Using Games To Change The Way We Teach

Fulbright Action Research interventions featured in 'Transform Lives' section of Education and Human Development page of Texas A&M University, USA

  

Validity & Item Response Theory

How to upload a pdf on a blogpost.

Fulbright Alumni Grant Activity 2016

Suresh's Alumni Grant Activity 2016: 

A workshop, Exploring Learning through Experiential Designing using Games & Models, and

A Lecture Presentation 

When: December 18 – 19’ 20016.

 Where: At Dr. D.D. Pant Memorial Children's Science Exploratory and Government Girls Inter College, Berinag (Uttarakhand), India.

For Whom: Students, teachers (from four different schools) and community members from a highly underserved population in and around a small town Berinag, Uttrakhand, India.

Summary of the proposed project: - I have utilized my alumni grant 2016 to educate students, teachers and community members from a highly underserved population in and around a small town Berinag, Uttrakhand, India through a workshop and a lecture presentation during December 18-19’ 2016. Workshop and lecture presentation were based on my alumni grant activities in the past and my Fulbright Distinguished Awards in Teaching Program experience in the United States. Proposed workshop was a first-hand experience to the students and teachers by involving them into hand-on activities using low cost pedagogical tools based on games and models. Moreover, it helped them to expose to the experiential learning opportunities. 

The workshop helped me to promote involvement of girls in educational activities in such rural areas as it comprized 60% girls and 40% boys, along with the teachers, from different schools in Berinag. 

The lecture presentation was a dissemination of my Fulbright capstone project, described outcomes of the current workshop and helped propagating outcomes of all alumni grant activities that I have organized till now.

The objectives of the activity: -

The four-fold purpose of my alumni grant is

(i)              To draw the attention of the students, teachers and community members from the rural areas towards the use and popularization of games and models as low cost pedagogical tools in teaching by disseminating my capstone project and related activities,

(ii)            To educate students, teachers and community from a highly underserved population through experiential 

            learning opportunities by exposing 

            them to ‘learning by doing’ activities

            using games and model first hand,

           (iii)          to bring girls into the forefront of educational activities in the community by ensuring higher involvement of girls through the grant activity, and to motivate educational leaders to invest (not for profit) in such educational activities within and outside the community. 

 Descriptions of the proposed activity:

A description of the need for the project and any activities I have already implemented to address this need: - The students in the demographics such as Berinag, Uttrakhand, India, particularly those from Government schools (target population of my alumni grant), does not have resources such as funds, tools and other supporting learning material.

These schools and students are segregated by most of the profit based corporations and organizations as the students in these schools are not capable of affording expensive tools and models. The willing non-profit organizations hardly able to reach to such rural areas, which automatically deprives these students from the new and differentiated learning opportunities available. 

There is a strong need to educate students, teachers and the community in such areas about alternative resources of developing low cost teaching-learning tools by using surrounding material. This project will encourage them to use low cost models and games, available in their surroundings, for teaching -learning purposes and thereby will make them self-resourced. 

Workshop and lecture of the project would also help them to make their knowledge concrete and experience based.

My alumni grant activities organized in the past (2013, 2015) were focused on training the trainers (teachers) from Delhi and NCR (National capital Regions), which were highly successful. Teachers benefitted from those activities use models and lesson plans, that they were able to develop during these alumni grant activities, in their schools. 

Acknowledgements: The U.S. Department of State & EPSO, Texas A&M University.

January 21' 2016

Regression and Regression Constants....

Regression: It is a prediction. Deriving an equation for predicting one variable from the other.

Algebraically, Errors of prediction = (Y - ^Y)

Least squares linear regression: In a cause and effect relationship, the independent variable (X) is the cause, and the dependent variable (Y) is the effect. Least squares linear regression is a method for predicting the value of a dependent variable Y, based on the value of an independent variable X.

The Least Squares Regression Line: It is a series of points arranged in a straight line that tells how much better the prediction is. Linear regression finds the straight line, called the least squares regression line that best represents observations in a bivariate data set. Suppose Y is a dependent variable, and X is an independent variable, the population regression line cab be written as:

Y = b X + a

In this linear equation, ‘b’ is the beta coefficient and ‘a’ is the Y- intercept of the regression line.

Line of Best Fit (Least Square Method): Minimizes the squared difference (squared deviations) between Y and ^Y (because we can have more than one predicted value for one X value). This method is a more accurate way of finding the line of best fit. A line of best fit is a straight line that is the best approximation of the given set of data. It is used to study the nature of the relation between two variables.

A line of best fit can be roughly determined using an eyeball method by drawing a straight line on a scatterplot so that the number of points above the line and below the line is about equal (and the line passes through as many points as possible).

