Classroom Independent Libraries

Timing is everything.  I subscribe to a number of blogs and although I often simply skim & scan, I was drawn to go deeper inside this particular post.....and I wasn't disappointed.  Follow the link and check out this teachers video describing her journey to reorganize her independent classroom library.
As we continue to upgrade our classroom libraries, I thought this was perfect timing.  Also, check out the other individual blog posts across the top tool bar.

RCAC Symposium 2013

The Western Regional Computer Advisory Committee (RCAC) Symposium was held in London, Ontario on Thursday, December 5, 2013.  Great Day!

Travis put into words my thinking.  He began by stating that it is not about putting technology in place of what we are already doing in the classroom but we need to think differently and use technology to enhance what we do.  Check out his initial Youtube video he made after using his first SMART phone in a class in his high school to help him keep organized

Gary highlighted that one good prompt is worth a thousand words (i.e. one good question).  It is less about us and more about them (the student).  The most powerful idea of all is the idea of powerful ideas.  Gary went on to say there is an epidemic of whole class instruction (i.e. too much focus of teacher directed instruction).  Check out his blog http://stager.tv/blog/?p=1857

















Did a lunch & learn with Kyle Pearce (http://tapintoteenminds.com/about-me/).  Very interesting.  Anybody who references Dan Meyer (http://blog.mrmeyer.com/) can't be all bad.  

Kyle Pearce is a Secondary Math Teacher and Intermediate Math Coach with the Greater Essex County District School Board leading a Ministry funded part-time, one-to-one iPad project. He is an Apple Distinguished Educator and Authorized Apple Education Trainer who leads professional development in both math and technology in his district and beyond. Teaching secondary mathematics at Tecumseh Vista Academy K-12 in the morning, Kyle shifts his focus to the Middle Years Collaborative Inquiry (MYCI) Project in the afternoon.
Join Kyle as he shares his journey of creating a digital learning environment. In Kyle’s secondary one-to-one iPad math class, the goal was to effectively deliver a 3 -part math lesson while eliminating wasted time copying useless facts. This resulted in increased student engagement and high levels of student
success. Positive results from the one-to-one iPad math classroom have led to the introduction of a One iPad Classroom model for instructional use through the Middle Years Collaborative Inquiry Project for intermediate teachers in 29 schools. Both one-to-one and One iPad Classroom models continue to grow as GECDSB educators strive to redefine digital learning in mathematics.

When Do I Move Students to the 'next' Guided Reading Group?

If we already haven't done so, guided reading groups should be 'on the move' as the students gain more consistency at their current level.  In Debbie Diller's book, Making the Most of Small Groups - Differentiation for All (I have a copy if you would like to borrow), she gives some 'things to consider' to assist us in making good decisions about when is the correct time to move students (see below).

Moving students to the 'next group' is different in Primary grades compared to Junior/Intermediate grades.  As Nelson Literacy is our main resource in Junior/Intermediate, moving students occurs as you change reading strategies.  Moreover, our CASI scores also help us determine 'areas of focus' and thus appropriate groupings.  In the Primary grades, we rely on our Running Records, Flexible Small Group Folder & PM Benchmarks to guide our instruction and form our guided reading groups.  However, what is good in one area of the school (eg. Primary, Junior or Intermediate) can also be good in other areas (i.e. it is only the size of the students that changes).

Flexible Small Group Folder - "Reading Levels & What to Focus on in Lessons

From 'Making the Most of Small Groups' - Debbie Diller

As you are making your new guided reading groups, please consider the lesson planning sequence.  Diller reminds us within the first part of her book that deciding on which kids and what book are not enough of a plan.  She says, "Thoughtful teaching in small groups is a lot different than sitting with a group of kids and listening to them read.".  Overall, precision teaching is purposefully planned.

