My Delicious tags
I just did a wordle of my tags of websites I have bookmarked on delicious…maybe this will help me focus my master’s thesis!
Hence my technological addiction...
K-8 article reflection: What is mathematical understanding?
What is mathematical understanding? Obviously, not an easy question to answer. Maybe it is one of those questions that is easier to pin down by saying what it is not….
After reading pages 1 – 15 of Making sense: teaching and
learning mathematics with understanding
(Authors: James Hiebert, Thomas P.
Carpenter, Elizabeth Fennema, et. al.)
My summarizing thinking questions (using the helpful verb list at http://www.teach-nology.com/worksheets/time_savers/bloom/) for us are:
1) What is mathematical understanding?
2) How do reflection and communication enhance mathematical understanding?
3) Prioritize the 5 dimensions in terms of your own classroom and outline what your personal approach is to each of them.
The 5 dimensions the article refers to are:
a) Nature of Classroom Tasks
b) Role of the Teacher
c) Social Culture of the Classroom
d) Mathematical tools as learning supports
e) Equity and Accessibility
4) Propose an opportunity for learning that you might envision in your class for students to reflect and communicate mathematically.
I love Bloom’s Taxonomy and how it fits in with good questioning. Check out the link from Manitoba Education and Youth’s Literacy with ICT document: http://www.edu.gov.mb.ca/k12/tech/lict/resources/handbook/section2.pdf see page 16
Laptops for achievement research article…Class 2 Research Methods
I read the article http://www.cjlt.ca/index.php/cjlt/article/view/158/152 in class on Friday and thought, “Why am I not doing something for my thesis on educational technology?” I need to talk with my advisor and see about doing a mixed-method research thesis on a brilliant topic that I am passionate about. I hope it comes to me soon.
Off to the dock to have lunch on the Cobalt with 3 nieces and family at the lake!
K-8 Mathematics Course – Contructivist Directions
http://www.edu.gov.mb.ca/k12/cur/math/framework_k-8/document.pdf
This is the link for the “new direction” that Manitoba Education and Training is hoping educators will buy into and live in their classrooms. I am already a living, breathing example of one who embraces constructivist and fostering a positive “affect” in the cognitive discipline called mathematics! I can’t wait for a critical mass of colleagues to build up.
Here are my reflections so far on the article, “Adding it up: helping children learn mathematics” by Kilpatrick, Swafford and Findell, Washington, 2001. I like the acknowledgement of the 5 interwoven strands of:
a) conceptual understanding
b) prodecural fluency
c) strategic competence
d) adaptive reasoning
e) productive disposition – see sense in math, feel it is useful, believe in one’s math ability through perseverance and positivity. The teacher has a major role in helping create, build and maintain a positive attitude towards mathematics.
These 5 strands provide a broader, deeper view of proficiency in mathematics. It also points to the need for educators to identify common pinch points (areas of trouble) in math for students and multiple ways to have students experience them.
This is why I’m involved in my school division’s Edutube project. I will be using Microsoft Community Clips and other software to record lessons relating to grade 9 curricular outcomes and sharing them online. Can’t wait to get started.
First Master’s Class: Research Methods…more than just stats!
Yeah, I may be switching blog hosts as I am having posting issues. Working on it!
Regardless of the issues, here is my first day of classes post from July 2nd, 2009!
Today was my first day of my masters study! My first instructor actually congratulated and welcomed those of us who were first timers as graduate students! Although I completed my ICT course on my PBCE, I feel that my first course I enrolled in as a Masters student is also an important first for me in my lifelong learning journey.
We are using the text Educational Research: Fundamentals for the Consumer byJames McMillan (2008 version). I actually am using the 2004 version from the library and am hoping to compare with a colleague tomorrow to make sure I’m not missing anything. Actually, I’m going to email the author of the textbook at his workplace provided in the forward to ask him what he thinks are the most prolific changes (possibly just to certain chapters…).
