# ACG School Jakarta

### Constructing Meaning – the Literacy of Numeracy

“It is important that that learners acquire mathematical understanding by constructing their own meaning…”

So how can children make sense of, and then competently use, the language of mathematics? This article looks at ambiguous language and operational language.

The following interaction between a teacher and student was recorded.

*T: Can you calculate the volume of this box? S: um .. [pause] .. no [has a puzzled look]*

*T: Do you know what volume is? S: Yes, it is a button on the remote.*

One of the issues with constructing meaning of the language of mathematics is the use of everyday English terms that have different meanings in the mathematics classroom.

Here is a list of just some of the many words that have a different meaning in mathematics. These words are just some of the homographs: *rational, mean, power, odd, face, property, common*

The operational language can also be confusing. In the early years ‘and ‘is used for operation of addition. In later years the word ‘and’ is used in an operation for multiplication, e.g. ‘What’s the product of 5 and 4?’

When assessing a student’s ability to solve word problems in mathematics it is so important to consider not only the wording of the question but also the order of the questions. Two consecutive questions, similar to these, appeared in a standardised test. The word ‘altogether’ is used for a different operation in each question. What meanings have the students constructed of the words ‘and’ and ‘altogether’?

Question 12.

Budi puts cards into 4 equal piles.

Each pile has 20 cards.

How many cards does Budi have altogether?

Question 13.

Wati collected 68 cans.

Puti collected 109 cans.

How many cans did Wati and Puti collect altogether?

The construction of operational language is so important for problem solving. In some classrooms students can identify words in a problem, referring to displayed visual mathematical vocabulary.

Although language is heavily involved in constructing meaning in mathematics, the use of visual representations and manipulation of concrete materials all support communication and success in the mathematics classroom. The literacy of numeracy is a challenge for all and an additional challenge if English is an additional language. Our role is to support students to construct meaning as part of the stages of learning mathematics.

*Melinda Mawson-Ryan*

*ACG School Jakarta*

*Melinda.Mawson-Ryan@acgedu.com*

### English Language Support and the PYP

The purpose of ELS is to support students to develop the language needed for learning so that they can actively participate in the PYP.

*ELS and the Learner Profile*

The ELS classrooms are supportive spaces where students work in small groups. Our ELS essential agreement is displayed and gives an example of a learning behaviour which demonstrates an attribute of the learner profile. The ELS teachers model the learner profile attributes in their teaching and learning. ELS teachers explicitly provide feedback to the students when they display an attribute of the learner profile. Risk taking is highly valued in the ELS classrooms as students build confidence and skills to ‘have a go’. Students reflect on their learning at the end of each lesson. Every fortnight a Primary ELS student is recognised with a PYP certificate for demonstrating the attributes of the learner profile.

*ELS and Key Concepts*

ELS learners have the opportunity to construct meaning by exploring English words using some of the key concepts. We use questions to explore the concepts. Here are two examples:

__Contractions__

- Form: What does a contraction look like?
- Connection: How is the contraction connected to the original two words?
- Change: How do the two words change?
- Function: How does the apostrophe work?
- Reflection: What have you learned today about contractions?
- Reflection for teachers: What worked well and what would you do differently next time?

__Word building: constructing morphemic knowledge__

- Change and function: How does this suffix change the function of the word?
- Connection: What other words can be built from the base word?
- Form: What letters do adverbs often have at the end?
- Causation and function: What prefix causes the word do have an opposite meaning?
- Reflection: What have you learned today about words?
- Reflection for teachers: What worked well and what would you do differently next time?

*ELS and Units of Inquiry *

Classroom and ELS teachers collaboratively plan teaching and learning tasks. Planning is documented and resources shared. This means that ELS teachers support the students to:

- understand and use key vocabulary so they can participate in class discussions
- use writing frames to support development of writing in a particular genre
- read texts, with a lower Lexile, related to the unit

The ELS teachers also:

- explicitly teach research skills
- source, and where needed, rewrite documents for research that are accessible
- develop differentiated assessments, including rubrics and checklists
- provide intensive support for ELS students as they develop their Exhibition.

In addition, through our work with the students, we support the development of the PYP transdisciplinary skills, in particularly thinking, communication and research skills.

*Melinda Mawson-Ryan*

*Senior ELS Teacher*

*ACG School Jakarta*