question I did, wonder, try, wonder more, ask why type of relation would be best to model this type of growth?  How would you change the question so it grew as linear, quadratic (would be fun to explore this), sinusoidal, etc, functions? and then to the site...wonder before you click each time...Ask then, how big would the original sheet have to be to be able to stand on the stack after X folds?

Sunday, November 26, 2017

The flaws of (some) textbooks

Recently, I was asked "Why do you dislike Textbooks?" and upon reflection, here are the issues I see:

Problem 1: Textbooks assume you need to be taught and shown how to solve a problem before you are given the problem.

This is absurd to me.  When I, and probably most, encounter something I do not know how to do, the first thing I rarely do is look for an instructional video on how to complete the task.

Ironically, the first thing I do is actually play with the problem and see how far I can get without any assistance.  That is right; I play!   This play cannot happen if my hand is being held and shown how to complete the task.  Learners, specifically children, are not afraid to be wrong, take chances, and try to truly problem solve, yet a textbook is designed around the idea that a child loves to be told what to do.

This ruins the fun!!!  I say again, this ruins the fun!  It is comparable to turning on a movie and someone telling you "The main character dies at the end!"; Joy lost!

Problem 2:  Pseudo - context

In almost every textbook I have seen there is always some sort of situation that can only exist in "textbook land", a magical place where the following is true:

Textbooks usually tell students all the information, in the order the need it, and then call it "Problem Solving".  My favourite question and answer was when I read the following question from a textbook:

Jason weighed a fish, and found out that if you took the weight of the fish and added it to half the weight, the result is 20 lbs.  How much does the fish weigh?

The best answer was from a student who exclaimed:

Ask Jason he weighed the damn thing!

Brilliant response to a horrible question!

Problem 3:  They "unitize" learning.

Again, a common problem I see with textbooks, is they assume you need to learn A, then B, then C, to master idea D.  In my experience, creating these disjoint learning situations, or what I call "silos of learning" causes problems for students.  

A common practice in textbooks are "Chapter Tests", which means the pages after these tests have rarely little or nothing to do with the previous pages.  In essence, the learning that happened yesterday will have nothing to do with tomorrow.  

A great practice is to weave essential learning outcomes throughout your entire course.  This contradicts the textbook.  If you feel a certain outcome is important for all to master, I would hope that your students work with that idea throughout the entire course and not just for a finite time (week, or month) and then move on and never relate new learning to previous learning.  

Disclaimer:  Does this mean I don't think textbooks belong in schools?  NO!

This means educators have to be aware of the shortfalls of textbooks.  The biggest idea we always have to remember is that these resources were created, usually in an office, to be sold across an entire continent or country.  They are not designed for "your" kids; or really anyone's kids for that matter.  

Textbooks should be used similar to encyclopedias in the classroom.  Reference material.  If a student is struggling with a concept, give them a textbook, show them a certain page and advise him/her to complete some (not all) questions.  When completed, have a conversation, and then ask him/her to return the textbook to the classroom shelf.

Saturday, November 18, 2017

5 things I was NOT doing as a Math Teacher... that I wish I did

Recently, I heard a Harvard researcher state,
Sometimes the problem is not in what you are doing, but instead in what you are NOT doing.
This made me reflect upon my first 8 years of teaching math. What was I NOT doing that may have increased learning? If I could go back in time, here are 5 things I wish I did more (or even at all), in no specific order:

  • I never gave pictures to students and asked them, "Where should the origin be placed to best understand, or work with, this image?". Instead I would always supply images to my students with a Cartesian coordinate already drawn on. If I could go back, I would make time for students to discuss and debate on where is the "best place" for the origin to be placed on an image to solve the problem given.

  • I never explained what "simplify" truly meant. I would give students loads of questions and I would write "simplify" as a directing word. In my classes "simplify" meant: Add, subtract, factor, expand, combine like terms, rationalize denominator, etc. I wish I showed students where, and ultimately why, each form may be simpler than other forms; however, change the question and then a different form may be actually simpler.

  • I never asked students to actually measure needed quantities to solve problems. I usually gave students problems with all the information needed, even in the order they needed it, and then asked the question. If I could go back, I would have started asking questions such as "To solve this problem, what would we need to measure and/or determine?". I think it is important that students know how to measure, but more importantly they know what is worth measuring.

  • I never allowed students to be individuals, not only in the instruction process, but also the assessment process. Most of my tests required students to learn the required material by the same day, and then even asked my students to demonstrate learning the same way. If I could go back, I would allow students to demonstrate learning when they have mastered the material, regardless of the speed and pace of the other students. In addition, I would also have asked students to relate their learning, when possible, to their passions and interests.

  • I never built my course to allow connections to be built between essential learning outcomes. Instead, I built my course in units where I would teach outcomes as disjointed ideas and rarely make connections between each unit; I created silos of learning throughout the year. If I could go back, I would actually remove all notions of "units" in my course and instead weave big ideas throughout my entire course. Instead of teaching a big idea in September, and then only discuss it again during our "final exam review", I would ensure big ideas spanned the entire length of the course.
What are things, thinking back, did you NOT do?