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# Second session 9 implementation

Presentation for Grade 9 Teachers regarding the new program of studies

by

Tweet## Margo Perry

on 15 April 2010#### Transcript of Second session 9 implementation

Grade 9 Mathematics Implementation Program of Studies Multiple Representations Begin K-8 Concept Development Time Line 2007 ........ 2008 ........ 2009 ........ 2010 ......... 2011 ........ 2012 ........ 2013 K, Grade1, Grade 4, and Grade 7 Grade 2, Grade 5, Grade 8 Grade 3, Grade 6, Grade 9, Grade 10c

PATs Grade 11 Grade 12 and Diploma Beliefs about Students & Mathematics Learning Affective Domain Goals for Students Mathematical Processes Communication Connections Mental Arithmetic and Estimation Problem Solving Reasoning Technology Visualization Instructional Focus Big Ideas Math 9 How does this relate to the processes and other important ideas in the Front Matter? New topic Circle Geometry Big Ideas outcomes materials o/h or tech or white board geometry tools

bicycle wheel

compasses

protractors

rulers

scissors

circular objects

geogebra/geometers' sketchpad

counters

plastic right triangles Prayer for New Beginnings

Lord God,

You have called your servants

to ventures

of which we cannot see the ending,

by paths as yet untrodden,

through perils unknown.

Give us faith to go out with good courage,

not knowing where we go,

but only that your hand is leading us

and your love supporting us;

through Jesus Christ our Lord.

Amen

Students learn by attaching meaning to what they

do, and they need to construct their own meaning

of mathematics. This meaning is best developed

when learners encounter mathematical experiences

that proceed from the simple to the complex and

from the concrete to the abstract. At all levels,

students benefit from working with a variety of

materials, tools and contexts when constructing

meaning about new mathematical ideas.

Meaningful student discussions provide essential

links among concrete, pictorial and symbolic

representations of mathematical concepts. Mathematical understanding is fostered when students build on their own experiences and prior knowledge. A positive attitude is an important aspect of the affective domain and has a profound impact on learning. Environments that create a sense of belonging, encourage risk taking and provide opportunities for success help develop and maintain positive attitudes and self-confidence within students. Students with positive attitudes toward learning mathematics are likely to be motivated and prepared to learn, participate willingly in classroom activities, persist in challenging situations and engage in reflective practices. To experience success, students must be taught to set achievable goals and assess themselves as they work toward these goals. The main goals of mathematics education are to

prepare students to:

• use mathematics confidently to solve problems

• communicate and reason mathematically

• appreciate and value mathematics

• make connections between mathematics and its

applications

• commit themselves to lifelong learning

• become mathematically literate adults, using

mathematics to contribute to society. Students who have met these goals will:

• gain understanding and appreciation of the

contributions of mathematics as a science,

philosophy and art

• exhibit a positive attitude toward mathematics

• engage and persevere in mathematical tasks and

projects

• contribute to mathematical discussions

• take risks in performing mathematical tasks

• exhibit curiosity. • Integration of the mathematical processes

within each strand is expected.

• By decreasing emphasis on rote calculation,

drill and practice, and the size of numbers used

in paper and pencil calculations, more time is

available for concept development.

page 8 The goals of all three course sequences are to provide

prerequisite attitudes, knowledge, skills and

understandings for specific post-secondary programs

or direct entry into the work force. All three course

sequences provide students with mathematical

understandings and critical-thinking skills. It is the

choice of topics through which those understandings

and skills are developed that varies among course

sequences. When choosing a course sequence,

students should consider their interests, both current

and future. Students, parents and educators are

encouraged to research the admission requirements

for post-secondary programs of study as they vary by

institution and by year. There are critical components that students must encounter in a mathematics program in order to achieve the goals of mathematics education and embrace lifelong learning in mathematics.

