Teaching considerations

When developing explicit learning programs for students working with emergent strategies, teachers need to consider:

Identifying or naming?

Identifying a numeral, when the name (in verbal form) has been provided for the student, is a different skill from naming a numeral which has been presented visually to the student. Some students working with emergent strategies may have particular difficulty with naming numerals compared to identifying them.

Teachers should ensure that students are given opportunities to both identify and name numerals, mastering both skills.

The distinction between identifying and naming is emphasised in the following example.

Identifying or naming activity - Teaching considerations - Emergent

Compare a student’s response to being asked to point to the card with the numeral five on it and asking the student to say the number word when shown a numeral card.

In the first task the students need to identify the numeral in response to its spoken name, whereas in the second task the student needs to be able to name the written numeral.

Developing strategies

Students working with emergent strategies often rely on a single strategy when dealing with number activities.

Students might, for example, have developed knowledge of the forward number word sequence from 1 to 5. When asked to count collections, they would use their knowledge of the forward count if the collection is limited to five items.

To support the development of numeral recognition, teachers should ensure that numeral cards are not always presented in sequence. When asked to identify the numeral 5, students working with emergent strategies often rely on their knowledge of the forward count and count the numeral cards to find the fifth one, rather than spontaneously identifying the numeral.

Students need to be provided with multiple opportunities to link concrete, verbal, visual and symbolic representations with a vast range of resources. At this stage, students should also be exposed to, and taught about, the principles of counting to help them understand how we count. 

Scaffolding

To assist students with emergent strategies, scaffolding or support will be necessary. The following ideas assist in supporting the learner:

  • model the learning activity, thinking aloud to clarify the intended level of thinking, communicating and reasoning before students are expected to work independently
  • explicitly and systematically teach the vocabulary students need to effectively participate and communicate within learning experiences
  • use a range of visual aids and concrete materials to support comprehension and scaffold conversation
  • use effective questioning strategies to support students in activating their prior knowledge
  • allow think time for students and provide regular opportunities to students to talk
  • break instructions and learning opportunities into manageable chunks, differentiating instructions, tasks and expectations as required
  • develop learning activities which repeat concepts using a variety of representations, thus providing meaningful repetition and revision of learning to support retention of skills and understanding
  • provide opportunities for students to work with students who are beyond the emergent stage
  • limit the range of numerals being presented.

Language

Language and vocabulary development play a significant role in learning mathematics. A student’s language (the way they talk about number problems, counting and mathematical concepts) needs to include specific words we use as mathematicians, the symbols we use as well as the language we use to talk about concrete and visual models.

Language such as: count, counting, forward, backward, more than, less than, the number words (zero, one, two, three, four, five, six, seven, eight, nine, ten), amount, many, much, dice, domino, pattern, fingers, match, number word, order, sequence, item, collection, etc. are examples of the language students need to learn about and incorporate into their vocabulary.

Students need learning opportunities that support their skills in describing, classifying, generalising, sorting, comparing and contrasting in order to support their mathematical understandings. In order to communicate their thinking students need explicit teaching in how to recall, recount, justify, speculate, explain, question, hypothesise and respond using mathematical language.

Picture books with a mathematical focus are useful in repeatedly practising language, exploring concepts and discussing mathematical ideas.