Discuss about the Mathematising and Contextualising.
Critical Numeracy is a term that refers to the capability to make perceptive and keen judgemental decisions concerning the whole range of critical issues using mathematical ideas. Numeracy is the capability to use mathematics in analyzing critically every issue arising as a means of participating in the community as well as governance. This makes critical numeracy crucial when working on all critical issues to give it meaning and make it simpler. It works in conjunction with other literacy and lenses apart from the critical numeracy lens that includes; emotional, spiritual, ethical, aesthetic, historical, social and many others eventually building capacity for wise citizenship. This concept can be used to devise assessment of any question of study from the classroom to the various fields of study. Critical Numeracy builds the capacities of a person to ask a question about the meaning, validity, and usefulness of texts containing mathematical concepts. By applying numeracy lens, students go deeper into a topic expanding on it and hence drawing more meaning out of statements of just figures (Mahmood, 2012). Mathematical tools such as averages help to give meaning to tabulated data, and by doing this, the researcher of the student can draw inferences from a research topic. Below is an example of how using a critical numeracy tools helps us understand and expound better on issues or information given;
The following is the topic of an issue published in FACTACK, January 25th, 2017 by John Gramrich and Kim Parker; most officers say the media treat police unfairly. Just by reading the title, it’s is not the clear proportion of the ‘most police officers’ and therefore this may be misleading or inaccurate (Askew, 2015). Before applying any critical numeracy tool, some steps must be followed; what are the terminologies being used in the context and what do they mean? For our case above it is worth noting terms like ‘treat police unfairly’ and try to figure out what they imply and their significance in the given context. What are the key mathematical concepts used in the text if any? At this stage, one should look out for any information given as figures, say, percentages or fractions. The next step is the meaning-making stage. In this stage the researcher should determine the following; what the next talks about. This refers to the topic under considerations of the text. In this case, the text refers to the inappropriate treatment of police officers by the media. Next, determine how the text refers to what we already know. Is there any information relating to this text we know and have proof of currently, from the recent future of the past relating to such topic? Are there known facts that prove the information in the text true or otherwise? There may be such a claim in the past, and the outcome gives us important clues as we go deeper to mathematize the problem (Stott, 2014).
Determine how the already available information can be used to interpret the text, this may be figures of percentages, averages and so on. This kind of information can be used to hypothesize on the findings which are also an invaluable tool for mathematization. With this in mind, the researcher can also be led to explore further into the topic and come up with even more reliable finding than the ones available from basic surveys. Exploring further also adds meaning to the data. For the context we have above, after the mathematizing to percentages, it becomes evident that an officers’ age is also a contributing factor to the decision they make on the issue (Hogan, 2012). This is made evident by the percentage of the officers who strongly agree with the claim making up 46% of those below 44 years and only 36% of those older than that.
Between the words used to describe the problem and the mathematical model we want to apply, which would express the information in a more comprehensive and credible manner? In the case of our issue above, the words alone appear vague since we do not know what proportion is ‘most referring to. Percentages would make this claim more credible and therefore make it more understandable. The choice of mathematical concepts also determines how better the context is understood, e.g. percentages would analyze and model our context better than just tabulated figure hence they are better suited (Pather, 2012). Also, does the model improve the understanding of the context or just change its form of representation? Giving the number of those officers who agree on the claim and those who do not may just change the form in which the claim is represented but not how understandable and credible it is.
To devise an appropriate mathematical concept it is inevitable to determine what is confusing in the context as it is so that the concept decided upon will solve that and make more comprehensive. For our case above, the statement ‘most’ is misleading in that it may be based on an individual’s opinion due to some personal reasons and this can only be confirmed by using an appropriate mathematical concept (Eickelmann, 2012). Some statements may not be necessarily misleading but confusing, that means the person reading or interpreting them is not able to get meaning out of them. This is an important guideline as to which mathematical concept to use. Finally, while still making meaning out of a concept, it is crucial to determine whether there are other meanings than can be drawn from the same concept. For our case, the same concept may also mean that there is a conflict of interests between the police and the media and maybe this can be demonstrated mathematically using the same data gathered (Epstein, 2010). This can bring an even meaningful idea that excludes the possibility of personal motives behind the formulation of the context. If our mathematical model can show that this is just a conflict of interest based on the same data collected, then it is clearer to the reader on what the problem is and there is no place left to attach opinions as is the case with just telling a person ‘police are treated unfairly by the media’.
After authenticating a mathematical model follows applying it in the given context. To do this, the numbers in the context are examined to ascertain whether they are significant or useful (“Overview – Numeracy in the News,” 2017).
