Thursday, 30 August 2012

Subtracting Integers

A short but quick one. When I was a kid, no one ever told me about the little trick of turning a negative into a positive.


Wednesday, 29 August 2012

Decoding Words, Bread Mold Growth Activity

Reading and writing traits need to permeate into every subject. For students to become better readers and writers, their strategies must have ample opportunity to be revisited by every teacher in every subject. Team meeting times ensure that team teachers can appraise each other of their curriculums and make connections between different classes.

Our warm up is on decoding words through their parts. I have an exemplar at the top of the graphic organizer, and two words which I want students to practice on their own. We'll follow up with two more terms at the end of class.

We're monitoring the growth of mold after two days. So far, its doesn't look like much, but it's bound to get pretty gross!

Monday, 27 August 2012


Last year, I had a great discussion with a colleague about how many times a student needs to demonstrate "learning'.

Learning is a broad concept and so is "understanding". I like to refer to Blooms taxonomy on what entry level understanding looks like and how it leads up to higher order thinking skills. See a rough chart below:

As a teacher, we want students to have a deep understanding of a concept rather than a surface level grasp that we see in the chart above under "knowledge" or "comprehension". For example a surface level understanding of the Vietnam war might be:
  • Being able to recall where Vietnam is on the map
  • Remembering the dates of the war.
Supericial. However, if we try to structure learning around deeper understandings of "evaluation" and "synthesis" students can begin to explain:
  • Lasting legacies of the war
  • Major policy changes following the conflict
  •  How the Vietnam war was similar or different to other conflicts in the past.
As learning is often scaffolded with surface level understanding which eventually builds to such deeper understandings of "knowledge" or "comprehension" there are many opportunities for formative checking to ensure that students are in fact learning towards this higher order thinking skills. However, if students show a deep level of understanding early in a unit of study, why should they be required to show it again and again?

I'm not the first person to coin this term, although it goes by many other names. Basically, it exempts students from subsequent demonstration if there are opportunities for higher level thinking that the students have meet early on. With our "challenge by choice" system (Green-Standard and Blue-Advanced) students are given some entry level application with "Green" level work but higher order evaluation and synthesis opportunities through some "Blue" level questions. It's meant to give the students that are challenged to meet the curriculum the chance to feel successful and diagnose their strengths and weaknesses. However, for students that quickly learn, they have the chance to "compact" out of future demonstration. See the example below:

The problem above is very entry level. It's assessing whether or not they can manipulate operations with negative numbers. This is a problem from our "Green Level" quiz. See the same problem on the advanced "Blue" quiz below:

Obviously the problem above is a word problem but implicit in it are a number of learning standards regarding operations, algebra and problem solving skills. Problems like this are more prominent in our summative and performance based assessments. It's obviously more difficult too. If a student gets the above COMPACT question correct, I exempt them from doing it again on a final test.

Conditions for COMPACTING
Taking a more challenging quiz is a gamble for students. The Blue level has three opportunities for compacting out and the green has only 1. (For this quiz only, but the number can be adjusted.) My policy regarding homework is that it is self-assessed by students but I do check their flipped notes at the beginning of class to ensure that they're done. To keep up with assignments is a necessary student skill, so if students have shown good work ethic, they may have this opportunity to "compact out'

Condition #1-Homework in that unit up to that point must be complete and on time
Students that have good homework skills will find that they will have opportunities to compact out of some our learning standards. If students struggle to get homework in on time, if they get a compact question correct, they still have to do it later. If all assignments have been completed, students can compact out. This is a powerful motivator but does not penalize students in any way which is consistent in the assessment philosophies of Tom Shimmer and Ken O Conner.

Compacting is a new pedagogy that I hope to try this year. I've read a little about it, but the theory is sound in mixed ability classrooms. Teachers must continue to provide opportunities for remediation, but must also consider the problem of "double taxation" of talented and gifted learners. I hope to collect data on compacting and share it by the end of the school year.

Related Posts
Understanding: If it's shown once, is that enough?
Challenge by Choice 

Thursday, 23 August 2012

Integers and Absolute Value

We're rolling along in math. The first week has been mostly about procedures such as lesson format, how to remediate and seek help, get organized and access assignments. The students are learning my expectations and the response to the learning environment has been very positive.

