mathematics proficiency, innovation capacity, and government effectiveness (concept paper)

Running head: CONCEPT PAPER DRAFT 1

Mathematics Proficiency, Innovation Capacity, and Government Effectiveness

Concept Paper

By Ivan F Rodriguez

CONCEPT PAPER DRAFT 2

Concept Paper Draft

Context

This quantitative research will be bound within the context of mathematics

proficiency, innovation capacity, and government effectiveness of the BRIICS countries

(Brazil, Russia, India, Indonesia, China, and South Africa). In addition, it may be further

restricted to China given my geographic proximity to several academic institutions, deep

understanding of their Innovation on Mathematics Curriculum revolution started in 2006,

and the access to government officials as I am the president of the Global Electronic Council

based in this country. China offers a very appealing opportunity to test the hypotheses of this

study as this country has overtaken America in the number of patents officially registered in

2011 (OECD, 2012). It is acknowledged that there is not a reliable approach (globally

accepted) to measure patent’s value; however in this study and with the intention to increase

its validity, the number of countries where inventors pursued patents registration is used to

assess the value of the patents, the more countries inventors registered their patents the

higher value the patent has.

Why Study Mathematics Proficiency and Government Effectiveness?

Industrial innovation is increasingly based on the results and techniques of scientific

research (Audretsch & Feldman, 2004). This connection is especially strong in areas where

innovation is contributing to the well-being of society, such as health, security,

communications, and environmental stewardship. Literature correlating mathematics

proficiency and innovation capacity is vast (George & Zhou, 2001; Oldham & Cummings,

2006, Scott & Bruce, 2004, West & Anderson, 2006), but linking these findings with

government effectiveness is limited. Finding generalizable correlations between government


effectiveness with mathematics proficiency, and innovation capacity may open a new realm

of knowledge that provides reliable frameworks to policy makers, entrepreneurs, and citizens

in general to predict the value of their investment in acquiring advanced mathematical skills.

The world is facing several challenges, uncontrolled gains on CO2 emissions, high

food prices, water scarcity, aging populations, poor education, gender issues, and

unprecedented unemployment rates; affecting both developed and developing countries.

Innovation is increasingly perceived as essential for tackling such challenges (West, 2002).

Meeting these challenges depends crucially on the pace of innovation in new technologies,

for example in the areas of renewable energy, carbon capture and storage, lower emissions,

bioremediation, smart grids, synthetic biology, bio-informatics, and personalized medicine.

People are at the heart of the innovation process and education systems play a key role in the

development o a highly qualified and flexible labor force. Relatively high levels of education

are often related to higher earnings and productivity, better career progress, health, and

outcomes (Van Dijk & Kluger, 2003). These authors provided quantitative references

supporting their assertion about the positive correlation between mathematics proficiency

and earnings:

Mathematics based qualifications conferred significant advantages in terms of

earnings – comparing income levels and educational backgrounds, the study

concluded that achieving an A-level in mathematics increased long-term earnings by

up to 7-10%. The positive association between mathematics and earnings held

regardless of the grades achieved (p. 129).


Research Question

What is the correlation between college graduate students’ mathematical aptitudes, country

innovation capacity, and government effectiveness?

Rationale For Inquire

Innovation is the key driver of competitiveness, wage, job enlargement, and long-

term economic growth (Audretsch & Feldman, 2004). The number of granted patents has

been accepted as one of the most appropriate measures for innovation capacity (Rassenfosse

& Potterie, 2009; Scherer, 2003). Less than 5% of the globally registered patents per year

come from underdeveloped countries (Hart, 2006). Underdeveloped countries present low

productivity learning-ratios among schoolchildren, 40% below developed countries (Sirin,

2005). In like manner, underdeveloped countries exhibit 65% lower STEM-trained (Science,

Technology, Engineering, and Mathematics) individuals per year compared with developed

countries, this is, for each 100 graduate-students from STEM in developed countries, only 35

are graduated in underdeveloped countries (Langdon, McKittrick, Beede, Khan, & Doms,

2011).