From 'Making the Most of Small Groups' - Debbie Diller

3 Part Math

We had our 2nd in a 6 part series of CILM (Collaborative Inquiry & Learning in Mathematics) this week.  In essence what we do is co-plan, co-teach & co-debrief.  A very positive way to develop the 'collective strength' as a school.  The unanimous comments from all involved were, "It wasn't so bad.  I wish we could do this more often."
The 3 Part Math strategy begins with a Learning Goal derived from a Big Idea.  Using our planning template we then began to 'fill in the blanks' of our 3 Part Lesson.  The lesson begins with 'Minds-On' to get the students engaged with the upcoming lesson (i.e. getting in the right frame of 'mind').  This is followed by the 'Action' (i.e. the 'getting messy' of the lesson).  The teacher moves around the room making observations (i.e. eves dropping) to gain important 'next steps'.  The final stage is called the 'Consolidation' in which the learning (from the students) is highlighted by the teacher.  Also during this stage the Success Criteria are co-created on an Anchor Chart to aid with the independent work.  The entire process doesn't have a specific time frame (i.e. it could be done in one day or take multiple days to complete the 3 parts).

During the Consolidation stage there are a number of 'Questions to consider'...

• What were the learning goals and big ideas of the lesson?  
• Stay focussed even if some students are 'working ahead'...
• What mathematics is evident in students communication (oral, written & modeled)?
• observation/notes
• What language was used to show the mathematics?  What vocabulary requires reinforcement?
• Word Wall, Math Journal, Anchor Chart, etc...
• How are the solutions linked?
• What misconceptions are present in the student work?
• key piece to independent success
• What are the next steps in instruction?
• assessment drives instruction

adapted from "Communication in the Mathematics Classroom", September 2010, Capacity Building Series.

Overall, our planning template & curriculum document (over time) will be our greatest resource as it becomes the 'road to student success'.  For example, if we had a copy of the curriculum for our particular grade along with the Planning Template, then we could 'highlight' the specific expectations as we move from lesson to lesson.  If you combine this highlighting and our notes on our planning templates, then the real strength comes to the surface as we move from week to week, month to month and term to term.  Looking back and utilizing these resources as our 'assessment for, as & of learning' we will see how this then 'drives our future instruction' and precision teaching.


Resources:

http://teachingrocks.ca/three-part-lessons-teaching-math-through-problem-solving/

Debriefing the Thinking Process

At our next Divisional Meetings, we will go through the student-led 'night' in preparation for the Term 1 Report Cards.  Basically, the 'How to' of Student-led (i.e. the script).  We already have a big 'piece of the puzzle' complete with all students having a Portfolio.  The next 'piece of the puzzle' is metacognition (thinking about their thinking).

The students just completed one form of metacognition activity with the student reflection on the Progress Reports.  Why wait for the next reporting period for the students to show their thinking.  Let's practice, practice & practice.  The article 'linked' to metacognition outlines 6 strategies for developing students 'thinking about their thinking'.  There are many good and practical ideas to help us teach our students the 'how to' of  'learning about your learning'.

As educators, we all have an innate ability to demonstrate metacognitive strategies.  Modeling these strategies with our students on a consistent basis is the key to success.  Students need to be able to not only describe the learning goals (i.e. the target(s) they are aiming for) but also how they plan to achieve the goals (i.e. the co-created success criteria).  Afterwards, the learning needs to be 'debriefed' so the students can internalize the learning.  It's not about the 'grade/mark' (i.e. once we put a grade on the page, then learning stops) but the learning that took place achieving that mark/grade that matters.  This is apart of a bigger conversation around Assessment FOR, AS & OF learning (future blog topic).

By modelling and 'debriefing the thinking process' we will instill true 21st century skills in our students. Check out the 2 resources below (located in the bookroom) for some good starting ideas.

Great ready made resources...or get an idea & create your own.

Open Response Questions

Individually we are one drop.  Together we are an ocean.

Ryunokuke Satoro

Open Response questions need to be 'deep thinking' types of questions that force students to both demonstrate & apply content knowledge in some way.  Our 'target' range should always be in the GREEN area of the chart below. This is not to say we ignore the other areas.  There is value here, however, the remaining three areas of the chart could/would potentially be revealed as we are probing the Level 3/4 questions (or used as 'lead-ins' to the 'bigger' questions).  

The real strength comes when we all 'move as one'  school in terms of being focused on all asking the 'deep thinking' types of questions regardless of grade level.  We know that this process is very complicated, in that, it requires precision planning & teaching of skills over time (i.e. grade by grade).  This 'pooling of drops' as an entire school is key to 'building the ocean' of success.  

