SHS2 Mathematics · Semester 2 Week 13: Statistical Reasoning and Its Application in Real Life

Lesson notes

Learning Objectives

Indicator: 2.4.1.LI.2 - Evaluate a given set of data and/or its instrument by identifying potential problems related to bias, use of language, gender, ethics, cost, time, privacy, cultural sensitivity, etc.

By the end of the lesson, learners can:

Identify at least five different types of problems (bias, use of language, gender, ethics, cost, time, privacy, cultural sensitivity) that can affect a data collection instrument or the data it produces.
Evaluate a given survey question and explain why it is biased or poorly worded, using specific vocabulary such as “directional,” “leading,” and “loaded.”
Rewrite a flawed survey question into a neutral, well-structured question that offers respondents a full range of response options.
Assess a data collection scenario for potential ethical, privacy, cost, and time problems, and justify which problems are most serious and why.
Recommend practical strategies to reduce cost, save time, protect privacy, and ensure cultural sensitivity when designing a data collection instrument.

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Curriculum details

Strand: Making Sense of and Using Data (Strand 4)
Sub-strand: Statistical Reasoning and Its Application in Real Life (4.1)
Content standard: 2.4.1.CS.1 - Demonstrate conceptual understanding of data handling in relation to designing and validating a variety of data collection methods. 2.4.1.LO.1 Design a data collection instrument and justify its appropriateness for collecting everyday life data to address a contextual issue.
Indicator: 2.4.1.LI.2 - Evaluate a given set of data and/or its instrument by identifying potential problems related to bias, use of language, gender, ethics, cost, time, privacy, cultural sensitivity, etc.
Suggested placement: Semester 2, Week 13 (Week 33 of the year)
Our suggestion, laid out in curriculum order across three terms of twelve weeks. NaCCA does not fix the week, so follow your school's scheme of learning.
Curriculum reference: NaCCA curriculum document, p. 273

Exemplars (from the NaCCA curriculum)

Using group discussions and think-pair-share activities, engage learners to discuss and decide on a survey to undertake, consider what facts/contextual issues to take into consideration in designing the survey questionnaire, and choose a suitable data collection method that includes the cross-cutting considerations and how to collect the data.
Encourage learners to extend their discussions on the need to be mindful of their choices in every situation and how to manage their emotions in such instances.
Example: Recognise that a given question on a survey questionnaire contains bias.
Suppose you tell your classmates that the response to the question in the Class Survey Question Form is to help you evaluate students' courses.
The course was well organised in terms of the time frame, assessment, and access to materials. 1. Yes 2. No
Such a question is directional and does not offer respondents the opportunity to express their opinion if they believe the organisation was done well to some extent.
A better question could be:
How organised was the course in terms of the time frame assessment and access to materials?
- Very organised
- Somewhat organised
- Neutral
- Disorganised
- Highly disorganised
Examples: i. Discuss the cost and time frame for collecting data on a particular area of interest and make recommendations on how to strategise to reduce the cost and time. ii. Discuss and decide on a survey to undertake, what facts/contextual issues to take into consideration in designing the survey questionnaire, and choose a suitable data collection method that includes the social considerations and how to collect the data.
Teaching and Learning Resources:
- * Samples of questionnaires, interview guides, observation guides, etc. * Computer application software such as Excel, MS Word, Wordpad, etc. * Mathematical sets * Technology tools such as computers, mobile phones, etc
Assessment (2.4.1.AS.2). The document marks these depth-of-knowledge levels for this indicator: Level 1 Recall; Level 2 Skills of conceptual understanding.