Mathematical literacy drives economic growth. In his acclaimed study Forfás (2008)

demonstrated the positive relation between student performance in cognitive tests and Gross

Domestic Product (GDP) growth. The findings from this work indicate that even relatively

small improvements in the mathematical skills of a nation’s labor force can have very large

impacts on future economic growth. A scenario whereby students are brought up to a

minimal skill level, defined here as obtaining a score of 400 on the PISA (Programme for

International Student Assessment) mathematics and science tests, or one standard deviation

below the Organization for Economic Cooperation and Development (OECD) average would


increase annual GDP growth in the long term. Comparative national mathematical

achievement is an important measure of future national competitiveness (Hanushek &

Woessman, 2010). National mathematics achievement is a vital strategic measure of

competitiveness, and it is entirely in people hands. National decisions can improve that

achievement immediately and in the intermediate term. Mathematical literacy is the building

block for a vibrant economy. Mathematics underpins many other disciplines such as science,

technology, business, and finance.

Methodology

The culture of inquiry is firmly rooted in the constructivist epistemological

perspective relying nearly exclusively on qualitative studies. There is an opportunity to

produce a significant contribution following a more positivist approach by assessing the

problem from a broader perspective, involving three variables, mathematics proficiency

(independent variable), government effectiveness (intervening variable), and innovation

capacity (dependent variable). Through this quantitative research, a deductive reasoning

from general theories to specific instances is performed and used to prove if there is a casual

relationship between the defined variables and confirm if they can be expressed as predictor

for future outcomes (see Figure 1).

The best performing country in the 2009 PISA assessment is Shanghai-China with a

GDP per capita ($6,781) significantly below the OECD average ($32,867), underlines that

low national income is not incompatible with strong educational performance. Korea, which

is the best performing OECD country, also has a GDP per capita ($26,679) below the OECD

average. Although there is a correlation between GDP per capita and educational

performance, this predicts only 6% of the differences in average student performance across


countries. The other 94% of differences reflect that two countries of similar prosperity can

produce very different educational results. Results also vary when substituting spending per

student, relative poverty or the share of students with an immigrant background for GDP per

capita.

The independent variable (mathematic proficiency) is evaluated extensively. A design

of experiments (DOE) is conducted to measure and quantify the effects that (1) poorly

qualified teachers, (2) lack of student application, (3) inadequate teaching techniques, (4)

school policies, (5) poor students’ guidance, and (6) evaluation system play in the level of

mathematic proficiency. Based on the number of involved factors (six) affecting

mathematics proficiency, paired with the lack of reliable sources of data on selected

countries, the DOE will use three factors only (poorly qualified teachers (Q), inadequate

teaching techniques (T), and evaluation system (E)). For a full factorial experiment a total of

eight experiments is required (DOE=2^3).

The DOE will be performed in mainland China using college students only, according

to the Center for International Students by the end of 2012 there were 2,236 colleges and

universities, with more than 20 million students enrolled in mainland China (CIS, 2013).

This study will apply the PISA Test and the customized surveys (see Appendix E) on 5% of

these colleges (i.e., 112). The ranges in which each factor fluctuates are defined in Appendix

B. The design matrix in both, normal, and coded form is shown in Appendix C and D

respectively. The software Minitab will be used to resolve the DOE and create a graphic

representation of the results, particularly, the cube and the main effect diagrams will be

obtained and depicted accordingly to support the results. The factorial design will be tested

using linear regression and the results of the DOE will establish the effect that independent


variables (e.g., poorly qualified teachers (Q), inadequate teaching techniques (T), and

evaluation system (E)) have in creating mathematics proficiency in a nation, this case, China.

To be specific, the following are the research questions to be examined and explored in

this study:

1. How improving students’ mathematical skills increases innovation capacity?

2. How higher government effectiveness index influences positively mathematical

proficiency?

3. How innovation capacity contributes to economic growth?

4. How can this phenomenon be explained in China?

5. Can the finding be generalizable to the BRIICS countries?

A series of hypotheses are proposed to address these questions.

H10: There is no significant difference in the average score on PISA math test between

college students in China (A) and Indonesia (B).

H11: There is a significant difference in the average score on PISA math test between

college students in China (A) and Indonesia (B).

H10: muA-muB = 0

H11: muA-muB <> 0

Note both countries have similar per capita GDP, $5,445 and $3,495 respectively, and

both are members of the BRIICS, consequently the null hypothesis is accurately defined

supporting what is expected based on the population data.