Q-Chart to guide forming 'deep thinking' Open Response questions

Math Journals

Right v. Wrong

Last year we talked about developing a 'collective strength' in the building to maintain the learning continuum from grade to grade.  After all, learning doesn't start and stop from one grade to the next. Learning moves along each individual persons 'continuum of learning' (smooth and gradual).  Thus, it is vital that we be able to provide smooth transitions to learning from year to year.  This doesn't mean everyone doing exactly the same things, however, there are a few things that are proven 'result oriented' best -practices.  For example, we all need to understand the Literacy & Numeracy Block, Small Group Instruction, Differentiated Instruction, etc...

In math the goal is to foster the thinking via a problem solving perspective.  It's not about 'correct' or 'incorrect' answers (i.e. not black & white).  For example, the correct thinking/procedures can be followed but still get an incorrect answer.  As a result, a Math Journal is a very good strategy to use for all.  Below is an excerpt from the Guide to Effective Instruction in Mathematics K-6  that talks about the 'big picture' in math...student self-assessment.

Student Self-Assessment

Students should have frequent opportunities to reflect on their own learning, to identify
their strengths and those areas requiring growth, and to set appropriate goals. Student
self-assessment can be accomplished through the use of journals; rubrics, checklists,
and rating scales; portfolios; and surveys and questionnaires.

JOURNALS (LEARNING LOGS)

Journal writing helps students think about what they are learning. Students can
record in their journals using written work, pictures, diagrams, stamps, and charts.
Through these forms students often communicate mathematical ideas that they 
cannot express orally. In their journals students also have opportunities to express
how they feel about a particular learning activity or about mathematics in general. 
Teachers can provide prompts to help students focus on what they did and learned 
in a mathematics activity:

• Sentence stems:
– In math, I am learning . . .
– I understand . . .
– I don’t understand . . .
– I find it easy to . . .
– I find it difficult to . . .
– My favourite part of math is . . .
– I do best in math when . . .

• Other journal prompts:
– Write everything you know about . . . (e.g., 50; a cube; multiplication).
– Imagine that a classmate is absent today. Write a letter to explain what we 
did and what we learned in math class today.
– Explain how you could . . . (e.g., find the most popular flavour of ice cream 
in the class; find the answer to 3 x 6 if you didn’t know the answer by heart; 
find the area of the classroom floor).
– Write a story that . . . (e.g., uses the fraction one-half or one-third; is about a 
symmetrical object; uses division).
– Write a math problem about . . . (e.g., telling time; subtraction; the graph that
the class created this morning; percent).
– Measurement is . . . ; Symmetry is . . . ; Division is . . .

Check out the Guide to Effective Instruction in Math K-6 V4 for more information.

Moving Beyond the Worksheet

I think this article does a nice job of encapsulating some of our own feelings.  I can relate to this article as I reflect on my own career.  I know how I taught when I first started and the progression I saw in my own practices.  I have come to realize that the cliche that there is 'only one right answer' in math might be true (a topic for another conversation), however, there are certainly numerous ways to get there.

 

 

The Math Standards and Moving Beyond the Worksheet

Teaching the common standards in math

http://www.edweek.org/ew/articles/2013/03/27/26crowley.h32.html

By Alison Crowley

When I started teaching algebra 12 years ago, I was given a textbook, a day-by-day plan listing the sections in the textbook that I was expected to teach, and a roster of students. I attended various trainings the summer before about state assessments, technology, and special education laws, and boom! I was off and running.

One of the things I remember most from those early years was a laminated poster I had that listed all of the state standards for algebra. I was instructed to cross them off as the year progressed so it would be very clear to myself, my students, and any visitors exactly what was happening in my classroom.

I have to admit that, as a math person, I loved my standards chart. It gave me a sense of accomplishment at the end of each lesson to cross off that related standard, confident that I was doing exactly what I was supposed to be doing. It gave me a sense of reassurance. If I graded a set of assessments with surprisingly low scores, I would be able to look at my chart and say to myself, "Huh, I wonder why they missed that question about exponents on the test. I mean, I can see right there on my chart that I covered the material. And I remember that I assigned all of the problems in the book. My students really need to spend more time on homework." Just like that, the responsibility had shifted from me to my students.

