This document discusses traditional versus constructivist approaches to teaching mathematics. Traditional instruction focuses on memorizing procedures and facts, which can lead to children seeing math as memorization and struggling with non-routine problems. Constructivism emphasizes that children actively construct their own understanding through experiences like patterning activities, math games, and problem-solving. The document provides examples of kindergarten math lessons and assessments that exemplify a constructivist approach through open-ended tasks, discussion, and allowing multiple solution strategies.
My Origami Journey- From Classroom Teacher to University ProfessorBoakes, Norma
This presentation was an invited session of the MAA Association and held as part of the 2016 Joint Mathematical Meeting. My presentation focuses on the growing body of evidence of the value of Origami as a teaching tool in the K-12 math classroom.
My Origami Journey- From Classroom Teacher to University ProfessorBoakes, Norma
This presentation was an invited session of the MAA Association and held as part of the 2016 Joint Mathematical Meeting. My presentation focuses on the growing body of evidence of the value of Origami as a teaching tool in the K-12 math classroom.
Additional Resources:
Website for Making Rubrics: www.rubistar.org
Create Your Own Board Game Competition - 2016 Winners: https://americanenglish.state.gov/create-your-own-board-game-competition
Additional Resources:
Website for Making Rubrics: www.rubistar.org
Create Your Own Board Game Competition - 2016 Winners: https://americanenglish.state.gov/create-your-own-board-game-competition
32 Ways a Digital Marketing Consultant Can Help Grow Your BusinessBarry Feldman
How can a digital marketing consultant help your business? In this resource we'll count the ways. 24 additional marketing resources are bundled for free.
Creating Mathematical Opportunities in the Early Years
Presenter, Dr Tracey Muir, for Connect with Maths Early Years Learning in Mathematics community
As teachers, we are constantly looking for ways in which we can provide students with mathematical opportunities to engage in purposeful and authentic learning experiences. On a daily basis we need to select teaching content and approaches that will stimulate our children through creating contexts that are meaningful and appropriate. This requires a level of knowledge that extends beyond content, to pedagogy and learning styles. As early childhood educators, we can also benefit from an understanding of how the foundational ideas in mathematics form the basis for key mathematical concepts that are developed throughout a child’s school.
In this webinar, Tracey will be discussing the incorporation of mathematical opportunities into our early childhood practices and considering the influence of different forms of teacher knowledge on enacting these opportunities.
308. Don't FAL out;Techno IN!
This session will share several formative assessment lessons, activities and strategies that we have used within our classes as well as technology resources we have found very useful. Handouts are available online. You will feel like a kid leaving a candy shop!
Presenter(s): Jo Harris, Olivia Valk, Cody Powell
Location: Biltmore
The workshop will provide middle level mathematics teachers with ideas for engaging students in the understanding of math concepts and the creative aspects of mathematics topics in the 6-8 curriculum. The workshop will be hands-on and based upon a constructivist approach to learning and teaching. Handouts will be provided.
Presenter(s): Shirley Disseler
How to make the LOTE classroom more engaging & communicativedesalynn
The activities focus on getting the students to speak, read, write and comprehend the target language. There are task-oriented activities that engage students in creative language use including games, information gap activities and using authentic resources.
An afternoon follow-up session after classroom demonstration. Strategies for all learners: power paragraphs, descriptive feedback and oral language with tesselations in math, questioning from pictures.
Effectively Differentiating Mathematics Instruction to Help Struggling StudentsDreamBox Learning
Donna Knoell will offer ideas for blended learning strategies to help students understand mathematical concepts, increase achievement, and enhance confidence. Learn how to incorporate vocabulary, problem solving strategies, and manipulatives to help students develop reasoning skills and proficiency.
Join the discussion of issues including:
• Using blended learning strategies to increase mathematical achievement
• Integrating mathematical discourse to help students develop effective reasoning skills and proficiency
• Combining manipulatives and problem solving strategies in the classroom
Similar to Kindergarten parent math morning copy (20)
2. The Coke Problem
• How will the length of string wrapped once
around the can compare to the can’s
height?
