Learning Science · Language, experience and cultural context
Connecting learning to familiar practices
Connect an unfamiliar academic representation to a familiar practice without assuming the connection is automatic.
Use the examples to connect this lesson with the earlier topics. No specialist equipment is needed.
Back to the chapterAfter reading, you can
- Identify knowledge embedded in an everyday practice.
- Bridge between contextual and formal representations.
Competence may be situated
A learner estimates prices and change accurately in a market but struggles with written arithmetic in class. The classroom result does not show that the everyday competence is imaginary; the everyday result does not show that formal notation is already mastered. Each task supplies different cues, purposes and representations.
Find the relation and build the bridge
Ask the learner to explain how the familiar task is done. Identify useful quantities, decisions and checks. Then connect those to the formal representation: which spoken step corresponds to a written operation, and what does the notation add or change?
Carraher, Carraher and Schliemann studied working youngsters in Recife, Brazil, and compared mathematical performance across contextual and school-like tasks. Their abstract reports differences across those conditions. This is evidence that task context can matter; it is not a description of every Brazilian learner or proof that all informal methods transfer automatically.
Use familiarity without narrowing the future
A familiar example can provide an entry point, but later practice should vary the setting. Otherwise the learner may continue to recognise the relation only in the original context. Explicitly compare the old and new cases and ask where the same reasoning applies.
Do not assume a practice is familiar because of a learner’s address, occupation, ethnicity or family background. Offer options and invite examples without requiring personal disclosure. Everyday practices may also contain approximations that are fit for their purpose but insufficient for a new academic question. Discuss that purpose rather than treating either setting as uniformly superior.
Worked example
From change-making to subtraction
How does counting up connect the change-making task to subtraction?
- A learner finds change from 7.60 euros to 10 euros by counting up: 0.40 to reach 8, then 2 to reach 10, giving 2.40. The teacher writes 10 minus 7.60 and shows how the same difference appears on a number line. A new problem asks for a height difference with no money. The learner explains the shared distance-between-values relationship, while learning the written subtraction notation as an additional tool.
- The number line also permits the learner to check the answer in the opposite direction: 7.60 plus 2.40 reaches 10. Written subtraction and counting up are now connected by a shared difference. Asking for both representations does not require declaring one inherently superior; it develops flexibility and reveals when a particular method becomes awkward or less informative.
Count €0.40 to reach 8 and €2 to reach 10, totalling €2.40. The shared difference is 10−7.60, checked by 7.60+2.40 = 10.
Change-making and subtraction share a difference
Try it yourself
Think through each question before opening the answer.
Why not infer formal arithmetic mastery from accurate market calculations?
Show the answer and reasoning
The learner may use context-specific cues and strategies.
Formal notation and transfer to other contexts need their own opportunities and checks.
What is the purpose of the non-money follow-up?
Show the answer and reasoning
It tests whether the learner can recognise the difference relationship beyond the familiar transaction setting.
A height difference retains the distance-between-values relationship while removing money cues.
What to carry forward
- Recognise existing competence and inspect how it works.
- Teach the bridge between representations and vary the later context.
References
Sources supporting the explanations and learning checks in this lesson.