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This course broadens students’ understanding of mathematics as it relates to managing data. Students will apply methods for organizing and analyzing large amounts of information; solve problems involving probability and statistics; and carry out a culminating investigation that integrates statistical concepts and skills. Students will also refine their use of the mathematical processes necessary for success in senior mathematics. Students planning to enter university programs in business, the social sciences, and the humanities will find this course of particular interest.

Mathematics of Data Management

Course Credit

1

Course Price

\$ 550.00

Course Developer

My Learning Oasis

Prerequisite(s) (Text)

Functions, Grade 11, University Preparation MCR3U, or Functions and Applications, Grade 11, University/College Preparation MCF3M

Course Code

MDM4U

Course Type

University

Course Development Date

June 10th, 2021

## Course Outline

Data Management Tools

Data Management is basically the collection and use of data. To make data management meaningful, there are many ways to organize and extract meaning from the data. Many software tools are available to help with this process. This unit will address some of them. Perhaps the easiest way to present data is graphically. Creating such graphs and deducing information from them will be introduced in this section. Every country has a website that carries important data about various variables regarding that country, e.g. the average consumption of energy in single family homes etc. That website in Canada is the Statistics Canada website. In this course, the students will have to do assignments that make them frequently use the Statistics Canada website.

Expected Hours of Instructions:10 hours

Data Collection

Tables and graphs help the analyst to determine the behavior of a variable. Here such tables and graphs are introduced. Students will study the graphs and tables to determine the variability that data can present. The characteristics of a sample of data and the sampling of data will be addressed eg. good samples, good sampling techniques, and acceptable data collection principles. Students will collect and organize the data to solve a particular problem. Students will discuss the use of data management in various industries e.g. media organizations and the advertising industries.

Expected Hours of Instructions: 12 hours

Statistics of One Variable

This section addresses one variable of statistics, e.g. the number of people who visited the CN tower. Students will learn to process, analyze, and draw conclusions from one-variable data. Techniques that will be used are central tendencies, spread, and distribution.
Students will use a different software to analyze the presentation of data that has been collected, organized, and processed by others and make a conclusion on what it is telling. The student will develop the critical thinking skills necessary to interpret and assess secondary data for validity. Students are made aware of some inherent bias that may exist in some data and in other cases accidental incorrect misrepresentation of data.

Expected Hours of Instructions:17 hours

Statistics of Two Variables

Two-variable statistics show the relationship between two variables and data can be used to determine a mathematical relationship between them. In this section students will tabulate two-variable data sets and plot them. The graphs and tables will be used to draw concussions on the relationship between these variables. Further, the students will use techniques to determine the correlation coefficient of the two variables, i.e. how strongly they correlate.
Students will then make conclusions about their initial hypothesis.

Expected Hours of Instructions:17 hours

Combinatorics

The logic that deals with the counting of possible arrangements, called permutation and combinations will be studied in this section. The students will learn to evaluate the combinations and determine the best one for a particular situation. Sometimes, not just the combination, but the order of the items within a combination affects the outcomes of a certain situation. This will be considered. One example is the sequencing of DNA to determine personality traits.

Expected Hours of Instructions: 18 hours

Probability

In this unit students will determine the possibility of certain events or combinations of events for discrete sample space; develop solutions involving the application of permutations and combinations. Eg. What is the probability of pulling a single set of 2 blue balls and 3 red balls from a bag that contains 15 red and 20 blue balls? They will determine the probability of an event and show an understanding of discrete probability distributions by representing them numerically, graphically, and algebraically and determine expected values, and solve related problems for various real-life applications.

Expected Hours of Instructions: 18 hours

The Normal Distribution

Students will study continuous distributions, and will look at and analyze different shapes of distribution, considering situations that may generate them. Students will discuss the normal distribution in detail, and investigate applications. Students will compare the normal and the binomial distributions. They will develop an understanding of the conditions under which they might be used interchangeably, and develop the necessary knowledge that will allow them to decide how and when to make use of these properties.
Expected Hours of Instructions: 16 hours

Exam

Expected Hours of Instructions: 2 hours

Total 110 hours

## Resources

All notes and assignments will be provided by the teacher. The students are responsible to have:

● A non-programmable, non-graphing, scientific calculator.
● A note taking device for online students
● Internet connection for online students

## Overall Curriculum Expectations

A. Counting and Probability
A1 solve problems involving the probability of an event or a combination of events for discrete sample spaces;
A2 solve problems involving the application of permutations and combinations to determine the probability of an event.

B. Probability and Distributions
B1 demonstrate an understanding of discrete probability distributions, represent them numerically, graphically, and algebraically, determine expected values, and solve related problems from a variety of applications;
B2 demonstrate an understanding of continuous probability distributions, make connections to discrete probability distributions, determine standard deviations, describe key features of the normal distribution, and solve related problems from a variety of applications.

C. Organization of Data for Analysis

C1 demonstrate an understanding of the role of data in statistical studies and the variability inherent in data, and distinguish different types of data;
C2 describe the characteristics of a good sample, some sampling techniques, and principles of primary data collection, and collect and organize data to solve a problem.

