Fun Ways to Assess Student Learning Informally

There are a variety of ways to assess a student’s progress and understanding. Two of the primary methods are formal and informal assessments. Formal assessments include tests, quizzes, and projects. Students can study  and prepare for these assessments in advance, and they provide a systematic tool for teachers to measure a student’s knowledge and evaluate learning progress. Informal assessments are more casual, observation-based tools. With little advance preparation and no need to grade the results, these assessments allow teachers to get a feel for student progress and identify areas in which they might need more instruction. Informal assessments can help teachers  pinpoint students’ strengths and  weaknesses and guide planning for upcoming lessons.   In the classroom, informal assessments are important because they can help identify potential problem areas and allow for course correction before students are required to demonstrate understanding at a formal evaluation. Many homeschooling families prefer to rely almost entirely on informal assessments because they are often a more accurate indicator of understanding, particularly for students who don’t test well. Informal assessments can also provide vital student feedback without the stress of tests and quizzes. Following are just a few examples of creative informal assessments for your classroom or homeschool. Observation Observation is the heart of any informal assessment, but it is also a key stand-alone method. Simply watch your student throughout the day. Look for signs of excitement, frustration, boredom, and engagement. Make notes about the tasks and activities that elicit these emotions. Keep samples of student work in  chronological order  so that you can identify progress and areas of weakness. Sometimes you don’t realize how much a student has progressed until you compare their current work to previous samples. Author Joyce Herzog has a simple but effective method of observing progress. Ask your student to do simple tasks such as writing an example of each math operation he understands, writing the most complicated word he knows he can spell correctly, or  writing a sentence (or short paragraph). Do the same process once a quarter or once a semester to gauge progress. Oral Presentations We often think of oral presentations as a type of formal assessment, but they can be a fantastic informal assessment tool, as well. Set a timer for  one or two  minutes and ask your student to tell you what he’s learned about a particular topic. For example, if you are learning about parts of speech, you could ask your students to name as many prepositions as they can in 30 seconds while you write them on the whiteboard. A broader approach is to present students with a sentence starter and let them take turns finishing it. Examples include: â€Å"My favorite thing about this topic was†¦Ã¢â‚¬ Ã¢â‚¬Å"The most interesting or surprising thing I learned about this was†¦Ã¢â‚¬ Ã¢â‚¬Å"This historical figure was†¦Ã¢â‚¬  Journaling Give your students one to three minutes at the end of each day to journal about what they learned. Vary the daily journaling experience by asking students to: list 5-10 facts they’ve learned about a topicwrite about the most exciting thing they learned that daylist one or two things they’d like to know more aboutnote something that they’re having trouble understandinglist ways that you could help them understand a topic better. Paper Toss Let your students write questions for each other on a piece of paper. Instruct students to crumple their paper, and let them have an epic paper wad toss. Then, have all the students pick up one of the paper balls, read the question aloud, and answer it. This activity wouldn’t work well in most homeschool settings, but it’s an excellent way for students in a classroom or homeschool co-op to get the wiggles out and check their knowledge on a topic they’ve been studying. Four Corners Four Corners is another fantastic activity for getting kids up and moving while also assessing their knowledge. Label each corner of the room with a different option such as strongly agree, agree, disagree, strongly disagree, or A, B, C, and D. Read a question or statement and have students go to the corner of the room that represents their answer. After students reach their corner, allow them a minute or  two to discuss their choice in their group. Then, choose a representative from each group to explain or defend that group’s answer. Matching/Concentration Let your students play matching (also known as  concentration) in groups or pairs. Write questions on one set of cards and answers on the other. Shuffle the cards and lay them, one by one, face down on a table. Students take turns turning over two cards trying to match a question card with the correct answer card. If a student makes a match, he gets another turn. If he does not, it’s the next players turn. The student with the most matches wins. Concentration is an extremely versatile game. You can use math facts and their answers, vocabulary words and their definitions, or historical figures or events with their dates or details. Exit Slips At the end of each day or week, have your students