"The good news is that the common-core standards provide an open playing field that encourages teachers to move away from the step-by-step model."

It wasn't until much later that I realized that "teaching math" and "covering textbook sections" were not synonymous.

Before I started implementing, or had even heard about, the Common Core State Standards, I had already begun shifting my instructional practices to include more hands-on activities and group work, and less book work. Project-based learning began trending in my math-teacher circles, and pursuing national-board certification forced me to rethink my instructional practices. Were my students actually learning the material for mastery, or were they just good at following directions and memorizing steps?

Fast forward to the 2011-12 school year, when I heard Ann Shannon, a mathematics educator and consultant then working with the Bill & Melinda Gates Foundation, describe what she refers to as math teachers' tendency to "GPS" students.

Think about it: If a teacher is explaining how to solve a system of equations using the substitution method, she might list on the board a set of steps for students to follow. Step 1: Solve one of the equations for one of the variables; Step 2: Substitute the value or equation found in Step 1 into the other equation. If you peeked inside her classroom on this particular day, you would likely see all the students copying notes, and then probably completing a worksheet with problems similar to the example. From an observer's perspective, you might think the lesson was going well.

But do the students really have a solid understanding of the mathematics they are using? And, more importantly, do they understand why they're using it? Do they have a graphical understanding of what it means to solve a system of equations? Can they explain their methodology to another student? Can they apply it to real-world situations? Is their knowledge transferable so that they will be able to draw upon it when they are solving more difficult systems of equations in future math classes?

My guess is that the answer to most of these questions is no. What Ann Shannon would say is that in this particular situation, the students have been "GPS'ed" from problem to solution. Just as when I drive in a new city using my global positioning system, I can follow the directions and get to where I need to go. But I can't replicate the journey on my own. I don't have a real understanding of the layout of the city. If a road were blocked because of a parade, for example, I would be in trouble because I have no real understanding of the city's geography.

So, how can we keep from GPS-ing our students, so that they understand the mathematics behind a series of steps? How can teachers help them grasp the why, instead of just the how?

The good news is that the common-core standards provide an open playing field that encourages teachers to move away from the step-by-step model.

 

Consider the following high school algebra standard for solving systems of equations:

Explain why the x-coordinates of the points where the graphs of the equations y=f(x) and y=g(x) intersect are the solutions of the equations f(x)=g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.

Remember the earlier example about the teacher showing the students how to solve a system of equations using a set of steps? The first sentence of the new standard, "Explain why the x-coordinates where the graphs intersect are the solutions," really pushes the teacher to introduce and explain a new concept in a way that goes beyond one-dimensional instruction. What is an x-intercept, and what does it look like on a graph? How is that related to the algebraic equation? Perhaps rather than starting a lesson with the steps for solving the equations, the teacher might first have students consider graphs of related equations, or better yet, a real-world example of a system of equations and what the values of the x-intercepts mean in that situation. This standard also challenges the teacher to present multiple types of equations from the beginning of the lesson so that the students can apply the concept of an x-intercept to many types of functions.

For many teachers, myself included, this is a fairly significant change in instructional practice. Although I have taught lessons on solving systems of equations using real-world applications and emphasizing graphical connections, I have not yet truly focused my instruction on the "why" behind the mathematics or given students opportunities to create their own understanding.

So how do math teachers make that shift away from GPS-ing students a reality? It won't be easy, and we can't do it alone. We need opportunities to collaborate, plan, and reflect with colleagues, both in our buildings and nationwide. We need quality resources and relevant, engaging professional development. We need time to learn from teachers who are already successfully implementing the common core, like Kansas educator Marsha Ratzel, who recently shared insights in her essay "The Talking Cure: Mathematical Discourse" (Education Week Teacher online, Dec. 31, 2012), on how her students' mathematical-thinking skills evolved when she gave the students time and space to have conversations about math. We need administrators and parents to support us and play an active role in helping us transform our classrooms into places where students are truly engaged in what they are learning.

