Standards for School Mathematics 1(KD4)

  

Based on National Council of Teachers of Mathematics (NCTM) 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

  

3. Teaching. Effective mathematics teaching requires

  understanding what students know and need to learn and then challenging and supporting them to learn it well Six principles for school mathematics:

  

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 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)

  5. SMA (10-12) 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

  5. Representation

  

  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,

• Work flexibly with fractions, decimals, and ways of representing percents to solve problems; numbers, relationship
• Compare and order fractions, decimal, and among numbers, and percents efficiently and find their approximate number system locations on a number l
• Develop an understanding of large numbers and recognize and appropriately use exponential, scientific, and calculator notation
• etc

  2. Understanding meaning of Use the associative and commutative properties of operation and how they addition and multiplication and the distributive relate to one another property of multiplication over addition to simplify computation with integers, fractions, and decimals, etc.

  3. Compute fluently and Develop and use strategies to estimate the result of make reasonable estimates rational number computations and judge the reasonableness of the result, etc Grades 9-12 Standard Example ofExpectation

  1. Understanding numbers,

• Develop a deeper understanding of very large ways of representing and very small numbers and various numbers, relationship representation of them among numbers, and
• Compare and contrast the properties of number system 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 Judge the effects of such operations as operation and how they multiplication, division, and computing powers relate to one another and roots on the magnitudes of quantities, etc

  3. Compute fluently and Develop fluency in operations with real numbers, make reasonable estimates vectors, and matrices, using mental computation or paper-pencil calculations for simple cases and technology for more complicated-cases. etc

  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

  4. Analyze change in various contexts 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

  Use graphs to analyze the nature of changes in quantities in linear relationship 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 Approximate and interpret rates of change from graphical and numerical data

  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. Use visualization, spatial reasoning, and geometric

modeling to solve problems

  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

  

2. Apply appropriate techniques, tools, and formulas to

  determine measurements

  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

  5. Understand and apply basic concept of probability

  

  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

  

  Monitor and reflect on the process of mathematical problem solving 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:

   Konten materi matematika; pengetahuan tentang strategi penyelesaian masalah; kemampuan monitoring diri yang baik /refleksi; dan memiliki disposisi yang baik dalam membuat masalah dan menyelesaikannya

  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

  

  Select and use various types of reasoning and methods of proof 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. Mampu membuat pertanyaan-pertanyaan yang tepat

  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

  

  Use the language of mathematics to express mathematical ideas 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 memahami literatur matematika dengan baik

  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

  

  Recognize and apply mathematics in contexts outside of mathematics 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

  

3. Banyak memberikan masalah yang memiliki berbagai

macam pendekatan dan solusi

  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

  

  Use representations to model and interpret physical, social, and mathematical phenomena 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 4.

  Membantu siswa menghubungan bentuk representasi miliknya dengan bentuk representasi yang baku

  

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 menurut NCTM dengan menggunakan materi yang terdapat dalam standar isi KTSP kelas 7-12