Communication is important in clarifying,

reinforcing and modifying ideas, attitudes and

beliefs about mathematics. Students should be

encouraged to use a variety of forms of

communication while learning mathematics. Communication helps students make connections

among concrete, pictorial, symbolic, oral, written

and mental representations of mathematical ideas. When mathematical ideas are connected to each other or to real-world phenomena, students begin to view mathematics as useful, relevant and integrated. Learning mathematics within contexts and making connections relevant to learners can validate past experiences and increase student willingness to participate and be actively engaged. The brain is constantly looking for and making connections. “Because the learner is constantly searching for connections on many levels, educators need to orchestrate the experiences from which learners extract understanding.… Brain research establishes and confirms that multiple

complex and concrete experiences are essential for meaningful learning and teaching” (Caine and Caine, 1991, p. 5). Mental mathematics and estimation are fundamental

components of number sense. Mental mathematics “provides the cornerstone for

all estimation processes, offering a variety of

alternative algorithms and nonstandard techniques

for finding answers” (Hope, 1988, p. v). Learning through problem solving should be the

focus of mathematics at all grade levels. When

students encounter new situations and respond to

questions of the type How would you …? or How

could you …?, the problem-solving approach is

being modelled. Students develop their own

problem-solving strategies by listening to,

discussing and trying different strategies. If students have already been given

ways to solve the problem, it is not a problem, but

practice. A true problem requires students to use

prior learnings in new ways and contexts. Mathematical reasoning helps students think

logically and make sense of mathematics. Students

need to develop confidence in their abilities to

reason and justify their mathematical thinking.

High-order questions challenge students to think

and develop a sense of wonder about mathematics. Reasoning skills allow students to use a logical

process to analyze a problem, reach a conclusion

and justify or defend that conclusion. Technology contributes to the learning of a wide range of mathematical outcomes and enables students to explore and create patterns, examine relationships, test conjectures and solve problems. Visualization “involves thinking in pictures and

images, and the ability to perceive, transform and

recreate different aspects of the visual-spatial world”

(Armstrong, 1993, p. 10). The use of visualization in

the study of mathematics provides students with

opportunities to understand mathematical concepts

and make connections among them. Visualization is fostered through the use of concrete

materials, technology and a variety of visual

representations. Personal Strategies Mental Mathematics and Estimation Algebra Scan through the Patterns and Relations Strand of the Program of Studies to see what algebra related outcomes are expected at each grade level from k-8 (what knowledge and skills are your students coming into your class with). At what grade do Algebra concepts begin? Notice when the concept of equality is related to balance. At your table,

Read through the Big Ideas for each Unit in the Grade 9 Math Makes Sense

choose a unit to focus on

identify the background knowledge needed for the big ideas

scan the grade 7 to 9 outcomes to see the progression of the outcomes.

Exam View Unit Plan Lessons Math Lab Investigations http://www.learnalberta.ca/Search.aspx?lang=en&search=circle&grade=Grade+9&subject=Mathematics The Unit Planning chart from teacher resource is available in

PDF or Word format. The Word format is editable, so you can

customize the plan to suit your schedule and teaching style.

There is an example of the unit planning chart on your table. Lets look at the teacher resource for this topic.

Don't let me forget to show you

Media items

Solutions

Differentiation

ProGuide Teacher Resources Agenda for the Day Math Makes Sense Teacher Resource New Topics

• Problem solving, reasoning and connections are

vital to increasing mathematical fluency and

must be integrated throughout the program.

• There is to be a balance among mental

mathematics and estimation, paper and pencil

exercises, and the use of technology, including

calculators and computers. Concepts should be

introduced using manipulatives and be

developed concretely, pictorially and

symbolically.

• Students bring a diversity of learning styles and

cultural backgrounds to the classroom. They

will be at varying developmental stages. Students are expected to:

• communicate in order to learn and express their understanding

• connect mathematical ideas to other concepts in mathematics, to everyday

experiences and to other disciplines • demonstrate fluency with mental mathematics and estimation

• develop and apply new mathematical knowledge through problem solving

• develop mathematical reasoning

• select and use technologies as tools for learning and for solving problems

• develop visualization skills to assist in processing information, making

connections and solving problems. Program of Studies Keep a running list of agree, disagree, and yah buts as we go through some of the beliefs from the front matter. After we visit a few of these beliefs and have a minute to think about them, we can have a general discussion about beliefs about students and mathematics learning What are your thoughts on the Beliefs of Students and Mathematical Understanding Well use the same process for Goals,list your agrees, disagrees

and yah buts, then discuss later What are your thoughts on these goals? Lesh, Post and Behr (1987) http://www.learnalberta.ca/content/memg/index.html

