1.
The Learning Space
Seems we hear so much about student-centred classrooms
involving collaborating learning, teachers moving about the room
for small group instruction, teaching through manipulatives,
interactive white boards and math applets or digital learning
supports, does anyone ever talk about the chalk board (or
whiteboard) anymore?
Even though we are changing our practice to involve students
more and provide more experiential learning, there will always
be a necessity of some explicit instruction in mathematics. Our
subject is extremely visual and procedural. Marzanno (2004)
lists explicit instruction among instructional strategies that have
significant effect size. Intensive-explicit instruction can be a way
to efficiently teach content (Knight, 2013). It is the reality of math
instruction that we need to demonstrate by writing, using
symbols and diagrams, either on a chalkboard, whiteboard, or
interactive board. Even though we want to spend lots of time
circulating around our classroom and interacting with our
students, we still need a focal point in the classroom.
Modeling logic and thinking are extremely important
instructional practices. As we write our mathematical processing
on the board, we are modelling logic and representation. Our
own organization or lack thereof will be reproduced in student
notebooks. If we want our students to have a collection of class
notes that are useful for reference and review, then we need to
attend to the logic and order with which we present the material.
Some things to consider are:
1. Visual Learners: It is estimated that between 30% and 65% of
our students are visual learners. These students rely heavily on
the representations that we write on the board. Sometimes after
we have finished talking and explaining and have moved on, these
students are still looking at what we’ve written and represented.
All students must learn visually in math some of the time. Visual
learners also benefit from multimedia, use of colour, and
manipulatives.
2. Cognitive Overload: Students that struggle with math are
processing slowly. Often we design exams with lots of white
space for these students, because they need to concentrate on a
small amount of material at a time. The same is true with how
Effective mathematical
Communication involves
expression and
organization of ideas
and mathematical thinking
(e.g., clarity
of expression, logical
organization), using
oral, visual, and written
forms (e.g., pictorial,
graphic, dynamic, numeric,
algebraic forms; use of
conventions, vocabulary
and terminology of the
discipline (e.g., terms,
symbols) in oral, visual, and
written forms .
Ontatrio Ministry of
Education, 2005
“The blackboard may
be verily called the
second tongue of the
Mathematics
teacher….It should not
be used in the manner
that the teacher goes
on writing and
drawing and the
students go on copying.
The entire matter to be
written on the
blackboard should be
developed with the
active cooperation of
the students…Students
should also be given
the opportunity to
write and draw on the
blackboard.”
K. Singh Sidhu
2.
and what we write on the board. Many students are
overwhelmed by math work on the board that is crowded,
overlapping, or out of sequence.
3. Summarizing and notetaking is another instructional
strategy with a significant effect size. In younger grades
students may just copy what we write, but as they move into
senior grades, students synthesize the information for
themselves. The logic and order that we model will become
part of the representation style of our students.
4. Communication: Effective mathematics instruction involves
communication that is both verbal and written. We
communicate, model, and explain our reasoning to students by
how and what we record on the board. We need to model
effective written mathematical communication that includes
logical reasoning, worked examples, units, appropriate
mathematical terminology, and explanations.
5. Adaptation: Since we want to adapt our teaching for
students with learning disabilities, hearing impairment,
attention and behaviour issues, and English as an Additional
Language learners, it makes sense to include a strong visual
component to our instruction.
6. Unlike technology, powerpoint, print, and video instruction,
explicit instruction that includes chalkboard, whiteboard, or
interactive board is very flexible. It allows the teacher to gauge
understanding and adjust instruction. Though we are using
direct instruction in these instances, we are still eliciting
student input, assessing for understanding, and adapting our
instruction to fit the learning that is taking place.
The TIMSS study which compared math instruction in several
countries including Japan, United States, and Germany, noted
that 100% of Japanese teachers use the chalk board for part of
their instruction. They use it as a record and running
documentary of the entire lesson. Teachers plan ahead of
time what the board will look like, what will be recorded,
they record sequentially and avoid erasing. They expect that
not all students will be focused in every part of the lesson at
the exact time. They expect students to look back to previous
parts of the lessons. Japanese students rank very high globally
in math ability. It is worth noting that Japanese students are
assigned less homework than most other countries, and that
“Most aspects of
Mathematics can be
clarified only through
writing. Verbal
explanation will not
suffice in such cases.”
K. Singh Sidhu
“Here, Germany and the U.S.
are virtually identical—the
purpose of seatwork is to
practice the procedure being
taught. In Japan, by contrast,
teachers placed much more
emphasis on getting students
to come up with new ways to
solve a problem that they’ve
never seen before or to use
mathematical reasoning
to prove something. Fifty-four
percent of the Japanese lessons
included proofs. None of the
American lessons included
proofs.”
From the TIMSS study.
California State University
Institute for Education
Reform.
“We found that 47% of the
American lessons only
included applications,
without any reference to any
kind of a math concept in the
lesson; that is, teachers taught
students that A to the M power
divided by A to the N power
equals A to the M minus N
purely by repeating examples,
rather than stating the
underlying math concept. This
was very rare in Japan
and Germany.”
From the TIMSS study.
