Mathematics Content Enhancement: Steps to an Effective ProgramPart 1: Computational Skills

Purpose

This professional development is designed for teachers to improve their Mathematics program, improve student achievement, and allow for maximum participation for every student in the classroom.

The focus is on upper elementary classrooms 3rd through 5th grade. There will be 25 to 30 educators present.

Part 1 Agenda

Introduction

Step 1: Computation Skills• Description: Math Review Component• Assessment: The Math Review Quiz• Differentiation• Mental Math

Introduction

How can teachers produce mathematically powerful students that can solve problems and also communicate their understanding to others?

Program Goals

Build computational skills

Develop mathematical reasoning and problem-solving abilities

Deepen conceptual understanding

Demonstrate understanding in a variety of assessment formats

Challenges

Many teachers feel that there is not enough mathematics professional development that is offered.• Why is there minimal offering?• Have they been effective?• Were they implementable?

Discuss

Challenges Continued

District Math programs may be confusing with too many components: standards, lessons.

Pressure to for achievement in high-stakes testing at student expense of conceptual building and problem solving abilities.

Discussion:

We all understand math anxiety for students. What about teacher anxiety for accountability?

Overcoming Challenges

Encourage students to look for multiple ways to approach a problem.

Value understanding communication verbally and in writing.

Promote problem-solving/conceptual skills vs. memorization of formulas and procedures.

Overcoming Continued

Provide structure for students with components of an effective program regardless of math series used.

Framework planning that aligns instruction, activities, and assessments around a specific math focus.

Computational Skills

Essentials Questions:• In what ways are you helping students

retain math concepts and skills that they have already learned?

• Are students developing and refining number sense?

Rationale

Number sense is essential to student success with computational skills. Effective practice involves quick and specific feedback, daily practice, and reflection. This all helps foster progress and responsibility towards learning .

• Reflection: Would you add anything to this rationale?

Math Review Component

The first element to an effective math program is a system for reviewing basic computational skills on a daily basis: Math Review. This is performed during the first 20 minutes of every math lesson. There should be no more than five problems that:

Math Review Elements

Represent specific standards for your grade level

Provide practice in multiple math strands

Match focus of current instruction of lessons

Reinforce prior learning and retention of former lessons and skills taught

Allow for practice on computation sections on district and state assessments

Purpose

This is a review, not a place to introduce new material.

It allows a portion of the math lesson to be a discussion with students of reasonableness of answer and estimation.

Instead of teaching procedure that there is only one way to solve a problem, emphasis is placed on modeling multiple ways in solving.

This fosters reasoning and number sense.

Problem Selection

The teacher deliberately selects specific problems problems representing different standards.

The focus is on student review on variations of the same problem throughout the week.

While practicing daily, students receive guidance from both peers and the teacher

There needs to a progression of concepts and skills, while difficulty increases throughout the year.

Selection Continued

Problems of the same type type continue week after week until the majority of the class masters them. Once this occurs, the teacher introduces a new type of problem to replaces the ones that students have sufficiently learned. This ensures that new types of problems are cycled through as the year proceeds.

The Template

Math Review is organized in a template that consists of:• Five labeled boxes• 1 problem in each box• A bonus problem for students that finish

early

• These problems focus on the five concepts that the teacher has selected.

Teacher’s Role

The teacher circulates the class and helps students individually. He/she may also have students individually or in a small group come to the board for more help.

These flex groups provide a safe haven for students that may not ask for help.

A collaborative atmosphere must be created in order for students to be encouraged to ask for help.

Processing

Students are allowed 10 minutes of solving time. Then, students and the teacher correct the problems together. This takes 10 minutes as well.

This helps students determine whether their answers are:• Reasonable• Make sense• Demonstrate Understanding

Processing Continued

Students in grades 3 through 5 need to develop number sense strategies instead of procedural methods.

The daily processing of the Math Review problems provides an excellent platform for students to do so.

Teachers that establish a safe environment and discuss how mistakes are critical to the learning process allow for students to embrace improving.

Error Analysis

Students become more receptive when an error analysis is performed.

Error Analysis allows for:• Identification of parts of problems done

incorrectly.• Pin pointing specific parts of the problems

done incorrectly.

Students gain confidence through analyzing their work and begin improving.