In our case, percentages are widely used as opposed to exact numbers since different police departments have different numbers and also the decision as to agreeing or refusing is influenced by other factors such as age (Neel, 2007). Due to these reasons, using raw figures wouldn’t simplify the meaning to the appropriate level. Numbers make it easy to comprehend the size of the agency, rather than saying; ‘large ‘ or ‘small’ agency, it is better saying ‘an agency with 2600 officers or 300 officer agency’. Once the numbers fit into the context, it is now clear the purpose of the text and the bigger picture can be seen. The bigger picture elaborates the picture even better and may make the researcher draw a different but more accurate conclusion. From our context, racial and ethnic lines are also a determining factor in the decision made by the individuals. To support this numerically, the percentage of those agree to the claim is higher amongst the white officers with 10% higher than those agreeing amongst the black officers (Neel, 2008). This shows that may be the reason the police are not in terms with media is that the media criticizes the police of mistreating the black race. This would also be the reason why the black officers do not seem to disagree so much with the media (Highfield, 2013). The high-ranking official also shows a tendency of disagreeing with this claim because regarding percentage those agreeing amongst the low-rank officers is 11% more than that of the high-rank officers.
The preceding that is not an agreed upon the decision, and hence it may have some personal opinions. The figures give more meaning to the claim prompting the researcher to dig even deeper so that the context is better understood. The figures also point out on the relationship between what the officers thought about knowledge of police work by the public and their opinion on the above question. The officers who agree to the claim also tend to believe the public is unaware of their work whereas a smaller percentage of those who disagree with the claim believe the same. Again this can clearly be observed from the percentages; 56% among those who agree and only 25% for the ones who do not. After close observation through the critical numeracy lens, it is also evident that the later percentages are also lower amongst those who agree but not strongly compared to those who strongly agree by as much as 26%. Those officers, who thought the media treated them unfairly, are also more likely to see a disconnection between the public and themselves. This clearly shows that other factors other than the relationship between the officers and the media were the cause of their decision. There are also those who strongly agree and those whose just agree which is evidence of variation the view of the issue even among those who agree with it. This calls for further research is the bigger picture and is only realized when a critical numeracy lens is applied (Paige, 2008).
The bigger picture now leads to a possibility of looking at the context from different viewpoints. The claim that the media mistreats the officers can be viewed as not resulting from the media’s fault but from the actions of the police which call for criticism. It can also be that the media are not carrying out positive criticism and instead they are accusing the police offensively in public. This again begs the question ‘who is offending who?’ which also gives another viewpoint to the problem. It can also be view as if one of the two parties is playing hero and they are just hitting back at each other since it is clear the claim is not unitary on the officers’ viewpoint (Dole, 2013). The claim by the police can be applied to validate the claim which would conceal malpractices in their department which are evident since not all the officers agree to the claim. If it is assumed that the media are criticizing the police offensively, it may obscure the media’s role in pinpointing evils in society and making them public whether by the government or even organizations. Taking it that one of the disagreeing parties is wrong and that further research should be done to determine who it is can result in no adverse impact on both parties and hence would provide the best option (Hillier, 2009).
Having the percentages of the individuals supporting or disagreeing in each category, we may decide that it is true the media mistreat the officers, but unlike the claim, there are other possible reasons as to why this is happening and not the mere reason that the media is in the wrong. Racism is a possible reason why the media may be criticizing the police, and hence it needs to be researched (Chartres, 2008). The decision may also be as a result of the officers’ view of their job because from the percentages; as much as 96% of those who strongly agree to confess that their job makes them feel either frustrated or angry. Those who don’t support the claim have less common feeling of frustration. It is clear now that after incorporating the critical numeracy lens, we don’t see the claim as it appeared at first. The claim now has more points of view and even a better meaning. From it, other issues that need attention have emerged among them racism, positive criticism and negative job feelings. As a result, the topic of media relationship with the officers is better understood and elaborated (Ares & Evans, 2017).
Close analysis shows that the decisions aforementioned are credible and have a much stronger base as opposed to the claim as it appeared at first. The context is also consistent with one inference directly leads to the other. Racism on the officers’ part would result in criticism by the media and, in the same way, negative or offensive criticism by the media would lead to complaints of unfair treatment from the officers. After application of the critical numeracy lens, the context is fair in that it does not favour any of the disagreeing parties and instead seeks to find a central ground for solving the issue (Healy, 2012). None of the parties has been silenced, and therefore everybody is given their say in a society which is the very core of human rights and equality. Therefore, everybody ends up satisfied.
It is evident that the mathematization process helps us to read the relationship between the officers and the media and now we can identify problem sources that lead to disagreement (Geiger, 2015). The reputation of the researcher is also not compromised since the new meaning of the context does not demean the findings of the original researcher but instead, makes them more detailed and credible therefore critical numeracy is inevitable in almost every context. The result of critical numeracy is a conviction first to the researcher and then to those reading the text. In the same way we can be able to read the world in the same way by analyzing the issues that emerge every day and by use of critical numeracy lens get to their roots, and by means of the various viewpoints we get, solve the issue in an efficient and informed way (“Critical Numeracy”, 2017).
Activity for students (beyond the mathematics class)
“The foods we eat today are the cause of most of the diseases today.”