In my daily classroom instruction, I am still sometimes guilty of GPS-ing students. But I am hopeful that as I learn how to fully implement the common standards, I will become less and less dependent on steps and crossing standards off a poster. After all, my students really deserve to navigate themselves.

Alison Crowley teaches Algebra 2 and Advanced Placement Calculus at Lafayette High School in Lexington, Ky. A national-board-certified teacher with 12 years of experience, she is also a member of the Center for Teaching Quality's Common Core Lab. For more stories on teachers' efforts to adapt to the common standards, see Education Week Teacher's new online package, "Common-Core Instructional Opportunities."

Vol. 32, Issue 26, Pages 29,31

Metacognition

Metacognition

What is a Portfolio?

S. Colautti                                                         May 2013                             Student-Led Conferences PLC

What is a Portfolio?

    A portfolio is a purposeful collection of selective significant samples of student work accompanied by clear criteria for performance which evidence student effort, progress or achievement. A portfolio is different from a folder in that it includes:

o Explicit guidelines for selection

o success criteria

o Clear objectives for each task

o Selective and significant pieces (evidence of progress, favourite work, etc.)

o Students’ self-reflection pieces

o Evidence of student participation in selection of some of the content

    A portfolio exhibits the student's progress and achievement in several subject areas, but should focus on reading, writing, and mathematical problem solving. The contents can be varied.  Some suggestions are: work samples, journals, compositions/essays, photographs, checklists, projects, videos, audio clips, self assessments, student reflections, summative evaluations, etc.

There are many online resources that can support teachers starting the journey towards portfolios and student-led conferences. Here are some for you to peruse:

1. Various types of portfolios, pedagogy, information for teachers

http://www.education.gov.sk.ca/default.aspx?dn=9bd9d964-02fb-445f-af46-80dc5b7a5f32

2. Portfolios for student growth for all grade levels http://www.gallaudet.edu/clerc_center/information_and_resources/info_to_go/transition_to_adulthood/portfolios_for_student_growth.html

3. How to build a portfolio for elementary students

http://k6educators.about.com/od/GradingStudents/a/5-Steps-To-Building-A-Student-Portfolio.htm

September Readiness

September Readiness

I want to put out a 'list' (for lack of better term) of some things to keep in mind as we prepare for the upcoming school year.  This 'list' is by no means an exhaustive/complete 'all encompassing' list but only a group of ideas to help guide our collective efforts.  Like we have talked about many times, we are all individually extremely strong at what we do.  However, it is our collective strength that makes the most impact on our students.  As a result, we need to collectively be 'on the same page' to allow the 'big picture' to materialize.  Please allow this 'list' to help guide your September Readiness.

• Planning (i.e. long-range, unit, short-term)... intentional & purposeful professional facilitation of year long road map of learning is key to student achievement...What teachers do in the classroom is the #1 predictor to Student Achievement.  Some students come to us with less than others which only means we need to be more deliberate in our practice.
• School Supplies (student purchased supplies) - list out with June Report Card
• Data driven instruction - classlists, IEP's, most current data all provided by end of June.  Most Data has been inputted into the document in Google.  If you have 'lost' your link, please let me know and I will resend. 
• Early Intervention (Goal/Priority) - We need to do everything we can early on in a students career to insure then can read.  The majority of our school level support will be spent trying to achieve this goal.  The research is clear that students who are not at grade level by Gr 1/2 will probably never be there.
• Classroom teaching practices have definitely moved to focused small group instruction (i.e. Guided Reading/Math).  All kids learn at different levels.  You might like to take the Spec Ed model literally (i.e. IEP - Individual Education Plan).  Some students require the officially paperwork but all kids require the concept of individualized teaching.
• LSST 'blitz' first couple of weeks -  JK staggered entry, IEP 'touch ups' & Guided Reading schedules will consume our LSST's over the first couple of weeks.  The goal is to be in 'full swing' by the third week.
• Class schedule...has guided reading time this year.  You will be getting a template to fill in and submit with your regular class schedule.
• Student-led Conference - meta-cognition.  The only thing you need to begin with is some form of student portfolio for each student.  Our first Divisional Meeting will cover the 'next steps'.  If you have any questions, please ask.
• Math from a problem solving perspective.  Last year was great and we would like to continue our growth in this area.  Open & Parallel questions (see Marian Small resource).  Giving students an open/parallel question allows them to attack the problem at their level and showcase their math knowledge.  This allows us to meet them at their level and move them to the next level (i.e. the curriculum is a continuum) and thus meets a goal previously stated regarding Individual learning.