Error Analysis Continued

When the majority of the class is stuck on a problem, the teacher leads:• A step-by-step procedure• Identifies elements that are crucial to the

problem• Encourages students to verbalize

Strategies for Processing

Student Directedo Student volunteers explain on the board

how they solved a problem.

o Pass the Penn• One student demonstrates one step,

another student performs the next step. This continues to the problem is solved.

Strategies Continued

Speedy System• Students go to the board and write down

the answer. They ask the class if they agree or disagree.

o Math vocabulary• Encourage students to key terms and write

number sentences next to the problem. • Teachers can create a Math Word Wall

CAUTION!!!

Math Review will become such an engaging and exciting activity that students will look forward everyday. It is not intended to take the place of a math lesson. Math Review and Mental Math should take 20 to 25 minutes of the math block. To ensure that this timeframe is utilized, teachers should start with only using 2 to 3 problems in the beginning of implementation.

Assessment: The Math Review Quiz

Essential questions:• How will you know if Math Review is

effective?• How will you access learning?

Discussion:

Rationale

The weekly Math Review Quiz allows for determination of what students do and do not understand.

It provides timely feedback.

Offers students reflection time.

Allows for students to plan for improvement.

This analysis of student results can reveal for removal of mastered concepts and the addition of reviewed concepts.

The Quiz

Consists of 2 problems for each of the 5 concepts practiced. 2 problems are selected for diagnostic purposes. If the student gets 1 wrong and the other right, the teacher can determine that it was an easy computation error. If both are wrong, the teacher knows that further instruction is required.

Enables the teacher to differentiate daily instruction based on need.

Proficiency is 80%, 8 out of 10 problems correct.

The Quiz Continued

Feedback should be immediate, with scoring done by the teacher or students.. A more effective method is to have the students correct their quizzes themselves. The teacher puts the answers, along with the work involved, on the board.

The students self correct using a red pen.

The students write a self reflection and improvement plan on the back of their quizzes

The Quiz Continued

Tutors and Tutees can also be implemented with peer volunteers that are consistently proficient assisting students that are struggling.

This provides relationships, cohesion, and collaboration.

The Quiz Continued

Parental Involvement is key as well. Students take grade quizzes home for their parents to sign. Parents can see student progress. If students fall under the 80% benchmark, practice problems can be sent home to be performed together.

During Math Review, the teacher works with these students one-on-one or in the flex group for more assistance.

Quiz Benefits

The Math Review Quiz provides the teacher with a weekly formative assessment that:• Identifies those that need remediation or

intervention.• Identifies those that need enrichment or

acceleration.• Identifies effectiveness of instruction.

Differentiation

It is a highly researched topic on how students learn differently than others. Math Review allows all students, at different levels and abilities, to participate effectively and become successful. Math Review provides all students with grade level academics, social skill training, student-led learning opportunities, and the platform to strive for high student achievement.

Discussion: How do you differentiate in Math?

Differentiation Continued

Flexible Grouping

• Use data and informal observation to create groups that receive more attention.

• Students that progress are encouraged to work independently.

• The access to the groups swings both ways. Students will come and go.

Differentiation Continued

Peer Assistance

• Pair students that are struggling with students that are doing well

• Encourage positive social interaction.

• Encourage manipulatives.

Mental Math

Essential Questions:• How are you providing students mental

number sense opportunities?• How do foster student development for

doing problems in their head

Discussion

Rationale

Students need the opportunity to enhance mental practice through a variety of methods and strategies to gain effective computational skills.

Calculation performed mentally, like all mathematics, has significant real world relevance.

Implementation

Mental Math is a 3 problem activity for the brain. It takes 5 minutes and should be done after Math Review.

The teacher selects a math theme or combination of themes and scribes a line of numbers and operations that students must do in their heads individually.

Implementation Continued

Themes may include:

• Number Facts (+, _ , x , /)

• Combining operations

• Multiplying by 10, 100, 1000

• Fractional Parts

• Skip counting

• Measurement Concepts

Implementation

Example:

• Start with 4 x 5 (20); double that product (40); take ¼ of that answer (10); multiply by 10 equals

• Pause after each step to allow for the students to calculate.

• Allow the students to write down the answer, but do not give the answer.

• Repeat the problem again.

Implementation Continued

The teacher asks for the students to read their answers aloud.

The answer is calculated step by step aloud, followed by working it out on the board for students that need clarification.

Once the process is grasped, students are encouraged to create their own. They can be used for the entire class Mental Math activity. Teachers should make sure that it is done correctly prior to.