• Will it be taller, shorter, or about the same
length as the height of the can?
4. Traditional Mathematics
Instruction:
• Students are expected to passively
“absorb” mathematical structures
through repetition.
• Teaching consists of “transmitting” sets
of established facts, skills, and concepts
to students.
5. Unfortunate Outcomes of
Traditional Mathematics
Teaching:
• Children see learning mathematics as
learning procedures to be memorized.
• Children have difficulty solving problems
that vary from the math they have
memorized, or that require a solution path
that is previously unknown.
6. What was your
math class like when
you were a child?
(Turn and talk to a neighbor)
9. Constructivism:
• Knowledge is actively constructed or
invented by the child, not passively
received from the environment.
• Ideas are made meaningful when children
integrate them into their existing structures
of knowledge.
10. Constructivist Teaching:
• Poses tasks that bring about conceptual
mathematical understanding in students.
• Values the child’s own intuitive mathematical
thinking as it gradually becomes more abstract
and powerful.
• Takes place in an environment that is conducive
to student discussion, reflection, and sense-making.
11. Sorting Blocks by Their
Attributes
• Choose a card and look for attribute
blocks that match the card.
• Identify an attribute of your own and sort
the blocks according to that attribute.
12.
13. Attribute “Look Fors”
• Are students able to focus on a particular
attribute to the exclusion of others?
• Can they discover other attributes besides
the card given? (open problem-solving)
• Do they use language to identify the
blocks? (edge, angle/corner, straight line,
flat, thin/thick, color, shape, etc.)
14. Racing Bears
• Object of the game is for a partner team to collect 10 buttons in all.
• When your bear lands on a button, you and your partner take and
keep that button.
• Use either a three counting dice or a six counting dice, or two six
counting dice for a challenge.
• Roll the dice and move your bear that number of spaces.
• Take turns rolling the dice and moving any bear. Try to land on a
button.
• You can split up the amount on the dice, and move more than one
bear.
• Try different strategies so you can collect the buttons with the fewest
number of moves.
15. Racing Bears Math “Look-Fors”
(Constructivism in action)
• Do students recognize dot patterns?
• Do they move the correct number of spaces? (one-to
one counting correspondence)
• How do students choose which bear to move? (are they
figuring out how many more spaces a bear has to go-subtracting
informally)
• Are students choosing to move multiple bears during one
roll of dice? (Are they adding informally?)
16. Break the Train
• Work in teams of two
• Each student in the team creates a repeating color
pattern using snap cubes. The pattern must repeat at
least three times.
• Students trade “trains” and try to identify each others’
pattern.
• Students “break the train” of each others’ pattern by
separating the pattern units into “cars” of the train.
• Students color in the different patterns on an activity
sheet.
17. Break the Train Math “Look-Fors”
(Constructivism in action)
• Are students able to identify the unit of a pattern?
(algebraic).
• Can students reconstruct the pattern train once they
have broken it apart?
• Are students able to construct/predict an AB pattern?
• Are students able to construct/predict a more complex
pattern such as AAB, ABBA?
• Students can transfer their color pattern to an AAB
abstract pattern by writing letters for a challenge.
18. Investigations
Kindergarten Curriculum
Number and Operations
Counting and Quantity:
• Developing an understanding of the magnitude and
position of numbers
• Developing the idea of equivalence
Whole Number Operations:
• Using manipulatives, drawings, tools, and notation to
show strategies and solutions
• Making sense of and developing strategies to solve
addition and subtraction problems with small numbers
19. Investigations
Kindergarten Curriculum
Patterns and Functions
• Repeating patterns: Constructing, describing, and
extending repeating patterns
• Repeating patterns: Identifying the unit of a repeating
pattern
Data Analysis
• Sorting and classifying
• Carrying out a data investigation
• Representing data
20. Investigations
Kindergarten Curriculum
Geometry
Features of shape:
• Describing, identifying, comparing and sorting two and three
dimensional shapes
• Composing and decomposing two and three dimensional shapes
22. Getting Back to the Coke
Problem:
• Is the string longer, shorter, or the same
length as the can?
