Six principles for school mathematics:
1. Equity. Excellence in mathematics education requires equity-high expectations and strong support for all students
2. Curriculum. A curriculum is more than a collection of activities: it must be coherent, focused on important mathematics, and well articulated across the grades
4. Learning. Students must learn mathematics with understanding, actively building new knowledge from experience and prior knowledge
5. Assessment. Assessment should support the learning of important mathematics and furnish useful information to both teacher and students
6. Technology. Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students’ learning
Structure of Curriculum
NCTM
1. Pre- K -2
2. Grades 3-5
3. Grades 6-8
4. Grades 9-12
Indonesia
1.
Pre-school/PAUD
2. TK (2 th)
3. SD (1-6)
4. SMP (7-9)
Standards for School Math
The Content Standards The Process Standards
1. Number and Operation 2. Algebra 3. Geometry
4. Measurement 5. Data Analysis
and Probability
1. Problem Solving
2. Reasoning and Proof
3. Communication 4. Connections
Instructional programs from pre kindegarden through grade 12 should enable students to:
1. Understanding numbers, ways of representing numbers, relationship among numbers, and number system;
2. Understanding meaning of operation and how they relate to one another;
3. Compute fluently and make reasonable estimates
Grades 6-8
Standard Expectation
1. Understanding numbers, ways of representing numbers, relationship among numbers, and number system
• Work flexibly with fractions, decimals, and percents to solve problems;
• Compare and order fractions, decimal, and percents efficiently and find their approximate locations on a number line;
• Develop an understanding of large numbers and recognize and appropriately use exponential, scientific, and calculator notation
• etc
2. Understanding meaning of operation and how they relate to one another
Use the associative and commutative properties of addition and multiplication and the distributive property of multiplication over addition to
simplify computation with integers, fractions, and decimals, etc.
3. Compute fluently and make reasonable estimates
Develop and use strategies to estimate the result of rational number computations and judge the
Grades 9-12
Standard Example ofExpectation
1. Understanding numbers, ways of representing numbers, relationship among numbers, and number system
• Develop a deeper understanding of very large and very small numbers and various representation of them
• Compare and contrast the properties of numbers and number systems, including the rational and real numbers, and understanding complex number system as a solution to quadratic equations, etc
2. Understanding meaning of operation and how they relate to one another
Judge the effects of such operations as
multiplication, division, and computing powers and roots on the magnitudes of quantities, etc 3. Compute fluently and
make reasonable estimates
2. Algebra Standards
Instructional programs for PK to grade 12 should enable students to:
1. Understand patterns, relations, and functions
2. Represent and analyze mathematical situations and structures using algebraic symbols
3. Use mathematical models to represent and understand quantitative relationships
Grades 6-8
Standard Sample of expetations Understand patterns,
relations, and functions
represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules; related and compare different forms of
representation for a relationship; identify functions as linear or nonlinear and contrast their properties from tables, graphs, or equation
Represent and analyze mathematical situations and structures using algebraic symbols
Develop an initial conceptual understanding of different uses of variables; explore relationship between symbolic expression and graphs of lines, paying particular
attention to the meaning of intercept and slope; etc
Use mathematical
models to represent and understand quantitative relationships
Model and solve contextualized problems using various representations, such as graphs, tables, and equation
Analyze change in various contexts
Grades 9-12
Standard Sample of expetations Understand patterns,
relations, and functions
Generalize pattern explicitly and recursively defined
functions; understand relations and functions and select, convert flexibly among, and use various representation of them; etc
Represent and analyze mathematical situations and structures using algebraic symbols
Understand the meaning of equivalent forms of
expressions, equations, inequalities, and relation; use symbolic algebra to represent and explain mathematical relationship; etc
Use mathematical
models to represent and understand quantitative relationships
Identify essential quantitative relationships in a situation and determine the class or classes of functions that might model the relationship; draw reasonable conclusions
about a situation being modeled
Analyze change in various contexts
3. Geometry
Instructional programs for PK to grade 12 should enable students to:
1. Analyze characteristics and properties of two-and three dimensional geometric shapes and develop mathematical arguments about geometric relationships
2. Specify locations and describe spatial relationships using coordinate geometry and other representational systems
3. Apply transformations and use symmetry to analyze mathematical situations
4. Measurement
Instructional programs for PK to grade 12 should enable students to:
1. Understand measurable attributes of objects and the unit, systems, and processes of measurement
5. Data Analysis and Probability
standards
1. Instructional programs for PK to grade 12 should enable students to:
2. Formulates questions that can be addressed with data and collect, organize, and display relevant data to answer them
3. Select and use appropriate statistical methods to analyze data
4. Develop and evaluate inferences and predictions that are based on data
1. Problem Solving Standard
Instructional programs for PK to grade 12 should enable all students to:
Build new mathematical knowledge through problem solving
Solve problem that arise in mathematics and other contexts
Apply and adapt a variety of appropriate strategies to solve problems
PB for grades 9-12
Problem solving seperti apa yang ada pada kelas 9-12?