My students are still adjusting to the concept of "flipped assignments". Whereas a traditional lesson might finish and ask students to take home an assignment, a flipped assignment is front-loaded so that when students come to class, they're more prepared and there is less teaching up front. Today's assignment that the students should have finished is as follows:

  1. Read page 14 and 15 under the heading: "Integers and Absolute Value"
  2. Write the following for each new vocabulary term. Integer-What is an integer? Can 2.5 be an integer? Additive Inverse-Write three sets of numbers that are additive inverses of each other. Opposite-Write down three sets of opposites that you know of. Examples: "Black and White are opposities. Mr. Johnston and ugly are opposities."Absolute Value: Write an example and a definition of this term.
  3. Draw a "less than" (<) and "greater than" (>) sign. What is a way of reminding you what each of them mean?
  4. Watch the videos from lesson 1.3 Examples 1, 2, 3, and 4.
  5. Reflect on this question: "What method do you prefer learning math? Through examples in the book or through watching videos?"
I'll start by debriefing this as a whole class activity this time (as opposed to small groups because I have a whole class activity that I'd like to do and I want to maximize my time with that) and following this, do a couple of "moving and shaking" activities to get the students moving around, interacting with each other and  applying what 'absolute value' of a number means. I have some laminated integers with their inverse opposite and through this, we'll be able to do the following;
  • Identify Additive Inverses
  • Order Integers from Least to Greatest
Following this, we'll have some time to do independent practice until the end of class. However, before students leave, they must apply a little creativity and write an expression that results with the answer "1" regardless of what you substitute in for it!

Tuesday, 21 August 2012

Translating Phrases into Expressions

We ordered these new student whiteboards. They're about a foot by a foot and a half, and blank on one side and have the coordinate plane on the others. I think they'll be great when we get into functions.

I decided to roll them out when the class was exploring the relationship between algebraic expressions and phrases, working in small groups, I started to debrief the homework and then move onto the discussion. "Flipped Learning" is a new thing for some students in my classroom, but basically it's coming prepared to class by taking notes, watching videos or a number of other tasks. The assignment which students had when they walked into class was this:

  1. Read pages 10-11 on algebraic expressions.
  2. Write down synonyms for the following words: Add, Subtract, Multiply, Divide. (A synonym is a word that means the same thing. For example a synonym for "add" would be "plus"
  3. Translate a word phrase of your own into an expression with algebraic language. Example: "Five apples plus 3 oranges = 5a + 3o"
  4. Translate an algebraic expression your own into a word phrase. Example: "4-7y = 4 minus the product of 7 and y"
  5. This assignment is about translating numbers to language. All of you can speak more than one language. What advice would you have to someone that is trying to translate something into a new language?
I like to think that it has more inquiry and analysis leading to higher order thinking skills and creates a better foundational understanding of the principles underlying mathematics that we can use to describe our world.

After discussing this assignment by eliciting notes and sharing our thoughts, we looked at translating phrases and expressions back and forth. They started easy to build confidence and got eventually harder. Some of the examples were:

Translate "3 more than 5" into an expression
Translate "4y + 2" into a phrase
Translate "The quotient of 9 and 'p' times 5" into an expression.

The Quandary of "3 less than 5"
This is deceiving and a question just within or out of a student's zone of proximal development. What's deceiving is that as an expression it becomes "5 - 3" as there are obvious connections to the associative property in mathematics applying to some operations and not the other. I was curious to know whether or not students could identify this misconception.

The Scientific Method-Variables, Control and Experimental Groups

The first investigation into the scientific method was great. Science is however a complex process, and instead of hitting all the elements of the S.M. and rendering students into a state of confusion, I decided to just let our first investigation focus on writing a hypothesis, a clear procedure and a conclusion based on observations.

Today's investigation was taking it to the next step. After introducing the question "Do shoes help you jump higher?" I'm hoping students will understand the need for an experimental and control group. Much as how when pharmaceutical companies trial a new drug, they must compare the data to a placebo group.

In addition to understanding control and experimental groups, I'm also hoping that students will get a better handle on variables. Which things should they keep the same, which should they change and what are they measuring. We will revisit these terms often, but I feel that spending the first two full lessons on the scientific method will be a good start into applying this procedure when we start exploring content.

Related Posts
Introduction to the scientific method
Using summative labs to demonstrate science skills

Monday, 20 August 2012

Introduction to the Scientific Method

I use the scientific method to kick off the start of the school year. My sixth graders are rusty with their scientific skills according to my pre lesson survey when only three of them remembered what a hypothesis was from last year. I find that it's good to use an experiment and use experimental design to help teach science and from that we can help teach concepts of:
  1. Writing a testable hypothesis
  2. Writing a clear and easy to follow procedure
  3. Drawing evidence based conclusions.
I'm rolling out this year's first edition of "Rock Star Science Productions" to showcase these activities for parents of my students and teachers. I welcome any feedback or criticism to make this work better!