I was inspired by my colleagues aspirations for their ideas when we brainstormed our first research hypotheses in class today. I love the diversity and the passion in all of the topics. Volunteers who shared their research topics included: use of school counsellors by students, the effect of class size on student learning, are math standardized test questions valid and reliable for all learners (EAL, immigrant and refugee students) and many more.
As for our assigned reading for tonight, I thought chapter 1 was interesting and hope to answer a few questions from the reading with my classmates or instructor on Friday
(if it is a good seguay to my instructor’s lesson maybe they will use something from my reflection here!):
(if it is a good seguay to my instructor’s lesson maybe they will use something from my reflection here!):
1) Is educational research (on the whole) usually quantitative? (I’m sure there is some number crunching out there on this, I’ll google it.) It seems my morning class with you has a quantitative lean to it while my afternoon class (Exploring the affective goals of the K-8 math curriculum) is leaning towards the qualitative side (we had 2 activities thinking about the assumptions curricula make qualitatively and are curricula socially constructed documents for what purposes?) I feel I picked perfect courses to balance myself this summer session – although the reading is already a time chunk! Luckily, I have a toolbelt of reading strategies at my disposal from colleagues with literacy talents.
2) Does using action research imply there is a deficiency in the classroom or school that you use it in or just imply sharing of best practice is desired?
3) What is a reliability co-efficient (page 21 r = .43 at first in the sample case study)? It’s been too long since my stats undergrad.
4) How can the sample researchers conclude that it isn’t the instructional materials but the students’ interactions with the materials (as determined as acheivement…) that is important…don’t get this yet.
5) Lastly, I thought the Table 1.1 (pg. 6) and Figure 1.1 (pg. 
were instrumental in getting the big picture of the characteristics and framework of scientific inquiry. I love the science and math integration!
were instrumental in getting the big picture of the characteristics and framework of scientific inquiry. I love the science and math integration!Here’s to a happy tomorrow.
Direct posting from Google docs…hmmm, maybe I should use WordPress instead…
Grade 9 Mathematics Outcomes
Add your name to the list below and pick a colour for yourself.
Add your name after an outcome of your choosing you’ll be preparing a lesson on.
Thanks to Carole Bilyk for the updated version here(as of Thursday June 18th).
Group Ideas Shared at Board Office (pre-requisite skills that mini-lessons could be prepared are mentioned as well as identifying PINCH POINTS for areas in which students need more direction on – feel free to add your ideas in your own colour of text in the strands below the appropriate outcome).
The document below was taken from: Carole Bilyk at Manitoba Education and Training from an email attachment to S. Snyder (June, 2009)
|
Number |
General OutcomeDevelop number sense. |
|
9.N. 1. Demonstrate an understanding of powers with integral bases (excluding base 0) and whole number exponents by: · representing repeated multiplication using powers **Pre-REQ: difficult concept,
· using patterns to show that a power with an exponent of zero is equal to one **Pre-REQ: difficult concept, show some patterns(whole number base) · solving problems involving powers [C, CN, ME, PS, R] |
|
9.N.2.Demonstrate an understanding of operations on powers with integral bases (excluding base 0) and whole number exponents.