H20: There is no significant difference in the average of the government effectiveness

index between Brazil (C) and Russia (D).


H21: There is a significant difference in the average of the government effectiveness


H20: muC-muD = 0

H21: muC-muD <> 0

H30: There is no significant difference in the average of poorly qualified teachers score

(Q), between China (A) and Brazil (C).

H31: There is a significant difference in the average of the government effectiveness


H30: muQC-muQC = 0

H31: muQC-muQC <> 0

H40: There is no significant difference in the average of inadequate teaching techniques

score (T), between China (A) and Russia (D).

H41: There is a significant difference in the average of inadequate teaching techniques

score (T), between China (A) and Russia (D).

H40: muTA-muTD = 0

H41: muTA-muTD <> 0

H50: There is no significant difference in the average of the evaluation system score (E)

between Indonesia (B) and Brazil (C).

H51: There is a significant difference in the average of the evaluation system score (E)

between Indonesia (B) and Brazil (C).

H50: muEB-muEC = 0

H51: muEC-muEC <> 0


The literature currently under review concerning this phenomenon comes from both

contemporary and seminal sources (e.g., Audretsch & Feldman, 2004, Dernis & Khan, 2004;

Boote & Beile, 2005; Hart, 2006; Hanushek & Woessman, 2010). Scholarly quantitative

research emerges shy and incomplete to document and probe entirely the relations between

these and other variables. Moreover, to build a model that can be accurately used to project

the competitiveness level a nation can achieved by assessing the quality of the PISA results

in mathematics, the quality of the government and innovation intensity constitutes a urgent

need.

Conclusion

The published empirical findings are overwhelming that low mathematical

proficiency limits a nation innovation capacity. Emerging scholarship focused on alternative

structural models has the potential to advance the discourse beyond studies looking at

qualitative attributes (e.g., lack of student application, school policies, and poor students’

guidance) that seem more symptomatic phenomenon. Rather, further research should

examine the structural underpinnings of poorly qualified teachers, inadequate teaching

techniques, and evaluation system. Industry faces problems that extend well beyond the

envelope of classical topics in mathematics. Many of these problems have a significant

mathematical component, and the intellectual challenges they pose fall in many cases within

topical areas of current research in the mathematical sciences. Stronger links between

mathematics and industry will be beneficial both to the partners and to national economies.

They will inspire new mathematics and enhance the competitive advantage of companies.


References

Audretsch, D., & Feldman, M. (2004). Knowledge spillovers and the geography of

innovation. Amsterdam: Elsevier Press.

Boote, D. N., & Beile, P. (2005, April). Scholars before researchers: On the centrality of the

dissertation literature review in research preparation. Educational Researcher, 34(6),

3-15.

Creswell, J. W. (2004). Educational research: Planning, conducting, and evaluating

quantitative and qualitative research (2nd ed.). Columbus, Ohio: Merrill Prentice

Hall.

CIS (2013). Center for International Studies. Retrieved from

http://www.cisabroad.com/china

Dernis, H. and M. Khan (2004), Triadic Patent Families Methodology, OECD Science,

Technology and Industry Working Papers, No. 2004/2, OECD, Paris.

Dosi, G., Pavitt, K. & Soete, L. (2010). The economics of technical change and international

trade. New York, NY: New York University Press;

Forfás (2008). Raising national mathematical achievement. EGFSN, 1, 1-14.

Glaser, B. G., & Strauss, A. L. (1967). Discovery of grounded theory: Strategies for

qualitative research. Chicago: Aldine.

Intergovernmental Panel of Climate Change (IPCC). (2012). Climate change 2007 synthesis

report. Geneva, Switzerland: IPCC.

Hart, P. D. (2006). Keeping our edge: Americans speak on education and competitiveness.

Washington, DC: Hart-Winston.


Hanushek, E., Woessman, L. (2010). The high cost of low educational performance. OECD

Journal, 2(2), 5-14.

Jones, C. (1998). Introduction to economic growth. New York, NY: W.W. Norton & Co.

Kerlinger, F. N., & Lee, H. B. (2000). Foundations of behavioral research (4th ed.). Holt,

NY: Harcourt College Publishers.