D. Statistical Analysis
D1 analyse, interpret, and draw conclusions from one-variable data using numerical and graphical summaries;
D2 describe the characteristics of a good sample, some sampling techniques, and principles of primary data collection, and collect and organize data to solve a problem.
D3 demonstrate an understanding of the applications of data management used by the media and the advertising industry and in various occupations.

E. Culminating Data Management Investigation
E1 design and carry out a culminating investigation* that requires the integration and application of the knowledge and skills related to the expectations of this course;
E2 communicate the findings of a culminating investigation and provide constructive critiques of the investigations of others.

## Special Accommodations

Only Some students are able, with accommodations, to be part of a regular course curriculum and to demonstrate independent learning. These accommodations allow access to the course without any dilution of the knowledge and skills the student is expected to demonstrate. These required accommodations to facilitate the student’s learning will be identified in his or her IEP (see IEP Standards, 2000, page 11*). It is likely that IEP for many or all courses will reflect the same accommodations. The instructions and accommodations are geared to meet the diverse needs of learners.

## Program Considerations For English Language Learners

Students from a variety of cultural and linguistic backgrounds. For many of these students, English is not their spoken language. They may be coming from highly sophisticated educational systems, while others may have come from regions where access to formal schooling was limited. These students offer a rich addition to the classroom experience by way of their background knowledge and experience. All teachers will assist with their English- language development. In mathematics the teachers will include appropriate adaptations and strategies in their instructions and assessments to facilitate the success of the English language learners in their classrooms. Some of these strategies and adaptations are: modification of some or all of the course expectations so that they are challenging but attainable for the learner at his or her present level of English proficiency, given the necessary support from the teacher.

## Teaching/Learning Strategy

The key learning strategy at My Learning Oasis Elite Private School is Constructivism. This format facilitates learning by many techniques, most or all of which will be adopted in the classroom. The most dominant of these is group learning. The facilitator places students of different backgrounds in the same group so that they can feed off each other. Each may bring to the table a different reasoning strategy to facilitate problem-solving. Now, each student becomes a learner and a teacher at the same time, as he/she has to communicate his/her solution. This builds the students' knowledge base and by default, increases their confidence to speak in a crowd, albeit a small group at the beginning. The famous educationalist, Vygotsky, proved that by placing students in a group they function at the upper level of their zone of proximal development, each one scaffolding the other.

This strategy is further enhanced by the teacher asking leading questions as opposed to giving the answer outright, then allowing for group discussion. The students are encouraged to make connections between what they have learnt and their life experiences, then share with the group. The effect of this strategy is intrinsic motivation and learning. Each student develops an expanded appreciation of the topic at hand by seeing how it applies in different settings around the world by way of listening to their group members.

This Constructivist approach will be further accentuated by implementing “fish-bowling”. There are many ways to implement this technique. The one that will mostly be used will be by dividing up the larger problem (technical, mathematics, science, or otherwise) into smaller bits and have each student thoughtfully master one part. That student then teaches the group and facilitates a discussion reflection about the strategy (computational or otherwise) used in the solution. Each student in turn does this.

The above techniques enable students to reflect on the material learnt, make real life connections, and develop problem solving skills. One important by-product of the technique of Constructivism is that each student develops an appreciation of each other’s culture. This cultivates healthy people’s skill, which is not only important for the professional world but for life itself.

Constructivism lends itself well to students whose first language is not the language of instruction and who is new to the class. While other strategies will be used for students having difficulty with the English Language, this technique will definitely be used to enhance their English skill.

## Assessment And Evaluation

At My Learning Oasis, course facilitators do not wait for a quiz or exam to determine how well a student is doing. Here, evaluation is an on-going exercise. The pedagogical techniques (refer to Teaching and Learning Strategies) used at My learning Oasis are perhaps the best techniques suited for on-going assessment, hence, they being an integral part of our delivery methodologies.

Concrete assessments are made through projects and assignments. However, the evaluation is based on “our flavor” of the Mastery Teaching technique. This ensures that the emphasis is on the quality of learning and NOT grading. Students' projects and homework will continuously be evaluated and re-evaluated with appropriate guidance to meet the school’s and Ministry’s expectations. At My Learning Oasis, we will work with the students until the projects meet a minimum of a B-grade, unless in extreme circumstances where the willful negligence of the students force lower grades. While this is a lot more taxing on the facilitator, it does not matter because My Learning Oasis is a Learner-centered institution NOT a Grade-Centered nor a Teacher-Centered institution.

Four categories of knowledge and skills are outlined in the achievement chart - knowledge and understanding, thinking, communication, and application. Student’s work is assessed and evaluated with respect to these categories, and that achievement of particular expectations is considered within the appropriate categories. A final grade will then be recorded for this course and if that grade is 50% or higher, a credit is granted to the student and recorded for this course. The final grade for this course will be determined as follows:

● For material evaluated throughout the course, seventy percent of the grade will be assigned. This portion of the grade should reflect the student's consistency in his/her level of achievement throughout the course, although special consideration should be given to more recent evidence of achievement.
● Thirty percent of the grade will be based on a final evaluation, which is administered towards the end of the course.

Final Exam: 30%
Grading for all course work, projects, presentation, participation, interim quizzes and exam: 70%

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