California State University
Institute for Education
Reform.
3.
math is taught through problem solving (The California State University Institute for
Education Reform, 1997).
Some helpful hints gleaned from countless web resources and blog postings on this topic:
Start with a clean board and organized learning space
Create a routine: Date, title, text book page, learning target, etc.
Keep writing large enough and neat.
Include diagrams.
Use colour.
Work in sequence.
Show logical steps.
Model logic and order.
Include margin notes, cautions, explanations, reminders, study hints,
additional references.
Avoid erasing too soon.
Ask for class participation. Have students contribute to board work when
applicable.
Provide worked examples.
Avoid clutter.
Consider using the board as “anchor notes” while students work through
collaborative activities.
Use part of the board for instructions for activities. Some students have
difficulty remembering and following instructions. It’s handy to be able to
redirect them to the activity instructions, group member, group roles,
expectations, etc. that are recorded on the board.
Look at how and what students are recording in their notebooks. Provide
specific feedback.
Instructional
Scaffolding
Means providing supports
for students to enhance
learning and aid in the
mastery of tasks.
Content
Task
Material
Instruction
-Riccomini, P. 2012
High Impact K-8
Mathematics
Teaching Strategies to
Maximize Learning
Of Essential Skills and
Concepts
References:
Brown, A. The Advantages of Using Chalkboards in Teaching. http://www.ehow.com/list_5872788_advantages-using-chalkboards-teaching.html
Retrieved April 2013
Buddle, C. In praise of chalk: the value of teaching without technology.
http://arthropodecology.com/2012/04/11/in-praise-of-chalk/ Retrieved April 2013
Jones, K. Teaching Math to a Visual Learner.
http://www.time4learning.com/teaching_math_to_visual_learner.shtml, retrieved April 2013
Knight, J. (2013). High-Impact Instruction. Thousand Oakes, CA.: Corwin Press.
Lessons in Perspective: How Culture Shapes Math Instruction in Japan, Germany
and the United States. A discussion sponsored by The California Education
Policy Seminar and The California State University Institute for Education
Reform. http://www.csus.edu/ier/reports/math.pdf Retrieved April 2013
Riccomini, P. High Impact K-8 Mathematics; Teaching Strategiesto Maximize Learning. Webinar, Nov.
2012
Singh Sidhu, K. (2006). The Teaching of Mathematics. Okhla, New Delhi. Sterling.
Teaching Math To A Visual Learner.
http://www.time4learning.com/teaching_math_to_visual_learner.shtml Retrieved April 2013
Teacher tips: Understanding the visual learner.
http://www.helium.com/items/1762331-educat-teach-communicat-visual-learn-style-thought-brain-
cognitive-skill-ability-school Retrieved April 2013
4.
Sciematics: The Changing Face
of Education. Saskatoon, May
9-11, 2012, College of
Agriculture and Biosciences, U
of S.
http://www.sciematics.com/
SUM conference: May 3-4,
Saskatoon. Featuring Dan
Meyer and Marian Small.
http://www.smts.ca/sum-
conference/
http://whatsonmyblackboard.wordpress.com/
Support for Teaching through
Inquiry:The Saskatchewan School
Library Association offers information
to help teacher-librarians improve
services and remove barriers in order to
effectively advocate school libraries as
an essential component of the
enhancement of student learning.
Teacher-librarians Constructing
Understanding through Inquiry is a
strategic partnership between the SSLA,
a special subject council of the
Saskatchewan Teachers Federation, and
the Ministry of Education. The intent is
to develop supports for instruction to be
used by educators, particularly teacher-
librarians, as they strive to understand
and actualize their role in an inquiry-
based learning environment. See
Webinar schedule below to see what
supports are being arranged for teachers.
Webinar #3 - Assessing Inquiry April 9
4:00-5:00
Webinar #3-Using Inquiry May 15 4:00-
5:15
For more information or to register, go to
http://ssla.ca/Inquiry%20Webinars
If you require further information about the
project, please contact Judy Nicholson via email
(judy.nicholson@gov.sk.ca) or by telephone
(306) 787-6098.
Web Resources:
ASCD is a A lesson on division of fractions from ASCD. http://www.ascd.org/ascd-
express/vol8/813-
englard.aspx?utm_source=ascdexpress&utm_medium=email&utm_campaign=express8
13#.UVRm-6H02pA.google_plusone_share
membership organization that develops programs, products, and services essential to
the way educators learn, teach, and lead.
http://www.ascd.org/about-ascd.aspx
Google sketchup: http://www.youtube.com/watch?v=gsfH_cyXa1o
Allows you to make easy 3D shapes, designs, isometric drawings
A cool visualization of numbers based on their factors:
http://www.datapointed.net/visualizations/math/factorization/animated-diagrams/
Great collection of math resources and applets: http://www.tsm-
resources.com/mlink.html
Paranormal Distribution
A pizza with radius, z, and
thickness, a, has volume
Murray Bourne
The Scale of the Universe. This nifty applet lets you zoom in an out
to see measurements in scientific notation for the tiniest atomic
particles to entire galaxies.
http://www.newgrounds.com/portal/view/525347
http://gridmaths.com/grid.html
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