Steps to find the equation of line of best fit:

1.      Calculate the mean of the x-values and the mean of the y-values.

2.      Find the slope of the line of best fit

3.      Compute the Y-intercept of the line by using the formula.

4.      Write equation of the line (Y = bX + a)

Properties of Regression Line: When the regression parameters (a & b) are defined by the equation above, the regression line has the following properties:

1. The difference between obtained and predicted value (Y - ^Y) is called an error of prediction called residual. We want to find a line that minimizes the squared difference between Y and ^Y and is known as least square regression line and the approach is called least squares regression.
2. Two important measures of the size of an effect in regression are r² and r.
3. The regression line passes through the mean of the X values (x) and through the mean of the Y values (y) or we can say that it passes through the centroid of the data.
4. The regression constant (a) = Y-intercept of the regression line.
5. To use the regression equation technique described in the text, we must have a logical pairing of the scores on the two variables and a linear relationship between them.

Intersection of two means fall on the regression line.

Regression coefficient (b, Slope, nonstandardized): The amount of change in Y for a one – unit change in X. Or the rate at which Y change with change in X. Larger the value (size) of the regression coefficient, the steeper the slope. It is (b) which a measure of how strongly each predictor variable influences the criterion (outcome) variable.

b_yx = r_xy (SD_y / SD_x); when Y – Outcome, X – predictor

And,           b_xy = r_xy (SD_x / SD_y); When X – Outcome, Y – predictor

‘b’ is measured in units of standard deviation. For example, a beta value of 2.5 indicates that a change of one standard deviation in the predictor variable will result in a change of 2.5 standard deviations in the outcome (criterion) variable.

1.     ‘b’ = 1.08 means when X increases by 1 point, outcome increases by 1.08.

2.     On multiplying two slopes b _y·x and b _x·y we are left with the square of the correlation coefficient which tells about percentage of variance of both variables together. It tells the percentage accuracy in predicting Y. It is better to have the knowledge of correlation coefficient to predict the outcomes.

3.     If b coefficient is positive, the relationship of predictor variable with dependent variable is positive (e.g., the greater the IQ the better the grade point average) and if b coefficient is negative then the relationship is negative (e.g., the lower the class size the better the average test scores).

4.     If b coefficient is equal to 0 then there is no relationship between the variables.

5.     ‘b’ can be anything (when b = +, r = +, and b = -, r = -  but b = +, r = - & vice versa is not possible)

6.     Many lines may have same slope (b) but cannot have the same intercept ‘a’ altogether (‘a’ is the unique identification of a line).

Beta coefficient (b, standardized regression coefficients): It is the change in Y for one unit standard deviation change in X. It is the slope of the regression line when both X and Y variables are converted to standardized z-scores. Thus, higher the beta value the greater the impact of the predictor variable on the criterion variable.

1.     When we have only one predictor variable in our model, then,

Beta (b) = r_xy.

2.     When we  have  more  than  one  predictor  variable,  we  cannot compare contribution  of  each  predictor  variable  by  simply  comparing  the            correlation coefficients. The beta coefficient allows to make such comparisons  and  to  assess  the  strength  of  the  relationship  between    each predictor variable to the criterion variable

Interpreting regression constants:

The regression coefficient (b) is the average change (increase or decrease depending on +ve or –ve b) in the outcome variable (Y) for a 1 – unit change in the predictive variable (X).  Slope (b coefficient) is a measure of how strongly each predictor variable influences the criterion (outcome) variable. Higher the beta value the greater the impact of the predictor variable on the outcome variable. Relationship is positive if b coefficient is positive and vice versa.

Regression constant ‘a’; Y – intercept: That anchors our line.

The constant term ‘a (regression constant)’ is the value at which fitted line (Line of best fit) crosses the y-axis. It is used as a ‘correction factor’ when using particular values of the x's to predict y.  If we don’t include the constant, the regression line is forced to go through the origin which means all of the predictors and the outcome variables must be zero at that point.

These notes are written by S C Joshi during EPSY 635 Course, Fall 2015, Texas A&M University. Acknowledgements to Dr. Bob Hall, Professor, EPSY, Texas A&M University for his assistance in understanding these terms during the course  

Scatterplot (what is it and why is it required?)..

Scatterplot: It is a graphical (pictorial) interpretation of the linear correlation between two continuous (interval / ratio) variables, predictive and outcome, plotted in X and Y axis respectively.

Why Scatterplot?

1.     Because describing a relationship through a number is not enough, we need to look at the relationship in a scatterplot or how points very (bunched-up) around regression line in a scatterplot.

2.     Graph (scatterplot) also helps in detecting the homoscedasticity (variability of points around the regression line) in a relationship which is rectified through transformation.

3.     Graph (scatterplot) tells about the outliers in the data, which are the threats to the interpretation and needs to be omitted.

4.     Scatterplot determines the situations where the correlation is curvilinear. Simply reporting r = 0 might be misleading because a relation still exists which might not be a linear one.