June Clean-up Reminders

June clean-up

Here is a list (not comprehensive) of some reminders for June.  

• Room clean-up - old materials (i.e. phonics cards, non-fiction resources, class sets of dictionaries, texts, etc...)
  • Learning space is the third teacher - What does yours teach?
    
• School resources (i.e. assessment kits, Learning PIT math resources, non-fiction back to PIT, Trait Crates, etc..) need to be returned to proper area
• Classroom libraries, class math resources stay in class (Libraries will move to PIT on last day for cleansing and be returned to classroom for you)
• OSR - sign & 'tidy'
• Portfolios - cull them (i.e. assessments remain - CASI & PM, rich work samples in reading, writing & math).  The idea of a Portfolio is to show growth over time (i.e. from grade to grade).  As a result, by the time the student is in Gr 3 there should be examples from each of the previous years.    We will set-up some boxes for you to place your class portfolios in for summer clean-up.  
• Paper usage...want to buy more technology - paper less not paper free. Double-sided, etc...
• Shred student personal information before leave for summer
• Save mark sheets...just in case until at least mid-Fall
• SEA equipment - collected by LSST's and stored
• IEP - LSST's to set IEP's in June for the Fall. Please have your notes ready
• Update PM Wall & Word Study binder & CBM data...find your students in new class lists and update.  The CASI data is far too 'bulky' for this process.  We will organize & distribute.

School-Wide Math Culture: Model & Nurture

MODEL AND NURTURE POSITIVE ATTITUDES, SELF-EFFICACY AND ENGAGEMENT.

As educators gain the mathematical knowledge for teaching, they become more capable – and confident – in helping students extend and formalize their understanding of mathematical concepts. This can contribute to students’ development of positive attitudes toward mathematics and an increase in their sense of self-efficacy. Self-efficacy, which is an individual’s belief in whether he or she can succeed at a particular activity, plays an integral role in student success. Bruce and Ross discovered that “increases in teacher efficacy led to increases in student efficacy and outcome expectancy and to student achievement” (2010, p. 10).  In turn, strong student self-efficacy can contribute to greater enthusiasm and engagement in mathematics (Ross, 2007, p. 52). (Maximizing Mathematical Learning in the Early Years).

Goal:  Reach ALL Learners.

How?

Create a Math Talk Community by developing students reasoning along with the capacity to articulate and communicate.

• Turn & Talk - "The Worker is the Learner" - get students to restate their thinking & get students to comment on that thinking with the teacher being the lead learner/facilitator.

• Revoice - "Mathematization" - when the students are 'grappling' with an idea/concept and need clarity and then the teacher with 'highlight' the idea/concept.  The 'struggle' will stretch the mind and thus provide a foundation for "mathematization" to build on.

• Slow down - Who heard what?  We are not looking for 'right' answers but 'right' thinking.  The Lead Learners (i.e. teacher) needs to ask more questions when questions are asked, repeat/repeat/repeat and thus hold students accountable for their talk.

• Problem-solving - teach students from a problem-based perspective focusing on the Big Ideas.  Utilizing 3 Part Math as a way to structure our 60 minute learning block is a great starting point.

By incorporating these concepts in our planning & assessment practices, our entire school will see a dramatic change in the mathematical output of each of our students. 

Student-led Conferences

Student-led Conference

Student Self-Assessment

Student-led conferences offer authentic opportunities for students to share their learning with their parents/caregivers.  They engage and motivate both students and parents to participate enthusiastically in the teaching-learning process.  Student-led conferences strengthen the relationship between home and school and also bring students and parents closer together.  