complete an exit slip before leaving the classroom. Index cards work well for this activity. You can have the questions printed on the cards, written on the whiteboard, or you can read them aloud. Ask your students to fill out the card with answers to statements such as: Three  things I learnedTwo  questions I haveOne thing I didn’t understandWhat I found most interesting This is an excellent activity for gauging what students have retained about the topic they are studying and to determine areas which may need more explanation. Demonstration Supply the tools and let students show you what they know, explaining the process as they go. If they’re learning about measurements, provide rulers or a tape measure and items to measure. If they’re studying plants, offer a variety of plants and let students point out the different parts of the plant and explain what each does. If students are learning about biomes, provide the settings for each (drawings, photos, or dioramas, for example) and model plants, animals, or insects that one might find in the biomes represented. Let students place the figures in their correct settings and explain why they belong there or what they know about each. Drawings Drawing is an excellent way for creative, artistic, or kinesthetic learners to express what they’ve learned. They can draw the steps of a process or create a comic strip to depict a historical event. They can draw and label plants, cells, or the parts of a knight’s armor. Crossword puzzles Crossword puzzles make a fun, stress-free informal assessment tool. Create puzzles with a crossword puzzle maker, using definitions or descriptions as the clues. Accurate answers result in a correctly-completed puzzle. You can use crossword puzzles to evaluate understanding of a variety of history, science, or literature topics such as states, presidents, animals, or even sports. Narration Narration is a method of student evaluation widely used in homeschooling circles and inspired by Charlotte Mason, a British educator, at the turn of the 20th century. The practice involves having a student tell you, in his own words, what he has heard after a read-aloud or learned after studying a topic. Explaining something in one’s own words requires comprehension of the subject. Using narration is a useful tool for discovering what a student has learned and identifying areas that you may need to  cover more thoroughly. Drama Invite students to act out scenes or create puppet shows from topics they’ve been studying. This is especially effective for historical events or biographical studies. Drama can be an exceptionally valuable and easy-to-implement tool for homeschooling families. It’s common for young children to incorporate what they’re learning into their pretend play. Listen and observe as your children play to evaluate what they’re learning and what you may need to clarify. Student Self-evaluation Use self-evaluation to help students  reflect on and assess  their own progress.  There are many options for a simple self-assessment. One is to ask students to raise their hands to indicate which  statement applies to them: â€Å"I fully understand the topic,† â€Å"I mostly understand the topic,† â€Å"I’m a little confused,† or â€Å"I need help.† Another option is to ask students to give a thumbs up, a sideways thumb, or a thumbs down to indicate fully understand, mostly understand, or need help. Or use a five-finger scale and have students hold up the number of fingers that corresponds to their level of understanding. You may also want to create a self-evaluation form for students to complete. The form can list statements about the assignment and boxes for students to check if they strongly agree, agree, disagree, or strongly disagree that the statement applies to their assignment. This type of self-evaluation would also be useful for students to rate their behavior or participation in class.

The Foreign Policy Of The United States Essay - 2141 Words

A civilian’s perspective on an event in which soldier’s acted will always be one of distance. ‘Distance’ in the sense that not only did the civilian not take part in the actual event, he has in most cases not bore witness to it as well. In modern western society, passively stumbling upon stories recounting first person perspectives on modern historical events is a rare form of communication, rather these perspectives have been substituted by the short clips news agency feel are appropriate for a public audience. Thankfully, the pricelessness of primary sources has not been lost onto the sources themselves, and there is a plethora of first person perspectives simply waiting to be revealed and valued. The invasion of Iraq, a most recent event, has also been greatly subjected to this trend of displacing ‘on-scene’ perspectives with the ease, comfort, and sensationalism modern media presents. The effects of the invasion are still potently lingering in the Middle East today, and news of them are shaping the foreign policy of the United States. An event of such impact on our most immediate future, and the future of an entire region of the globe, demands a closer look. The autobiographical account titled The Last True Story I’ll Ever Tell by John Crawford and the Last Letters