**Pre-REQ: the meaning of what a power is ** Difficult concept [C, CN, ME, PS, R, T] |
|
9.N.3. Demonstrate an understanding of rational numbers by: § comparing and ordering rational numbers. § solving problems that involve arithmetic operations on rational numbers. [C, CN, ME, PS, R, T, V] |
|
9.N.4. Explain and apply the order of operations including exponents, with and without technology. Pre-REQ: basic order of operations skills review
[ME, PS, T] |
|
9.N.5. Determine the square root of positive rational numbers that are perfect squares. [C, CN, ME, PS, R, T] |
|
9.N.6. Determine the approximate square root of positive rational numbers that are non-perfect squares. [C, CN, ME, PS, R, T] |
|
Patterns and Relations |
General OutcomeUse patterns to describe the world and solve problems. |
|
9.PR.1. Generalize a pattern arising from a problem-solving context using linear equations, and verify by substitution. [C, CN, PS, R, V] |
|
9.PR.2. Graph linear relations, analyze the graph, and interpolate or extrapolate to solve problems. [C, CN, ME, PS, R, T, V] |
General OutcomeRepresent algebraic expressions in multiple ways. |
|
9.PR.3. Model and solve problems, using linear equations of the form: · ax = b · ax + b = c · ax = b + cx · a(x + b) = c · ax + b = cx + d · a(bx + c) = d(ex + f) · , x ≠ 0 where a, b, c, d, e and f are rational numbers. [C, CN, ME, PS, V]
**Pre-REQ: adding and subtracting integers, concept of an equation (equality)
|
|
9.PR.4. Explain and illustrate strategies to solve single variable linear inequalities with rational number coefficients within a problem-solving context. [C, CN, ME, PS, R, V]
**Pre-REQ: using number lines to represent numbers and order fractions/decimals/percents |
|
9.PR.5. Demonstrate an understanding of polynomials (limited to polynomials of degree less than or equal to 2). [C, CN, R, V] |
|
9.PR.6. Model, record and explain the operations of addition and subtraction of polynomial expressions, concretely, pictorially and symbolically (limited to polynomials of degree less than or equal to 2). [C, CN, ME, PS, R, V] |
|
9.PR. 7. Model, record and explain the operations of multiplication and division of polynomial expressions (limited to polynomials of degree less than or equal to 2). by monomials, concretely, pictorially and symbolically. [C, CN, R, V] |
|
Shape and Space |
General OutcomeUse direct or indirect measurement to solve problems. |
|
9.SS.1. Solve problems and justify the solution strategy using circle properties including: § the perpendicular from the centre of a circle to a chord bisects the chord. § the measure of the central angle is equal to twice the measure of the inscribed angle subtended on the same arc. § the inscribed angles subtended by the same arc are congruent. § a tangent to a circle is perpendicular to the radius at the point of tangency. [C, CN, PS, R, T, V] |
General OutcomeDescribe the characteristics of 3-D objects and 2-D shapes, and analyze the relationships among them. |
|
9.SS.2.Determine the surface area of composite 3-D objects to solve problems. [C, CN, ME, PS, R, V] |
|
9.SS.3.Demonstrate an understanding of similarity of polygons. [C, CN, PS, R, V] |
General OutcomeDescribe and analyze position and motion. |
|
9.SS.4.Draw and interpret scale diagrams of 2-D shapes. [CN, R, T, V] |
|
9.SS.5. Demonstrate an understanding of line and rotation symmetry. [C, CN, PS, V] |
|
Statistics and Probability |
|
General OutcomeCollect, display and analyze data to solve problems. |
|
|
9.SP.1. Describe the effect of · bias · use of language · ethics · cost · time and timing · privacy · cultural sensitivity. on the collection of data. [C, CN, R, T] |
|
|
9.SP.2. Select and defend the choice of using either a population or a sample of a population to answer a question. [C, CN, PS, R] |
|
|
9.SP.3. Develop and implement a project plan for the collection, display and analysis of data by: · formulating a question for investigation · choosing a data collection method that includes social considerations · selecting a population or a sample · collecting the data · displaying the collected data in an appropriate manner · drawing conclusions to answer the question. [C, PS, R, T, V] |
|
General OutcomeUse experimental or theoretical probabilities to represent and solve problems involving uncertainty. |
|
|
9.SP.4. Demonstrate an understanding of the role of probability in society. [C, CN, R, T] |
Edutube…a new divisional project I’m a member of…
I can’t wait to record some 3 min. or less lessons on pinch points in the grade 9 curriculum document.
I will post a link to the GoogleDoc of our outcomes and highlights so far.
Go technology!
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Professionally down the rabbit hole
Today I started a list of firsts.
I registered for my first masters in mathematical education course.
I attended my first virtual conference via sims in Second Life.
I went for my first 2 hour dog walk after surgery last week. I watched “Snakes on a Plane” for the first time (all right, the ONLY time) because of my Samuel L. Jackson addiction.
I look forward to a whole lot of new “firsts” in my journey in the digital learning world. I hope to share them here with you, and work this aspect into my professional growth model.
Cheers to a new professional learning network together!