1. Problem solving merupakan salah satu strategi dalam proses pembelajaran matematika untuk mengajarkan hal-hal mendasar (PB sebagai alat)
2. PB sebagai tujuan utama : melengkapi siswa dengan pengetahuan dan ketrampilan yang dibutuhkan untuk menyelesaikan masalah sesuai dengan konsep-konsep yang telah dipelajari siswa
Bagaimana peran guru dalam membangun PB di dalam kelas?
Dalam menciptakan PB dibutuhkan beberapa persyaratan diantaranya:
2. Reasoning and Proof Standard
Instructional programs for PK to grade 12 should enable students to:
Recognize reasoning and proof as fundamental aspects of mathematics
Make and investigate mathematical conjectures
Develop and evaluate mathematical arguments and proofs
Penalaran dan pembuktian pada tingkat 9-12
Penalaran dan pembuktian seperti apa yang ada pada kelas 9-12?
1. Penalaran dan pembuktian secara alamiah merupakan bagian dari
proses pembelajaran
2. Siswa dapat menjelaskan dan menjustifikasi kesimpulan mereka
3. Membuat siswa dapat melakukan absraksi dan kodifikasi dari hasil
observasi
4. Penalaran dibangun melalui pertanyaan-pertanyaan “mengapa?”
5. Siswa terbiasa membuat argumentasi langsung untuk membuat
validitas dari sebuah konjektur
Bagaimana peran guru dalam membangun PB di dalam kelas?
1. Memahami matematika dengan baik
2. Menciptakan situasi yang kondusif agar siswa dapat mencari,
merumuskan, dan membuat kritik atas penjelasan dalam suatu diskusi
3. Communication Standard
Instructional programs for PK to grade 12 should enable students to:
Organize and consolidate their mathematical thinking though communication
Communicate their mathematical thinking coherently and clearly to peers, teachers, and others
Analyze and evaluate the mathematical thinking and strategies of others
Komunikasi matematis untuk tingkat 9-12
Komunikasi matematis seperti apa yang ada pada kelas 9-12?
1. Membangun kemampuan berpikir runtut/terstruktur dan logis,
mengekspresikan gagasan secara koheren dan jelas,
mendengarkan ide-ide matematis dari orang lain, dan memikirkan kepada siapa mereka menyampaikan gagasan dalam berbicara atau menulis.
2. Siswa harus dapat menggunakan bahasa dan simbol matematika
dengan benar dan tepat dalam berbagai bentuk representasi
Bagaimana peran guru dalam membangun PB di dalam kelas?
1. Menciptakan iklim kondusif di kelas agar siswa dapat merasa
nyaman dalam berkomentar, membuat konjektur dan
memberikan penjelasan
2. Mmebuat klarifikasi dari statetment mereka dan memperbaikinya
3. Membantu siswa agar dapat menulis dan membaca menggunakan
bahasa matematis dengan tepat dan membantu mereka
4. Connections Standard
Instructional programs for PK to grade 12 should enable students to:
Recognize and use connections among mathematical ideas
Understand how mathematical ideas interconnect and build on one another to produce a coherent whole
Koneksi matematis untuk tingkat 9-12
Koneksi matematis seperti apa yang ada pada kelas 9-12?
1. Siswa harus dapat meningkatkan kapasitas dalam membuat hubungan antar ide-ide matematika
2. Siswa harus dapat menggunakanberbagai macam pendekatan yang berbeda dalam menyelesaikan masalah
Bagaimana peran guru dalam membangun koneksi matematis di dalam kelas?
1. Memilih atau membuat masalah yang sesuai agara dapat menciptakan berbagai kemungkinan koneksi antar konsep
2. Membuat inisiatif khusus agar dapat menyatukan berbagai konsep aljabar, geometri,dan statistik atau yang lain dalam suatu proses pembelajaran disesuaikan dengan kurikulum
5. Representation Standard
Instructional programs for PK to grade 12 should enable students to:
Create and use representations to organize, record, and communicate mathematical ideas
Select, apply, and translate among mathematical representations to solve problems
Representasi matematis untuk tingkat 9-12
Representasi matematis seperti apa yang ada pada kelas 9-12?
1. Siswa harus dapat menggunakan berbagai jenis representasi konsep matematika dengan luwes
2. Siswa dapat mengenali struktur matematik dari berbagai macam konteks 3. Siswa dapat menciptakan dan menginterpretasikan berbagai model dari fenomena dengan cara mengidentifikasi hal-hal esensial dari situasi dan menemukan representasi yang menangkap hubungan matematis dari konteks-konteks tersebut
Bagaimana peran guru dalam membangun representasi matematis
di dalam kelas?
1. Mengenalkan siswa pada bentuk-bentuk representasi matematis dan membantu mereka dalam menggunakan representasi tersebut
2. Menggarisbawahi bahwa bentuk representasi yang berbeda dari konsep yang sama dapat memberikan informasi yang berbeda pula
3. Membantu siswa agar dapat memilih jenis representasi yang sesuai dengan tujuan
Tugas 4
1. Buatlah analisis mengenai standar isi dari kelas 6-12 menurut NCTM dan bandingkan dengan standar isi dalam KTSP! (individual)
2. Butlah situasi/konteks/masalah/soal yang sesuai dengan 5 standar pembelajaran matematika