Home, a compilation of letters written by soldiers serving in the Iraqi invasion and presented by Life Magazines, are the two primary sources I will be focusing on in the following paper. My aim is to offer aShow MoreRelatedThe United States Foreign Policy1667 Words   |  7 PagesAs Kelly Anderson’s Foreign Policy Analyst, the following memo will address three areas of the United States’ foreign policy. The U.S. has gone through may transition when it comes to its foreign policy. The United States has been an isolationist, neutralist, and internationalist country from the year it was founded to now. The executive branch and the presi dent apply their power to influence and change the nation’s foreign policy. There are specific departments within the Executive Office of theRead MoreThe United States Foreign Policy Essay1470 Words   |  6 PagesThe United States foreign policy is an interaction between the United States and foreign nations. Foreign policy sets standards on how different organizations, corporations, and individual citizens should interact with one another. Some Americans believe the United States should remain withdrawn from the affairs of foreign countries, but other Americans believe the United States should involve itself in the affairs of foreign countries. In 1796, George Washington included these words in his farewellRead MoreForeign Policy Of The United States1042 Words   |  5 Pages The foreign policy of the United States of America is the process in which it cooperates with foreign nations and sets guidelines of communication for the rest of the world. The foreign policy of the United States is the strategy by which the United States communicates with foreign countries. The U.S. has a powerful influence in this world. The global reach of the United States is backed by a $14.3 trillion dollar economy, roughly a quarter of worldwide GDP, and a protection spending plan of $711Read MoreThe United States And Foreign Policies870 Words   |  4 PagesDurning 1913 and 1916 Woodrow Wilsons domestic and foreign policies weren t both equally successful but both were successful. AlthoughWilson had primarily been elected to reform national politics and initiate new progressive policies in Washington, he spent the majority of his time as President dealing with foreign policy rather than domestic. Wilson s predecessors, including McKinley, Theodore Roosevelt, and Taft, had v iewed the United States as an emerging power that needed to extend its influenceRead MoreThe United States And Foreign Policy Essay982 Words   |  4 Pagesthe rest of the world, and its foreign policy reflected these ideas and beliefs. The United States was on its way to becoming a world power and advancing its own interest in the world, especially in the North and South America. Isolationism caused the United States to avoid being involved in other countries politics and for the U.S. to remain neutral in foreign policy Americans in the 19th century were more interested in domestic events than the affairs of foreign countries. Economic growth andRead MoreThe United States And Foreign Policy Essay4400 Words   |  18 PagesIn contemporary, international society the United States is at the forefront of global affairs. Moreover, scholars have argued that after the First World War, American hegemony led a path for a liberalized world, where cooperation and harmonious institutions unit the world. However, the United States historically has never been this type of hegemonic leader. Rather from their conception as a nation they had a foreign policy which isolated them from foreign affairs of the world, from President WashingtonRead MoreThe United States And Foreign Policy881 Words   |  4 Pagesthe rest of the world, and its foreign policy reflected these ideas and beliefs. The United States was on its way to becoming a world power and advancing its own interest in the world, especially in the North an d South America. Isolationism caused the United States to avoid being involved in other countries politics and for the U.S. to remain neutral in foreign policy Americans in the 19th century were more interested in domestic events than the affairs of foreign countries. 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This view emanates from all the conflicts going in the Middle East that have the potential to threaten numerous strategic interests for the united Stated such as oil, terrorist, and Israel. Yet Middle East has never seen as problematic as it is now due to the excessive flux of problems the MiddleRead MoreThe United States And Foreign Policy1786 Words   |  8 Pagesthe United States showed little interest in foreign affairs. The U.S. relied on previous foreign policies which resulted in inconsistent international trade in the years leading up to the twentieth century. However, following the rise of the industrial revolution in the United States American business began to recognize the vast potential of the international market place. The U.S. sought out to expand its territory globally to increase trade and protect its assets more effectively. The United States

Leadership and Organizational Dynamics for Shell Downstream