Full transcriptPATs Grade 11 Grade 12 and Diploma Beliefs about Students & Mathematics Learning Affective Domain Goals for Students Mathematical Processes Communication Connections Mental Arithmetic and Estimation Problem Solving Reasoning Technology Visualization Instructional Focus Big Ideas Math 9 How does this relate to the processes and other important ideas in the Front Matter? New topic Circle Geometry Big Ideas outcomes materials o/h or tech or white board geometry tools

bicycle wheel

compasses

protractors

rulers

scissors

circular objects

geogebra/geometers' sketchpad

counters

plastic right triangles Prayer for New Beginnings

Lord God,

You have called your servants

to ventures

of which we cannot see the ending,

by paths as yet untrodden,

through perils unknown.

Give us faith to go out with good courage,

not knowing where we go,

but only that your hand is leading us

and your love supporting us;

through Jesus Christ our Lord.

Amen

Students learn by attaching meaning to what they

do, and they need to construct their own meaning

of mathematics. This meaning is best developed

when learners encounter mathematical experiences

that proceed from the simple to the complex and

from the concrete to the abstract. At all levels,

students benefit from working with a variety of

materials, tools and contexts when constructing

meaning about new mathematical ideas.

Meaningful student discussions provide essential

links among concrete, pictorial and symbolic

representations of mathematical concepts. Mathematical understanding is fostered when students build on their own experiences and prior knowledge. A positive attitude is an important aspect of the affective domain and has a profound impact on learning. Environments that create a sense of belonging, encourage risk taking and provide opportunities for success help develop and maintain positive attitudes and self-confidence within students. Students with positive attitudes toward learning mathematics are likely to be motivated and prepared to learn, participate willingly in classroom activities, persist in challenging situations and engage in reflective practices. To experience success, students must be taught to set achievable goals and assess themselves as they work toward these goals. The main goals of mathematics education are to

prepare students to:

• use mathematics confidently to solve problems

• communicate and reason mathematically

• appreciate and value mathematics

• make connections between mathematics and its

applications

• commit themselves to lifelong learning

• become mathematically literate adults, using

mathematics to contribute to society. Students who have met these goals will:

• gain understanding and appreciation of the

contributions of mathematics as a science,

philosophy and art

• exhibit a positive attitude toward mathematics

• engage and persevere in mathematical tasks and

projects

• contribute to mathematical discussions

• take risks in performing mathematical tasks

• exhibit curiosity. • Integration of the mathematical processes

within each strand is expected.

• By decreasing emphasis on rote calculation,

drill and practice, and the size of numbers used

in paper and pencil calculations, more time is

available for concept development.

page 8 The goals of all three course sequences are to provide

prerequisite attitudes, knowledge, skills and

understandings for specific post-secondary programs

or direct entry into the work force. All three course

sequences provide students with mathematical

understandings and critical-thinking skills. It is the

choice of topics through which those understandings

and skills are developed that varies among course

sequences. When choosing a course sequence,

students should consider their interests, both current

and future. Students, parents and educators are

encouraged to research the admission requirements

for post-secondary programs of study as they vary by

institution and by year. There are critical components that students must encounter in a mathematics program in order to achieve the goals of mathematics education and embrace lifelong learning in mathematics.