Literacy & Numeracy Secretariat

Student-led conferences is the next step in our students evolution that will tie in and exemplify the power of learning goals, success criteria, anchor charts, etc...  The students will use their metacognitive skills to tap into their learning at an entirely new level. Moreover, as we move forward as a community of learners, the student success will reach new heights due to our consistent and collective strength.  

Our classrooms are set-up with the kids in mind, for the kids to utilize and thus there is meaning for the kids with everything in our rooms.  

When students articulate their learning, they consolidate their thinking. As they learn to express themselves, they are developing their communication skills and strengthening their understanding.

Literacy & Numeracy Secretariat

Follow the link to the Curriculum Services Canada website to watch a number of web casts that support Student-led conferencing.  

The Capacity Building Series (Literacy & Numeracy Secretariat) has a monograph on Student Self-Assessment.  This is a good resource.

School-Wide Math Culture: Mathematization

FACILITATE EXPERIENCES THAT ALLOW FOR MATHEMATIZATION OF EVERYDAY KNOWLEDGE.

Knowledgeable educators help students transform their everyday mathematics into a more formalized understanding that can be transferred and applied to other situations. Several researchers refer to this as “mathematization” which requires students to abstract, represent and elaborate on informal experiences and create models of their everyday activities (Clements & Sarama, 2009, p. 244). The educator can play an integral role by making meaningful connections between the mathematical strands, the real world and other disciplines, and most importantly, “between the intuitive informal mathematics that students have learned through their own experiences and the mathematics they are learning in school” (Ontario Ministry of Education, 2003, p. 14). For example, as a child naturally creates and extends a pattern while making a necklace, the educator can effectively pose questions that provoke the student not only to describe the pattern, but also to make predictions and generalizations. (from Maximizing Student Mathematical Learning in the Early Years)

Can U Beat These Mathematicians?

"Mathematization' can be an uphill battle but one worth fighting.

Honouring the Student Voice in the Mathematics Classroom is a webcast that highlights the goal of mathematization.  

The 'Student Voice' is exactly where your students are in their math journey.  It is important to listen to this 'Voice', support it and move it forward along the mathematical continuum (i.e. curriculum) through mathematization.

School-Wide Math Culture: Everyday Mathematics

IDENTIFY AND USE EVERYDAY MATHEMATICS KNOWLEDGE TO PLAN INSTRUCTION.

Knowledgeable educators begin planning by carefully observing children at play or engaged in other activities in order to identify their everyday mathematics. Next, they accurately interpret the mathematics underlying the behaviours and how it fits into the key mathematical concepts and curricula. Once identified, educators can create activities which allow assimilation of new concepts into the children’s prior knowledge (Ginsburg, 2008, p. 59). As educators observe student problem-solving, they can document what children say, do and represent in order to make both planned and “in-the-moment” decisions about how to respond, challenge and extend student thinking. (Maximizing Student Mathematical Learning in the Early Years)

Even though the above excerpt is taken from the Capacity Building Series: Maximizing Student Mathematical Learning in the Early Years it can be applied to all grades from a problem-solving perspective.  Consider the following thinking:

1. Understand your curriculum to the point you shape/form it into 'Big Ideas'
2. Find interesting ways to match the 'Big Ideas' to problems for your class to solve
3. Allow students to 'play' with the problem
4. Observe & Learn with your students
5. Intervene when necessary to 'mathematize' student thinking/work

Dan Meyer on Real-World Math

Many students struggle with math or have difficulty understanding the subject. Educator Dan Meyer has come up with various scenarios that can help students enjoy math and add some fun to learning it.

  

Dan Meyer blogs at http://blog.mrmeyer.com.

Challenge:

If you want to try something new and give it a 'fair' opportunity for success, then you must eliminate your current system (at least for a specified time period).  For example, one area to remove would be the reliance on 'class sets' of photocopies &/or textbook work.  If this is an area you currently use, then remove it for a period of time (i.e. 2-3 weeks).  See what happens....the 'withdrawal' symptoms are only temporary.

School-Wide Culture: Math Talk

(The concepts come from The Capacity Building Series: Maximizing Student Mathematical Learning in the Early Years)

The Starting Point...

