DISTRICT MATHEMATICS PROGRAM

DISTRICT MATHEMATICS PROGRAM

Instructional Guides Secondary

Los Angeles Unified School District 2008 - 2009

Vision, Coherence and Balance

The LAUSD Mathematics Instructional Guide (MIG) helps promote a balanced and designed mathematics curriculum for students as part of a coherent educational system. The Los Angeles Unified School District's vision is to provide its students with:

? A designed curriculum based on the Mathematics Content Standards for California Public Schools and the Mathematics Framework for California Public Schools.

? A balanced curriculum that teaches computational and procedural skills; conceptual understanding of mathematics; and problem solving.

? A coherent educational system in which the standards, the assessments, the curriculum, and the teacher professional development are closely aligned to one another.

Designed Curriculum: A designed curriculum is one that follows a deliberate design in which its elements act synergistically to provide all students access to content and reasoning standards. It is more than any single textbook. If taught completely and satisfactorily, this curriculum provides students with the experiences they need to become mathematically literate.

Balanced Curriculum: According to the Mathematics Framework for California Public Schools, mathematics education must provide students with a balanced instructional program. in such a program, students become proficient in basic computational and procedural skills, develop conceptual understanding, and become adept at problem solving. All three components are important; none is to be neglected or under emphasized. Balance, however, does not imply allocating equal amounts of time for each of the three components. At some times students might be concentrating on lessons or tasks that focus on one component; at other times the focus may be on two or all three. Basic computational and procedural skills, conceptual understanding, and problem solving form a web of mutually reinforcing elements in the curriculum.

Coherent Education: The California mathematics standards provide the basis of such an educational system. A close examination of the standards reveals certain big ideas, concepts and skills that students need to learn and use. An appropriate curriculum is designed to allow all students access to the concepts and skills. Proper use of the California Standards Test (CST) blueprints and the data from periodic assessments allow teachers to adapt the curriculum to the needs of their students. Appropriate teacher support in the form of professional development and resources provides additional avenues to reach students. Each of these components is crucial to form a coherent educational system.

Vision, Coherence and Balance

Conceptual Understanding

Understanding concepts means that students can use them to solve simple and complex problems, represent solutions in multiple ways, and explain procedures to someone else. Mathematics makes sense to students who have a conceptual understanding of the domain. Students know not only how to apply skills but also when to apply them as well as why they are being applied. Through this process students are able to see the structure and logic of mathematics and to use it flexibly, effectively, and appropriately. In seeing the larger picture and in understanding the underlying concepts, students are in a stronger position to apply their knowledge to new situations and problems and to recognize when they have made procedural errors. Work on conceptual understanding involves the opportunity to use; represent; explain.

Problem Solving

This is a goal-related activity that involves applying skills, understandings, and experiences to resolve new, challenging, or perplexing mathematical situations. The first phase in solving problems includes analyzing the problem (e.g. looking for patterns and making connections to known mathematical structures), making or formulating conjectures, and translating or expressing the problem into student language. The second phase involves integrating or putting together all the different pieces of information and representing the problem in mathematical language (e.g. an equation). Finally, the problem is solved using a wide variety of basic and technical skills with reasons or justifications made for each step in the solving process. Students might further identify relevant mathematical generalizations and seek connections to similar problems. Problem solving involves the opportunity to formulate, analyze, and translate; integrate and represent; solve and justify.

Computational and Procedural Skills

For each level of mathematics, a specific set of basic computational and procedural skills must be learned. For example, students need to memorize the number facts of addition and multiplication of one-digit numbers and their corresponding subtraction and division facts. The ability to retrieve these facts accurately and automatically from long-term memory, in turn, makes the solving of more complex problems, such as multi-step problems that involve basic arithmetic, quicker and less likely to result in errors (Geary and Widaman 1992). Computational and procedural skills are those that all students should learn to use routinely and automatically. Students should practice basic computational and procedural skills and use them frequently enough to commit them to memory. Work on skills involves the opportunity to practice; use accurately and automatically; memorize.

HOW TO USE THE MATH INSTRUCTIONAL GUIDE

This guide graphically organizes and clusters the California content standards to:

? promote the connections between and among mathematics skills, concepts, and problem solving strategies within and across different areas of mathematics content areas

? provide opportunities for students to develop a deep conceptual understanding as a foundation for their learning

? continue the use of strong teaching strategies ? provide students with a coherent learning experience that includes access to the necessary skills,

concepts and problem solving

Organization of the Guide

Instructional Units ? The content standards are grouped into instructional units. Some units may take less time than others to complete based on students' prior knowledge and the depth and complexity of the skills and concepts presented. A Unit Concept Organizer (see sample below) is found at the beginning of each instructional unit in order to facilitate instructional planning and student learning.

UNDERSTAND...

UNDERSTAND...

? Big Ideas ? Each unit is designed around a big idea within which work on conceptual understanding, specific skills, and problem solving is balanced.

? Concept Box ? "UNDERSTAND" in the concept box refers to a balanced approach which includes conceptual understanding, specific skill building, and problem solving.

? Skills Box ? This box contains a list of all the skills that are connected to the concept described. ? Content Standards ? Each instructional unit will contain the content standards for the unit.

6

? Assessment Tools ? Blueprints aligned with the periodic assessment program are provided in this MIG. Teachers are encouraged to use them when planning a coherent standards-based program. The assessment items for 2006-2007 may be found on line at

? Instructional Resource Table ?Sample Instructional Resources specific to each textbook will be provided to each teacher according to the courses taught by the teacher.

? Concept Lessons ? Each unit may contain one or more mathematically rigorous task lesson. This multi-standard lesson is an essential part of the unit.

? Periodic Assessments ? Assessment blueprints will be written for each unit assessment. All assessments will be available online to review prior to the assessment window.

Using the Guide to Plan Lessons

Before using the guide to plan instruction, teachers should be familiar with the mathematics content standards for California public schools and the Mathematics Framework for California Public Schools. In particular, teachers should be familiar with the standards for the grade level/course they are teaching.

In order for this Mathematics Instructional Guide (MIG) to be of greatest benefit to students, teachers may want to follow these steps:

? Become acquainted with the Mathematics Instructional Guide (MIG) and its components by answering he following questions: o How is this MIG different than others we have used? o What are the different elements of the MIG? o What does a balanced curriculum look like? o What do I teach in each unit? o What are the key standards in each unit? o What parts of my textbook should I use?

? Focus on one unit at a time. Use the Concept Unit Organizer for that unit to assist in guiding instruction by answering the following questions: o What are the key concepts and skills my students will learn in this unit to increase these mathematical understanding and prepare them for success on the CST? o What concepts should my students learn well for this unit? o What skills should my students practice for this unit? o What problems should my students be able to solve for this unit?

? Examine the instructional resources document for the unit. Examine the lessons from the textbook. Determine how to design classroom lessons which provide a balanced understanding of the concepts, conceptual and procedural skills, and problem solving for each student by answering the following questions: o Does every page of the textbook have to be used? o What other support materials could be used to teach students the concepts they need to learn?

? Study the concept lesson for the unit. This will help to answer the questions: o Which standards should I emphasize? o What scaffolding should I provide for my students to be successful? o What vocabulary should my students be familiar with? o What skills do my students need to successfully complete the lesson? o What questions may need to be addressed during the lesson? o How will students share their results/products?

7

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download