Question: Discuss about theLeadership and Organizational Dynamics for Shell Downstream. Answer: As an executive of Shell Downstream, I would try to take various types of financial assistance for the company. The right of the people must also be fulfilled and the people must also be allowed to control their own property. The process must be participatory and it must include various stakeholders. It is also necessary for me to monitor and track the progress and thus confirm whether the objectives are met. I must also ensure that the investment will continue to lay a positive impact on the local community of South Africa. It is also essential that there is sustainability in providing the required energy for the growing population of the country and their safety. It is also necessary for the company to deliver the energy safely and to protect the environment. This will help in protecting the contractors, employees and the local communities. The radical economic transformation will also turn the investors of the company (Yulk 2005). Shell Downstream is trying critically to achieve r adical economic transformation. As an executive of the company, it is my responsibility to entrench the overall policy of the government and plan the key challenges of industrial and economic growth. This will help in the removal of poverty, unemployment and inequality among the people. This is important for the inclusive growth of South Africa. There must be new initiatives which are regarded as part of the various concentrated efforts and this is necessary to shift the productive base of the economy for the creation of decent and sustainable jobs. There must be upscale efforts for the inclusive and the shared growth and this is necessary for the control of management and transformation of different kinds of ownership. Shell also needs to restructure the business and change it so as to gain the position in the market. It is trying to retain the position of largest chemical and energy company and this is offering an adequate return to the shareholders in an increasing pace (Bryman 2 013). The radical economic transformation will help me in putting the coherent initiatives in a similar way and it will also help in shifting the productive base of the economy to much higher level of investment. There are some steps which are needed to be followed and this will also help in reducing the corruption. The social investment opportunities of Shell will also provide the people certain development programmes and this has helped them to combat unemployment and poverty levels. This has helped in improving the safety measures of the children who are travelling through different modes of transport. It is my duty as an employee to co-ordinate and collaborate with the other partners and thus this will help in the assistance of the children. It will also help in creating more employment opportunities such as direct employment or through various supply chain activities. It will also help in providing additional training programme and thus help in stimulating the business. Thus, it can b e said that as an employee it is necessary and vital to provide proper medical training to the people. The challenges must also be met in assistance with the partnerships from other organization (Storey 2004) References Bryman, A. ed., 2013.Leadership and organizations. Routledge. Storey, J. ed., 2004.Leadership in organizations: Current issues and key trends. Psychology Press. Yulk, G., 2005. Leadership in Organization. Pearson Publication India.

Statistical Analysis

Question: Write an essay onStatistical Analysis. Answer: In this assignment, the number of admissions to the movies in Australia was surveyed from the year 1994 to 2014. Other factors were also surveyed in this assignment. The data for the variables of Screens, Theatres, Films Screened, Real Ticket Price and Capacity were also collected from the year 1994 to 2014 (Bickel and Lehmann 2012). These data were used in this assignment for the analysis. Statistical analysis would be done on this data set. Descriptive statistics, inferential statistics and concepts of linear regression methods would be given in this assignment based on these data (Vogt and Barta 2013). Graphs and charts would also represent the data and provide conclusion about the data and their relations. Methodology The descriptive statistics for the variables are given below: Screens Mean 1213.52381 Standard Error 103.6609083 Median 1028 Mode #N/A Standard Deviation 475.0339587 Sample Variance 225657.2619 Kurtosis -1.569616636 Skewness 0.410014464 Range 1264 Minimum 645 Maximum 1909 Sum 25484 Count 21 Largest(1) 1909 Smallest(1) 645 Confidence Level (95.0%) 216.2328649 Admissions (millions) Mean 61.82380952 Standard Error 5.151804606 Median 68.1 Mode 92.5 Standard Deviation 23.60853457 Sample Variance 557.3629048 Kurtosis -1.666346431 Skewness -0.055528974 Range 63.6 Minimum 28.9 Maximum 92.5 Sum 1298.3 Count 21 Largest(1) 92.5 Smallest(1) 28.9 Confidence Level (95.0%) 10.74647607 Theatres Mean 545.0952381 Standard Error 9.45840638 Median 547 Mode 520 Standard Deviation 43.34386319 Sample Variance 1878.690476 Kurtosis 8.375821966 Skewness 2.445313468 Range 201 Minimum 501 Maximum 702 Sum 11447 Count 21 Largest(1) 702 Smallest(1) 501 Confidence Level (95.0%) 19.72988992 Films Screened