Communication is important in clarifying,

reinforcing and modifying ideas, attitudes and

beliefs about mathematics. Students should be

encouraged to use a variety of forms of

communication while learning mathematics. Communication helps students make connections

among concrete, pictorial, symbolic, oral, written

and mental representations of mathematical ideas. When mathematical ideas are connected to each other or to real-world phenomena, students begin to view mathematics as useful, relevant and integrated. Learning mathematics within contexts and making connections relevant to learners can validate past experiences and increase student willingness to participate and be actively engaged. The brain is constantly looking for and making connections. “Because the learner is constantly searching for connections on many levels, educators need to orchestrate the experiences from which learners extract understanding.… Brain research establishes and confirms that multiple

complex and concrete experiences are essential for meaningful learning and teaching” (Caine and Caine, 1991, p. 5). Mental mathematics and estimation are fundamental

components of number sense. Mental mathematics “provides the cornerstone for

all estimation processes, offering a variety of

alternative algorithms and nonstandard techniques

for finding answers” (Hope, 1988, p. v). Learning through problem solving should be the

focus of mathematics at all grade levels. When

students encounter new situations and respond to

questions of the type How would you …? or How

could you …?, the problem-solving approach is

being modelled. Students develop their own

problem-solving strategies by listening to,

discussing and trying different strategies. If students have already been given

ways to solve the problem, it is not a problem, but

practice. A true problem requires students to use

prior learnings in new ways and contexts. Mathematical reasoning helps students think

logically and make sense of mathematics. Students

need to develop confidence in their abilities to

reason and justify their mathematical thinking.

High-order questions challenge students to think

and develop a sense of wonder about mathematics. Reasoning skills allow students to use a logical

process to analyze a problem, reach a conclusion

and justify or defend that conclusion. Technology contributes to the learning of a wide range of mathematical outcomes and enables students to explore and create patterns, examine relationships, test conjectures and solve problems. Visualization “involves thinking in pictures and

images, and the ability to perceive, transform and

recreate different aspects of the visual-spatial world”

(Armstrong, 1993, p. 10). The use of visualization in

the study of mathematics provides students with

opportunities to understand mathematical concepts

and make connections among them. Visualization is fostered through the use of concrete

materials, technology and a variety of visual

representations. Personal Strategies Mental Mathematics and Estimation Algebra Scan through the Patterns and Relations Strand of the Program of Studies to see what algebra related outcomes are expected at each grade level from k-8 (what knowledge and skills are your students coming into your class with). At what grade do Algebra concepts begin? Notice when the concept of equality is related to balance. At your table,

Read through the Big Ideas for each Unit in the Grade 9 Math Makes Sense

choose a unit to focus on

identify the background knowledge needed for the big ideas

scan the grade 7 to 9 outcomes to see the progression of the outcomes.

Exam View Unit Plan Lessons Math Lab Investigations http://www.learnalberta.ca/Search.aspx?lang=en&search=circle&grade=Grade+9&subject=Mathematics The Unit Planning chart from teacher resource is available in

PDF or Word format. The Word format is editable, so you can

customize the plan to suit your schedule and teaching style.

There is an example of the unit planning chart on your table. Lets look at the teacher resource for this topic.

Don't let me forget to show you

Media items

Solutions

Differentiation

ProGuide Teacher Resources Agenda for the Day Math Makes Sense Teacher Resource New Topics

• Problem solving, reasoning and connections are

vital to increasing mathematical fluency and

must be integrated throughout the program.

• There is to be a balance among mental

mathematics and estimation, paper and pencil

exercises, and the use of technology, including

calculators and computers. Concepts should be

introduced using manipulatives and be

developed concretely, pictorially and

symbolically.

• Students bring a diversity of learning styles and

cultural backgrounds to the classroom. They

will be at varying developmental stages. Students are expected to:

• communicate in order to learn and express their understanding

• connect mathematical ideas to other concepts in mathematics, to everyday

experiences and to other disciplines • demonstrate fluency with mental mathematics and estimation

• develop and apply new mathematical knowledge through problem solving

• develop mathematical reasoning

• select and use technologies as tools for learning and for solving problems

• develop visualization skills to assist in processing information, making

connections and solving problems. Program of Studies Keep a running list of agree, disagree, and yah buts as we go through some of the beliefs from the front matter. After we visit a few of these beliefs and have a minute to think about them, we can have a general discussion about beliefs about students and mathematics learning What are your thoughts on the Beliefs of Students and Mathematical Understanding Well use the same process for Goals,list your agrees, disagrees

and yah buts, then discuss later What are your thoughts on these goals? Lesh, Post and Behr (1987) http://www.learnalberta.ca/content/memg/index.html