Thursday, 9 August 2012

10 Ways to Foster Better Parent Relationships for Student Achievement

This article was first published at Bright Hub Education media on August 3rd, 2012.

I was recently directed to a cartoon from a colleague entitled “In 50 years, a lot has changed in schools” wherein 50 years ago a child with a poor report card was being questioned by the child’s parents and teacher. “What’s the meaning of these marks?” they all ask the child. Fast forward to the present, when the same poor report card was now directed at the teacher who was presumably at fault and being questioned by the parents AND the child with the same caption: “What’s the meaning of these marks?” 

What has changed? In our quest for education reform have we really absolved the learner and their parents from responsibility? To be sure, teacher quality is the biggest indicator of student achievement, but parents must share some responsibility as well. Getting these parents involved in their child’s learning is essential if our students are to build good habits outside of the school setting and build lifelong learning skills. Generally, my highest achieving students are poked and prodded by highly driven parents and my poorest performers have parents that are indifferent to what is happening in the classroom. Here are some things that you might consider doing this year to motivate and invite parents into the learning process:

  • Introduce yourself. Start the year with a letter about yourself that you give to the students on the first day of class to take home and give to their parents. 

  • Make your policies transparent. Don’t be shy in explaining your pedagogical philosophy, grading criteria so that there is full disclosure. If you have a number of class policies, ask for a parent signature so that they understand your expectations. 

  • Do an inventory of your parent’s professions. Parents of students have a wealth and variety of professional experience. A number of them may be able and willing to serve as a guest speaker or have places of work that may be a good field trip destination. They’ll appreciate the consideration.

  • Build a classroom blog. A blog of student work and news of what is happening in the classroom is a great tool to communicate to parents what their child is doing and what their tuition money is going towards. It will also serve as a nice portfolio of work to showcase later. Tell them how to subscribe to feeds and invite comments. 

  • Be patient with their learning curves. Education has changed a lot since they were children. I you have any online learning portholes where parents and students can access grades, course syllabus’ and pending assignments, you may need multiple sessions to fully brief parents with these resources. Our school has tried to meet this by offering a number of tech software evening sessions for new parents.

  • Give parents updates if you’re tutoring their child. If students are coming in for help after school, take two minutes to write a quick email summary of what was accomplished. Likewise, if students don’t come in, be quick to notify parents as well.

  • Make a learning/support contract. I’ve used learning contracts with students but I’ve started using contracts with parents too. If there are problems with students not completing work at home, negotiate with parents the best course of action to prevent this from happening. A parent contract might include language like: “We will provide a public and designated time and place to ensure that Kyle finishes his math homework. We will log onto “Moodle” and help him understand what is expected before he starts his work at the kitchen table after dinner.” Such writing also provides a paper trail which proves helpful for streaming, enrichment and course placement. 

  • Understand parents have limitations. Although we assume parents are willing to help, there comes a time when they are unable to because the content is too difficult. A colleague of mine learned this year that the mother of well meaning 8th grader could simply not comprehend math done at that level. As the student gets into high school, this may prove extremely difficult, as parents may struggle in helping their child with higher math, foreign languages, science and English if it is not their first language. Some parents may not be very forthcoming with this shortcoming.  

  • Keep the lines of communication open. I usually have a handful of students that are “on the radar” for a variety of reasons. When these students have a great success, I fire off a quick email alerting the parents of it, and if they struggle or relapse on an assessment or student skill, I debrief it carefully with the student and communicate that discussion with the parent. The parents really seem to appreciate me taking a minute of my day to let them know what is happening.

  • Get involved in the PTA. Your school’s parent teacher association often has its pulse on the beat of the school. You might learn of a number of hot issues that are of interest to school. Some parents may have come from schools with programs that they’d like to see come to your school. Get them on board! A friend of mine sends their child to a school in Santa Barbara California that requires all parents to commit to volunteer in their child’s classroom every week. 

Parents and teachers have the same goal: we want our children to succeed and be successful. This job is much easier if we build a network that supports on another, rather than direct the finger of failure. Because we see the child in different settings, we are able to provide a different perspective that the other may not see. What we definitely do see as educators, is parent commitment on a spectrum that swings from obsessive to apathetic and the more that we can make them feel like participants instead of spectators, the more their child will benefit as well.

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