It is a common belief in many parts of the world today that the kinds of food being consumed are the major cause of diseases ranging from lifestyle diseases to even more complex disease types.
You are required to find out the terminologies used in the above claim and what they mean, define the key mathematical concepts that can use, processes and procedures for critical numeracy on the above topic (Horsthemke,2007).
Meaning-making; explain what the text is about, how mathematical concepts can make sense in the above context; how they can help you better understand the context.
Determine what is misleading in this context?
Are there any other possible meanings?
Given the following information;
65% of those interviewed thinks the above is true,
83% of those whose think it’s not true are ladies between 18- 40 years,
83% of those who said this is not true confessed they don’t do anybody exercise,
15% of those who thought this is true were low-income class,
80% of those who said it’s true to think it’s the fault of food products manufacturers,
95% of those who thought this were true thought it was the sake of the government.
Required;
In what ways are the percentages useful in giving the context more meaning?
What is the bigger picture(s) that come into play after incorporating the critical numeracy lenses?
Mention the various viewpoints visualized after analysis using the critical numeracy lens?
Is the context logical, is it consistent?
Reference
Ares, N. & Evans, D. (2017). Mathematics and Numeracy as Social and Spatial Practice. Retrieved 13 March 2017, from
Askew, M. (2015). Numeracy for the 21st century: a commentary. ZDM, 47(4), 707-712.
Chartres, M. (2008). Are my students engaged with critical mathematics education?. In Mathematics Education and Society Conference (p. 186).
Critical Numeracy. (2017). Tas-education.org. Retrieved 13 March 2017, from https://www.tas-education.org/numeracy/critical_numeracy/critical_numeracy.htm
Dole, S., Hilton, G., Hilton, A., & Goos, M. (2013). Considering Density through a Numeracy Lens: Implications for Science Teaching. In Proceedings of the Second International Conference on New Perspectives in Science Education. libreriauniversitaria. It.
Eickelmann, B., Drossel, K., Wendt, H., & Bos, W. (2012). ICT-use in primary schools and children’s mathematics achievement-a multi-level approach to compare educational systems through an international lens with TIMSS data. In Joint AARE APERA International Conference, WERA Focal Meeting, Sydney (Vol. 2012).
Epstein, D., Mendick, H., & Moreau, M. P. (2010). Imagining the mathematician: Young people talking about popular representations of maths. Discourse: Studies in the Cultural Politics of Education, 31(1), 45-60.
Geiger, V., Goos, M., & Forgasz, H. (2015). A rich interpretation of numeracy for the 21st century: A survey of the state of the field. ZDM, 47(4), 531-548.
Healy, L., & Powell, A. B. (2012). Understanding and overcoming “disadvantage” in learning mathematics. In the Third International handbook of mathematics education (pp. 69-100). Springer New York.
Highfield, K., & Goodwin, K. (2013). Apps for mathematics learning: A review of ‘educational’apps from the iTunes App Store. Mathematics Education: Yesterday, today, and tomorrow, 378-385.
Hillier, Y. (2009). The changing faces of adult literacy, language, and numeracy: Literacy policy and implementation in the UK. Compare, 39(4), 535-550.
Hogan, J. (2012). Mathematics and numeracy: Has anything changed?: Are we any clearer?: Are we on track?. Australian Mathematics Teacher, The, 68(4), 4.
Horsthemke, K., & Schafer, M. (2007). Does’ African mathematics’ facilitate access to mathematics? Towards an ongoing critical analysis of ethnomathematics in a South African context. Pythagoras, 2007(65), 2-9.
Mahmood, A., Othman, M. F., & Yusof, Y. M. (2012). A Conceptual Framework for Mathematical Ability Analysis through the Lens of Cultural Neuroscience. Procedia-Social and Behavioral Sciences, 56, 175-182.
Neel, K. I. S. (2007). Numeracy in Haida Gwaii, BC: Connecting community, pedagogy, and epistemology. ProQuest.
Neel, K. I. S. (2008). Numeracy in Haida Gwaii, BC: Connecting community, pedagogy, and epistemology (Doctoral dissertation, Faculty of Education-Simon Fraser University).
Overview – Numeracy in the News. (2017). Tas-education.org. Retrieved 13 March 2017, from https://www.tas-education.org/numeracy/
Paige, K., Lloyd, D., & Chartres, M. (2008). Moving towards transdisciplinarity: an ecologically sustainable focus for science and mathematics pre?service education in the primary/middle years. Asia?Pacific Journal of Teacher Education, 36(1), 19-33.
Pather, S. (2012). Activity Theory as a lens to examine pre-service teachers’ perceptions of learning and teaching of Mathematics within an intervention program. African Journal of Research in Mathematics, Science and Technology Education, 16(2), 253-267.
Stott, D. (2014). Learners’ numeracy progression and the role of mediation in the context of two after-school mathematics clubs. Unpublished doctoral dissertation, Rhodes University, Grahamstown.
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