Two Characteristics of a scatter-plot:

1.     The slope of the scatter-plot, and

2.     The degree to which the points in the scatter-plot cluster around an imaginary line representing the slope.

  These notes are written by S C Joshi during EPSY 635 Course, Fall 2015, Texas A&M University. Acknowledgements to Dr. Bob Hall, Professor, EPSY, Texas A&M University for his assistance in understanding these terms during the course 

Covariance: It is a measure of the degree to which two random variables (X, Y) change together.

Cov_xy = Sum of products of errors / (n-1)

r² (Coefficient of determination):

Indicates how well data points fit a line or curve. It is mainly used in models to predict future outcomes or test hypotheses on the basis of other related information.

The squared correlation coefficient (r²) is the proportion of variance in Y that can be accounted for by knowing X. Conversely, it is the proportion of variance in X that can be accounted for by knowing Y. Further, I can say that it is a statistic which indicates the percentage change in the amount of the outcome variable (dependent) that is ‘explained by’ the changes in the predictor variable (independent). In other words, shared / common variance, means how much percentage of the relationship can be explained by the regression (or predicted) and rest is unexplained. It is the indicator of accuracy of a prediction. We can also call it a proportion of the variance in outcome variable (Y) that is predictable from the predictor variable (X) or it is the fraction of the variation in Y that is explained by least-squares regression of Y on X.

1.     The coefficient of determination ranges from 0 to 1 (proportion or percentage, cannot be more than 1 or 100% respectively).

2.     It is important to note that a high coefficient of determination does not guarantee that a cause-and-effect relationship exists. However, a cause-and-effect relationship between the independent variable and the dependent variable will result in a high coefficient of determination.

3.     An R² of 0 means that the dependent variable cannot be predicted from the independent variable.

4. An R² of 1 means the dependent variable can be predicted without error from the independent variable.

These notes are written by S C Joshi during EPSY 635 Course, Fall 2015, Texas A&M University. Acknowledgements to Dr. Bob Hall, Professor, EPSY, Texas A&M University for his assistance in understanding these terms during the course

Threats to Correlation Coefficient...

Threats to PPMCC (Factors affecting correlation):

1.     Outliers: the data that stands out in the scatterplot does not contribute to the relationship and must be omitted. (for small group outlier has large effects). Outliers does not go with the linear relationship (must have performed poor in exam 3 and outstanding in exam 4). Value of r will increase if the outliers are removed and more accurate depiction of the relationship between the predictor and the outcome measures because outliers are the threats to the PPMCC and results decrease in r value. So, on removing outliers data shows better liner relationship thus increase in r value.

2.     Combined groups: Two groups separately may not show any relationship individually but together may show a strong relationship.

3.     Extreme groups: There is no relationship (r = 0) between two variables for low performing groups and high performing groups individually, but together they show the relationship.

4.     Range restriction (truncated range): If we restrict the range (means accept only high SAT scorers we will not be able to see the relationship on how low SAT scores are going to do in college so) relationship is going to be lower. Truncated range lowers the correlation.

5.     Nonlinear relationship (curvilinear relationship): is not explained by PPMCC.

Assumptions Underlying the Pearson Product Moment Correlation Coefficient....

Assumptions Underlying the PPMCC: PPMCC is appropriate when three conditions exists: underlying measurement scales for the variables being correlated must be interval or ratio level, Scores for each variable should be normally distributed (no skewness should be there), relationship between the two variables should be fundamentally linear.

1.     The underlying measurement scales for the variables being correlated must be interval or ratio level (i.e., they are continuous).

Examples of variables that meet this criterion include revision time (measured in hours), intelligence (measured using IQ score), exam performance (measured from 0 to 100), weight (measured in kg), and so forth.

2.     Bivariate Normality (Bivariate normal distribution): Scores for each variable should be normally distributed. No skewness, neither positive nor negative should be there.

3.     Relationship between the two variables should be fundamentally linear.

4.     There should be no significant outliers (single data points within the data that do not follow the usual pattern).

5.     Homoscedasticity: It means variance around regression line should be same for all values of predictor variable (X). A relation is called heteroscedastic when all the points very (bunched up) near the regression line. Homoscedasticity is violated when there is much more variability (points are scattered away from the regression line) around the regression line. 

Serious violations in homoscedasticity (assuming a distribution of data is homoscedastic when in actuality it is heteroscedastic) result in underemphasizing the Pearson coefficient.  Assuming homoscedasticity assumes that variance is fixed throughout a distribution.

Heteroscedasticity is caused by non-normality of one of the variables, an indirect relationship between variables, or to the effect of a data transformation.  Heteroscedasticity is not fatal to an analysis, the analysis is weakened, not invalidated.  Homoscedasticity is detected with scatterplots and is rectified through transformation.

These notes are written by S C Joshi during EPSY 635 Course, Fall 2015, Texas A&M University. Acknowledgements to Dr. Bob Hall, Professor, EPSY, Texas A&M University for his assistance in understanding these terms during the course