Mean 257.3809524 Standard Error 5.769573802 Median 255 Mode 259 Standard Deviation 26.43950868 Sample Variance 699.047619 Kurtosis 1.256326286 Skewness -0.057083837 Range 124 Minimum 194 Maximum 318 Sum 5405 Count 21 Largest(1) 318 Smallest(1) 194 Confidence Level (95.0%) 12.03512002 Real Ticket Price Mean 19.77952381 Standard Error 0.091997609 Median 19.66 Mode #N/A Standard Deviation 0.421586008 Sample Variance 0.177734762 Kurtosis 0.085043332 Skewness 0.91600328 Range 1.51 Minimum 19.25 Maximum 20.76 Sum 415.37 Count 21 Largest(1) 20.76 Smallest(1) 19.25 Confidence Level (95.0%) 0.191903649 Capacity ('000s) Mean 362.8095238 Standard Error 15.57082422 Median 332 Mode 295 Standard Deviation 71.35448062 Sample Variance 5091.461905 Kurtosis -1.582996919 Skewness 0.44357307 Range 186 Minimum 285 Maximum 471 Sum 7619 Count 21 Largest(1) 471 Smallest(1) 285 Confidence Level (95.0%) 32.48017007 Considering the variable admission (millions), the central tendency the variable, i.e. the mean is 61.8238. The median of the variable is 68.1. This is the middle value of the admission (millions) is 68.1. The modal value of the variable was 92.5 (Plonsky 2015). This is the maximum frequency for the number of people who were admitted for the movie. The variability of the variable; i.e. the standard deviation is 23.6085. This depicts that the variable had a moderate amount of variability in the admission (millions) over the years (Vogt and Barta 2013). The shape of the distribution is platykurtic and the distribution is negatively skewed. The mean of the variable screens was found to be 1213.5238. The median of the variable was 1028 and there was no mode for this variable. The standard deviation of the variable was 475.0339 (Thiem 2014). This depicts that there was moderate variation in the number of screens available in Australia for screening of movies. The shape of the distribution id platykurtic and it is positively skewed. The average value of theatres was found to be 545.095. The median of the variable is 547 and its mode is 520. The standard deviation was 43.34. There was a low deviation in the number of theatres open in Australia during 1994 to 2014 (Campbell and Knapp 2013). The shape of the distribution is leptokurtic and the distribution is positively skewed. The average value of the variable films screened was found to be 257.38. The median value was 255 and the modal value was 259 (Ang and Van 2015). The standard deviation was found to be 36.439. This variable had a low deviation of the number of theatres opened in these years. The shape of the distribution is leptokurtic and it is negatively skewed. The mean of the variable real ticket price is 19.779 and its median is 19.66. the standard deviation of the variable is 0.42 (Kleinbaum et al. 2013). This is a very low standard deviation and the price of the tickets fluctuated little during the period of 1994 to 2014. The shape of the distribution is leptokurtic and the distribution is positively skewed. The average value of the variable capacity was found to be 362.8095. The median was 332 and the mode was 295. The standard deviation of the variable was 71.3544. This depicts that there was moderate variation among the daily capacity of the customers over the years. The shape of the distribution is platykurtic and the distribution is positively skewed. Graph displaying the distribution of admission Box-and-whisker plot for the distribution of the real ticket price is given below The likelihood that the admission is greater than 70 million when the real price of the ticket is more than $20 is given by P(X Z) = 1 P( X Z) = 1- 0.613 = 0.387 (Campbell and Knapp 2013). The admissions are statistically independent of price. This is because the value of the chi square test was found to be zero. The contingency table is as follows: Sum of probability of admission Column Labels Row Labels 28.9 29.7 30.8 35.5 37.4 39 43 46.9 47.2 55.5 68.1 69.9 73.9 76 80 82.2 88 89.8 91.5 92.5 Grand Total 19.25-19.35 0.036 0.071 0.107 19.35-19.45 0.030 0.036 0.043 0.063 0.172 19.45-19.55 0.068 0.071 0.139 19.55-19.65 0.024 0.069 0.093 19.65-19.75 0.022 0.029 0.051 19.75-19.85 0.023 0.062 0.084 19.85-19.95 0.027 0.027 19.95-20.05 0.070 0.070 20.05-20.15 0.059 0.059 20.15-20.25 0.057 0.057 20.35-20.45 0.033 0.033 20.45-20.55 0.054 0.054 20.75-20.85 0.052 0.052 Grand Total 0.022 0.023 0.024 0.027 0.029 0.030 0.033 0.036 0.036 0.043 0.052 0.054 0.057 0.059 0.062 0.063 0.068 0.069 0.070 0.142 1 The 95% confidence interval of mean theatre capacity is given by (mean 1.96* s.d.), (mean + 1.96* s.d.) = (460.1412662, 630.0492099) At 5% level of significance, the admission from 2008 to 2014 had exceeded the constant amount of 84 millions in Taiwan had the hypothesis as follows: H0 = the admission from 2008 to 2014 did not exceed the constant amount of 84 millions in Taiwan H1 = the admission from 2008 to 2014 had exceeded the constant amount of 84 millions in Taiwan On testing the two variables, the p value of the one-tailed test was found to be 0.02732, which is less than the p value (Levy and Lemeshow 2013). The null hypothesis in this case is rejected and the admission from 2008 to 2014 had exceeded the constant amount of 84 millions in Taiwan. The output of