# ACE Mathematics Newsletter

## 3 - 8 Mathematics | SEP 2018 YEAR 3: VOL. 1

## In this Edition:

**Mathematics Instructional Block:** Academic Routines

**Instructional Resources:** 2nd Six Weeks Instructional Planning Calendars & K-2 Work Mats

**Instructional Trends in Mathematics:** Teaching with Manipulatives

**Upcoming PD:** ACE Team Thursdays & ACE Super Saturday

**Announcements:** ACE Website - Teacher Portal Tab

## Mathematics Instructional Block: Academic Routines

## What is a routine?

A routine is a whole-group structured activity that provides students with an opportunity to develop over time any or all of the following:

Operational sense

Fluency (efficiency, accuracy, and flexibility)

Good intuition about numbers and their relationships

Reasoning

Problem solving

Mental math

Routines are a time to:

Preview new concepts

Review concepts that have been previously explored

Practice those concepts which continue to be fragile

## What time of the instructional day? How long does a routine last?

In our block schedule, a routine kicks off the mathematics instructional block.

Routines last approximately 10-15 minutes per day.

## How many different routines should be implemented during the school year?

It is advisable to focus in depth on several rich routines that are repeated throughout the year.

Most of the routines should be introduced early in the year so students can become comfortable with the format of each routine.

As students become comfortable with the format, learning will become more efficient and the mathematics rather than the format will be the focus.

## Why implement routines?

Develop fluency in basic computational and procedural skills, an understanding of mathematical concepts, and the ability to use mathematical reasoning to solve mathematical problems, including recognizing and solving routine problems readily and finding ways to reach a solution or goal when no routine path is apparent.

Communicate precisely about quantities, logical relationships, and unknown values through the uses of signs, symbols, models, graphs, and mathematical terms.

- Provide an opportunity to schedule spaced practice which allows students to see concepts over a period of time promoting their transfer to long term memory.

## What is the evidence of your routine implementation?

- Routines are aligned to the TEKS listed on the six-weeks YAG and IPC.
- Daily implementation is evident in lesson plans, posted schedule, and student exemplars.
- Students are able to articulate the connection between the routine and the learning.

## Instructional Resources:

## 2nd Six Weeks Instructional Planning Calendars

**Hot off the press: 2nd Six Weeks Instructional Planning Calendars**

When reviewing these calendars, pay close attention to the proposed unpacking of the targeted standards in order to facilitate conceptual understanding. Please place close attention to the instructional resources section where you can find suggested strategies, manipulatives, and anchor charts to incorporate into your lessons.

## K-2 Work Mats

Several work mats are linked in the K-2 mathematics section on the ACE website. These work mats can be instrumental in developing concepts and number sense in early learners. For instance the hundreds grid can be used to explore patterns, place value, addition, subtraction, counting coins, and many other concepts. Using the work mats to develop conceptual understanding can also be a routine in the kindergarten, first, and second grade mathematics classrooms. The work mats can also be great scaffolds for students as they process the abstract nature of mathematics.

The work mats can be assembled into a foldable for efficient use and storage by teachers and students. Access the link below for easy-to-follow directions.

## Instructional Trends in Mathematics: Teaching with Manipulatives

Since the early 1900s, manipulatives have come to be considered essential in teaching mathematics at the elementary-school level. In fact, for decades, the National Council of Teachers of Mathematics (NCTM) has recommended the use of manipulatives in teaching mathematical concepts at all grade levels.

Manipulatives are strongly recommended for teaching a wide variety of topics in mathematics including:

- sorting - a pre-mathematical skill that aids in comprehension of patterns and functions
- ordering - a pre-mathematical skill that enhances number sense and other math-related abilities
- distinguishing patterns - the foundation for making mathematical generalizations
- recognizing geometric shapes and understanding relationships among them
- making measurements, using both nonstandard and standard units with application to both two- and three-dimensional objects
- understanding the base-ten system of numbers
- comprehending mathematical operations - addition, subtraction, multiplication, division
- recognizing relationships among mathematical operations
- exploring and describing spatial relationships
- identifying and describing different types of symmetry
- developing and utilizing spatial memory
- learning about experimenting with transformations
- engaging in problem-solving
- representing mathematical ideas in a variety of ways
- connecting different concepts in mathematics
- communicating mathematical ideas effectively

Manipulative use is recommended because it is supported by both learning theory and educational research in the classroom.

How Learning Theory Supports the Use of Manipualtives

The theory of experiential education revolves around the idea that learning is enhanced when students acquire knowledge through active processes that engage them. Manipulatives can be key in providing effective, active, engaging lessons in the teaching of mathematics. Manipulatives help students learn by allowing them to move from concrete experiences to abstract reasoning. Experts in education posit that this learning takes place in three stages.

The use of manipulatives helps students hone their mathematical thinking skills. Manipulatives can be important tools in helping students to think and reason in more meaningful ways. By giving students concrete ways to compare and operate on quantities, such manipulatives as pattern blocks, tiles, and cubes can contribute to the development of well-grounded, interconnected understandings of mathematical ideas.

Teachers play a crucial role in helping students use manipulatives successfully, so that they move through the three stages of learning and arrive at a deep understanding of mathematical concepts.

How Research from the Classroom Supports the Use of Manipulatives

Over the past four decades, studies done at all different grade levels and in several different countries indicate that mathematics achievement increases when maipulatives are put to good use.

With long-term use of manipulatives in mathematics, educators have found that students make gains in the following general areas:

- verbalizing mathematical thinking
- discussing mathematical ideas and concepts
- relating real-world situations to mathematics symbolism
- working collaboratively
- thinking divergently to find a variety of ways to solve problems
- expressing problems and solutions using a variety of mathematical symbols
- making presentations
- taking ownership of their learning experiences
- gaining confidence in their abilities to find solutions to mathematical problems using methods that they come up with themselves without relying on directions from the teacher

Research also indicates that using manipulatives helps improve the environment in math classrooms. When students work with manipulatives and then are given chance to reflect on their experiences, not only is mathematical learning enhanced, math anxiety is greatly reduced. Exploring manipualtives, especially self-directed exploration, provides an exciting classroom environment and promotes in students a positive attitude towards learning.