• Is there a way to make sense of this
problem? Is this a problem that has no
clear solution pathway?
23. Constructing Math Sense
• Students who have had extensive experience with the
properties of circles will have constructed the knowledge
that a circle’s circumference is a little over three times its
diameter.
• So if you look at the top of the Coke can and imagine
about three times the diameter, the string would be
longer than the can’s height.
• This understanding of pi goes beyond the mere
memorizing of a formula.
24. Memorizing Procedures
Versus Making Sense of
Mathematics
• Students who construct their own
understanding of the relationship between
circumference and diameter are better
equipped to apply this knowledge to
non-routine problem-solving situations.
Here’s an interesting problem that we’ll start out with.
So let’s vote: How many think the string will be taller that the can? Shorter than the can? The same length as the can?
You can ponder this for a while and we’ll come back to this problem after the talk is over.
Here at LREI, our math philosophy is grounded in what we call constructivism.
The main focus of today’s talk is to give you an idea of what constructivism means and what it looks like in kindergarten.
So first, we’ll start out with how constructivist math education contrasts from the traditional approach to mathematics instruction.
This probably was the way you might have experienced math teaching in school.
There are many disadvantages to teaching mathematics using this traditional approach.
The major one being that children do not generalize concepts and are not equipped to solve problems that differ from what they’ve seen in the textbook.
This actually has a lot to do with the coke problem we just talked about.
Here is a clip of what a traditional classroom experience looked like.
Even though this is a dated black and white clip, so many math classes are still taught in the same way today.
Students graduating today will need to be able to solve problems that have never been solved before.
Piaget originally theorized the concept of constructivism, and there is a wealth of scholarly articles on the subject.
I have an article by Douglas Clements and Michael Battista that I like to give out as a handout because it’s short and to the point- easy to understand.
I have some here on hand.
Students in Kindergarten are actively working on carefully selected tasks and games that help children construct their own meaning of the mathematics involved.
They work both independently and collaboratively.
Here is an activity that requires classifying according to attributes- a big word for Kindergartners!
Classifications are used later in collecting data.
Words and language are also developed to describe geometric attributes.
Children coming up with words to define attributes.
This is a good example of a rich “Low Floor, High Ceiling” activity because all students can be successful at identifying attributes, but students can also identify more sophisticated attributes.
For example, a child identified a square as having pointed corners, but sorted it differently from a triangle, which had really pointed corners (right angle versus acute angle).
Here’s a game we’re going to play that has lots of math inherent in it for children to discover.
While you’re playing the game, see if you can identify these mathematical learning concepts.
This is a favorite of students in kindergarten.
Here is the underlying math for Break the Train.
Numeration in kindergarten is sophisticated. It’s much more that merely counting from one to 20.
Understanding one-to-one correspondence, understanding that an abstract number represents a certain quantity, Sequential numeration, and comparison of numbers (greater than/less than), are all explored.
Kindergartners continue the study of patterns and data in a more formal way.
…As well as geometry.
Understanding that things can be measured using standard units of linear length
Let’s go back to the original perplexing Coke can problem.
Do you want to change your vote?
Is the string going to be longer?
Is the string shorter?
Is it the same length of the can?
If you learned a traditional approach to mathematics, you probably memorized a formula way back when, but also, probably have forgotten it.
However, if you learned through a constructivist approach, you probably would recall the general underlying concept that a circle’s circumference is a little over three times its diameter.
We also ask students to memorize a formula, but attached to that formula is a deep understanding of the underlying concept.
We think that students who graduate in today’s world, need to be thinkers who can reason through difficult problems: not just memorize formulas.