multiple linear regression is given in sheet named regression in the excel file. Using the result of regression analysis, the hypothesis is as follows: H0 = there is no difference between the ticket price in 2014 and zero at 5% level of significance H1 = there is difference between the ticket price in 2014 and zero at 5% level of significance The p value of the regression analysis for the variable real ticket price had the value of 0.044, which is less than 0.05. This leads to the rejection of null hypothesis. Thus, there is difference between the ticket price in 2014 and zero at 5% level of significance. The slope of the variable is 5.2766, which is positive (Montgomery et al. 2015). This states that the variable effects the admission in a positive way. The change in price in the ticket leads to the change in the admission in the similar direction. The value of intercept was found to be negative. This suggests that the admission would be negative in absence of all the factors. The slope of Screens was 0.0878, which was slightly positive (Draper and Smith 2014). This value aims to influence the admission in a positive manner, as the value is positive. The value of the slope of Theatres was found to be 0.04508, which is positive. This depicts that the factor had a weak positive influence of the admission. The slope of Flimsy screened was 0.001 and it is weakly negative (Csikszentmihalyi and Larson 2014). This also influences the admission positively and the change in value of this variable changes the value of admission in the same direction (Kleinbaum et al. 2013). The slope of capacity (000s) has a negative slope of -0.2819. This indicates that the variable influence the admission in a negative way. The increase in capacity decreases the admission. All the slope of the variables had the same sign as was expected. The sign of capacity (000s) was expected to be positive whereas it turned out to be negative. The value of adjusted r square is 0.971. This indicates that 97.1% of variation is explained by only the independent variables that actually affect the dependent variable (Fox 2015). The p value of the variables theatres and film screened are more than 5% level of significance. The other three variables have their p value less than 0.05. Thus, this overall model is statistically not significant as the p values of all the variables are not less than 0.05. Scatter diagram and histogram The variable is heteroscadastic, normal and linear. Variables like location of the theatre, facilities provided in the theatre and the type of movie influence the admission positively. These factors would increase the value of regression coefficient and would thereby, influence the regression coefficient. The sampling process of random sampling would not be appropriate one at the first instance. The organisation must identify all the households of native-born Australians. They could then use the process of random sampling to select the households from the identified households. Conclusion It was seen from the analysis that the variable admission is influenced by various factors like the Screens, Theatres, Films Screened, Real Ticket Price and Capacity. The average, standard deviation and the type of distribution of each variable vary from each other over the period from 1994 to 2014. The graphs show the distribution of each variable and the tables give an idea about the type of admission with the real ticket price. The degree of association between the variables was also analysed. Thus the analysis gave a clear picture about the variables and the effect of admission over the years 1994 to 2014 and the influence of the other factors on the admission. References Ang, S. and Van Dyne, L., 2015.Handbook of cultural intelligence. Routledge. Bickel, P.J. and Lehmann, E.L., 2012. Descriptive statistics for nonparametric models I. Introduction. InSelected Works of EL Lehmann(pp. 465-471). Springer US. Campbell, J.P. and Knapp, D.J. eds., 2013.Exploring the limits in personnel selection and classification. Psychology Press. Csikszentmihalyi, M. and Larson, R., 2014. Validity and reliability of the experience-sampling method. InFlow and the Foundations of Positive Psychology(pp. 35-54). Springer Netherlands. Draper, N.R. and Smith, H., 2014.Applied regression analysis. John Wiley Sons. Fox, J., 2015.Applied regression analysis and generalized linear models. Sage Publications Kleinbaum, D., Kupper, L., Nizam, A. and Rosenberg, E., 2013.Applied regression analysis and other multivariable methods. Nelson Education. Levy, P.S. and Lemeshow, S., 2013.Sampling of populations: methods and applications. John Wiley Sons. Montgomery, D.C., Peck, E.A. and Vining, G.G., 2015.Introduction to linear regression analysis. John Wiley Sons. Plonsky, L., 2015. Statistical power, p values, descriptive statistics, and effect sizes: A" back-to-basics" approach to advancing quantitative methods in L2 research. Thiem, A., 2014. Membership function sensitivity of descriptive statistics in fuzzy-set relations.International Journal of Social Research Methodology,17(6), pp.625-642. Vogt, A. and Barta, J., 2013.The making of tests for index numbers: Mathematical methods of descriptive statistics. Springer Science Business Media.