# PTA ES Curriculum

**Math Curriculum in Pretoria ES **

AISJ uses the American Education Reaches Out (AERO) mathematical standards and benchmarks for grades PreK – Gr12. Our developmental approaches are derived out of researched best practices from countries on the Pacific Rim. We strive to monitor and develop conceptual understanding, procedural fluency and problem solving in Counting and Cardinality (CC), Numbers in Base Ten (NBT), Operations: Algebraic Thinking (OA), Measurement and Data (MD) and Geometry (G). These can be seen through the PreK – Gr5 scope and sequence documents.

## Math Workshop

At AISJ math is taught using a workshop approach rather than a whole class methodolgy. This is a way of differentiating instruction to help all students develop knowledge, skills, strategies and conceptual understanding. The workshop approach is a predictable structure that provides students with routines and time to work at their just right math level.

**MINI-LESSONS**

**MINI-LESSONS**

Each workshop has a mini lesson. This is a brief 10 – 15min whole class lesson focussing on a skill, mathematical practice or concept that is relevant for all students in the class.

**INDIVIDUAL PRACTICES**

**INDIVIDUAL PRACTICES**

Students work independently or in small groups to practice skills and strategies, and/or develop their mathematical knowledge and conceptual understanding. Independent practice is usually connected to the small group instruction and/or each student's numeracy goals.

*GROUP PROBLEM SOLVING*

Students are also challenged weekly with group problem solving tasks and/or projects. Tasks of this nature are a time for students to apply their knowledge, skills and understanding in real life and life like situations.

*SMALL GROUP INSTRUCTION*

Teachers use data from pre-assessments and the individual student number profiles to form small groups. Students then work with a teacher and engage in an interactive lesson that is geared to their needs. These groups are flexible and constantly change depending on student needs and the concepts and skills being taught.

**INDIVIDUAL CONFERENCES**

**INDIVIDUAL CONFERENCES**

Students meet one-on-one with a teacher to demonstrate new learning, and review and set mathematical goals

**SHARING / REFLECTION**

**SHARING / REFLECTION**

The math workshop ends with a time for student sharing, self-reflection, questions or opportunities to connect learning to other curricular areas and/or experiences.

## KNOWLEDGE

Number knowledge describes the key items of knowledge students need to learn. It is important for students to continually increase their number knowledge to reduce the cognitive stress on the brain when solving challenging problems. The ability to solve problems accurately and efficiently is based on knowing and being able to retrieve key items of knowledge with minimal effort. Knowledge is important because using knowledge can decrease the load on working memory and enable students to solve more complex problems. Strong knowledge is essential for students to broaden their repertoire of operational strategies and for the development of more advanced strategies.

## OPERATIONAL STRATEGIES

Operational strategies describe the mental processes students use to estimate answers and solve operational problems with numbers. Students’ operational strategy stage indicates an expansion in knowledge and in the range of strategies students have available to choose from. Students build new strategies on their existing strategies and these existing strategies are not subsumed. Students frequently revert to previous strategies when presented with unfamiliar problems or when the mental load gets high.

Students learn to interpret and solve problems using the four operations using a variety of operational strategies.

Examples of the different mathematical situations are:

THE APPLICATION OF NUMBER KNOWLEDGE AND OPERATIONAL STRATEGIES IS OFTEN DESCRIBED AS ‘NUMBER SENSE’. STRONGLY DEVELOPED NUMBER SENSE LEADS TO STRONG ALGEBRAIC THINKING.

## MATH PRACTICES

For mathematics to be relevant for the 21st century learners, it must develop knowledge and strategy (number sense) as well as mathematical practices. Mathematical knowledge, skills and content reflect new needs and goals, but are essentially unchanged. Nevertheless, because the world is changing so rapidly, more is needed. Being prepared to compete in an increasingly complicated and unpredictable world means developing stamina and dispositions to struggle through unfamiliar, challenging problems. The confidence to approach new and unfamiliar problems and tackle them without a pre-learned solution or method is vitally important.

**THE EIGHT PREK – GR 12 MATHEMATICAL PRACTICES ARE:**

**THE EIGHT PREK – GR 12 MATHEMATICAL PRACTICES ARE:**

1. MAKE SENSE OF PROBLEMS AND PERSEVERE IN SOLVING THEM.

2. REASON ABSTRACTLY AND QUANTITATIVELY.

3. CONSTRUCT VIABLE ARGUMENTS AND CRITIQUE THE REASONING OF OTHERS.

4. MODEL WITH MATHEMATICS.

5. USE APPROPRIATE TOOLS STRATEGICALLY.

6. ATTEND TO PRECISION.

7. LOOK FOR AND MAKE USE OF STRUCTURE.

8. LOOK FOR AND EXPRESS REGULARITY IN REPEATED REASONING.

## ASSESSMENT

## Assessment

In the Elementary School, we conduct an internal standardized numeracy assessments twice a year to measure the students’ numeracy development in both mathematical knowledge and strategic thinking for students in KG – Gr 5. For PreK, this information is obtained using informal assessments such as observation, conferring and student work samples. The numeracy assessment we use are:

**JAM**

**JAM**

The Junior Assessment of Mathematics (JAM) is a one-on-one interview and assesses the achievement of a student in relation to early stages of numeracy development. This assessment is primarily used with students in K – Gr2.

**GLOSS**

**GLOSS**

The Global Strategy Stage (GloSS) one-on-one interview is used to assess the achievement of a student in relation to intermediate and advanced stages of mathematical strategic thinking. This assessment is primarily used with students in Gr 3 – 5.

**IKAN**

**IKAN**

The Individual Knowledge Assessment of Number (IKAN) is used to assess the achievement of a student in relation to intermediate and advanced stages of number knowledge. This assessment is primarily used with students in Gr 3 – 5.

**Developmental Stages and Approximation of Proficiency for the end of each grade**

Stage | End of Year | Assessment Used |
---|---|---|

0-1 Emergent | PK | Obersvation |

2-3 Counting All | Kindergarten | JAM Interview |

4 Advanced Counting | Grade 1 | JAM Interview |

5 Early Additive | Grade 2-3 | JAM/GloSS/IKAN |

6 Advanced Additive | Grade 4-5 | GloSS/IKAN |

**NUMBER PROFILE**

**NUMBER PROFILE**

We use the data from the JAM, GloSS and IKAN assessments to complete an individual number profile for students from Kindergarten through to Grade 5. A number profile (link) is also generated for students in Pre-K but this is done using observations, not the JAM interview. The number profile helps teachers and students track their growth through the stages of numeracy development. A student’s number profile is shared with parents throughout the year, so there is clear communication regarding strengths and areas for growth. Student number profiles are passed on to the following year’s teacher at the end of each academic year.

This is an example of what a completed number profile (link) for a child at the end of Grade 2 might look like.

**MAP**

**MAP**

At AISJ, we also implement the Measures of Academic Progress (MAP) achievement test in mathematics, twice a year, for all students in Grades 3 – 5.