Immerse yourself in the curriculum and supporting documents. 
Attain a better understanding of the expectations and the seven mathematical processes by reading about the explanations and rationale in the front matter of the Full-Day Early Learning Kindergarten Program and Grades 1 to 8 Mathematics curriculum. (p11-17)

Look before and beyond the grade you are teaching to see how concepts build upon each other. 
Utilize the document provided during our Divisional Meeting which shows the Math Curriculum on a continuum from grade to grade. 

There is a wealth of resources that can offer extra insight into the mathe- matics itself and can help to identify and connect the key mathematical concepts. 
Some of these include the Guides to Effective Instruction in Mathematics and the works of Dr. Marian Small, Catherine Twomey Fosnot and John A. Van de Walle. 

Your professional learning journey will be most effective when you delve into mathematical ideas with colleagues and together inquire about how your understanding impacts your related teaching.

Culture of Classroom Discourse

(Lucy West)

Teacher-facilitated “math talk”  significantly increases children’s growth in understanding of mathematical concepts.  Knowledgeable educators recognize that although children may have a beginning understanding of mathematical concepts they often lack the language to communicate their ideas.  By modelling and fostering math talk throughout the day and across various subject areas, educators can provide the math language that allows students to articulate their ideas.  

It is also important to encourage talk among students as they explain, question and discuss their strategies while co-operatively solving problems.  In order to facilitate mathematical thinking rather than direct it, knowledgeable educators recognize when student thinking is developing or stalled. If it is developing, the educator observes but leaves the students to work through their thinking (Sarama & Clements, 2009, p. 325). If it is stalled, probing questions can be asked that provoke thinking about alternate ways to perceive the problem.

After students have worked through solving a problem, educators facilitate consolidation time (either with individual students or with small groups or large groups) in order to allow students to talk about their thinking. This consolidation time is sometimes referred to as the third part of the three-part lesson in mathematics.  As educators value a variety of strategies and solutions, they guide students to make connections between them, to recognize how the thinking relates to the key mathematical concepts and to make further conjectures and generalizations.

Five productive talk moves ...to create meaningful mathematics discussions.

Gives the educator an opportunity to embed mathematics vocabulary

1. Revoicing – Repeating what students have said and then asking for clarification 

"So you’re saying it’s an odd number?"

2. Repeating – Asking students to restate someone else’s reasoning 

"Can you repeat what he just said in your own words?"

3. Reasoning – Asking students to apply their own reasoning to someone else’s reasoning     

"Do you agree or disagree and why?"

4. Adding on – Prompting students for further participation 

"Would someone like to add something more to that?"

5. Waiting – Using wait time   "Take your time ... We’ll Wait .."

(Chapin, O’Connor & Anderson, 2009, p.13)

Guidelines for Whole-Class Math-Talk

(taken from - Student Interaction in the Math Classroom: Stealing Ideas or Building Understanding)

Explain: “This is my solution/strategy ...” “I think _____ is saying that ...”

• Explain your thinking and show your thinking.

• Rephrase what another student has said.

Agree with reason: “I agree because ...”

• Agree with another student and describe your reason for agreeing.

• Agree with another student and provide an alternate explanation.

Disagree with reason: “I disagree because ...”

• Disagree with another student and explain or show how your thinking/ solution differs.

Build on: “I would like to build on that idea...”

• Build on the thinking of another student through explanation, example, or demonstration.

Go beyond: “This makes me think about ...” “Another way to think about this is ...”

• Extend the ideas of other students by generalizing or linking the idea to another concept.

Wait time:

• Wait to think about what is being said after someone speaks (try five seconds).

The Value of Student Interaction

In the math reform literature, learning math is viewed as a social endeavour.1,2 In this model, the math classroom functions as a community where thinking, talking, agreeing, and disagreeing are encouraged. The teacher provides students with powerful math problems to solve together and students are expected to justify and explain their solutions. The primary goal is to extend one’s own thinking as well as that of others.3

Powerful problems are problems that allow for a range of solutions, or a range of problem-solving strategies. Math problems are powerful when they take students beyond the singular goal of computational mastery into more complex math thinking. Research has firmly established that higher-order questions are correlated with increased student achievement, particularly for conceptual understanding.