Langdon, D., McKittrick, G., Beede, D., Khan, B., & Doms, M. (2011). STEM: Good jobs

now and for the Future. U.S. Department of Commerce, Economics and Statistics

Administration, 3(11), 9-20.

Miller, J.C. (2009). Statistics for Analytical Chemistry. Ellis Horwood: Chichester

OECD (2006), Indicators of regulatory management systems quality. Paris: OECD

Publications.

OECD (2012), OECD Science, Technology and Industry Scoreboard. Paris: OECD

Publications.

Porter, M. E., Stern, S. (1999). The new challenge to America’s prosperity: Findings from

the innovation index. Washington (DC): Council on Competitiveness.

Rassenfosse, G., & Potterie, B.P. (2009). A policy insight into the R&D–patent relationship.

Res Policy, 38, 779–792.

Simon, M. K., & Francis, B. J. (2004). The dissertation cookbook: From soup to nuts a

practical guide to start and complete your dissertation (3rd. Ed.). Dubuque, Iowa:

Kendall/Hunt.

Sirin, S. R. (2005). Socioeconomic status and academic achievement: A meta-analytic

review of research. Review of Educational Research, 75(3), 417–453.


St. James’s Palace Memorandum. (2009, May 28). Retrieved March 21, 2013, from

http://www.nobelcause.org/Conclusions/Pages/Memorandum.aspx.

Trajtenberg, M. (1990). Patents as indicators of innovation: Economic analysis of product

innovation. Cambridge, MA: Harvard University Press.

Union of Concerned Scientists. (2002). World scientists’ warning to humanity. Retrieved

March 21, 2013, from http://www.ucsusa.org/ucs/about/1992-world-scientists-

warning-to-humanity.html.

Van Dijk, D., & Kluger, A.N. (2003). Feedback gains: Success in creative tasks and failure

in error-detection. Poster presented at the conference of the Society for Industrial and

Organizational Psychology, Orlando, Florida, April.

West, M.A. (2002). Sparkling fountains or stagnant ponds: An integrative model of

creativity and innovation in work groups. Applied Psychology: An International

Review, 51, 355–386.

Zhang, X. (2010). Mathematics: The technology of information processing & information

transforming. Studies in Dialectics of Nature, 8(1), 22-29.


Appendix A Comparing Countries Performance in Mathematics Proficiency,

Government Effectiveness, and Innovation Capacity

Country PISA

Mathematics

Scalea

Government

Effectiveness

Indexb

Innovation

Capacityc

R&D as

Percentage of

GDPd

Brazil 386 42.8% 0.50 1.2%

Russia 468 30.6% 0.75 1.3%

Indonesia 371 35.8% 0.20 0.1%

China

(Shanghai)

496 44.2% 0.65 1.7%

Notes: Comparing countries performance. aData from OECD, PISA 2009 Database.

http://dx.doi.org/10.1787/888932343342. bData from World Bank, World Governance

Indicators 2010. cTriadic patent families per capita. Data from OECD, Patent Database, May

2011; US Patent and Trademark Office (2011), http://dx.doi.org/10.1787/888932485386.

Data of 2009 from The World Bank.


Appendix B Fixing the Factors Levels

Factor Unit of

Measurement

Range

Low High

Q Poorly qualified teachers % (Annual

examination)a

<60 >90

T Inadequate teaching

techniques

Ratio (customized

survey)b

<0.60 >0.85

E Evaluation system Ratio (customized

survey)c

<0.60 >0.85

Notes: Ranges are proposed assuming strict criteria to discriminate effectively low

performers from high performers. aThis is the only factor that will use information available

in the internet. Teachers are evaluated annually using a standard and institutionalized

examination that is applied country wide in China. bRatio value goes from zero to one and it

is based on a survey to be built as part of this study. bRatio value goes from zero to one and it

is based on a survey to be built as part of this study.


Appendix C Design Matrix Normal Values

Experiment Factors

Q T E

1 60 0.60 0.60

2 90 0.60 0.60

3 60 0.85 0.60

4 90 0.85 0.60

5 60 0.60 0.85

6 90 0.60 0.85

7 60 0.85 0.85

8 90 0.85 0.85


Appendix D Design Matrix Coded (Standard) Values

Experiment Factors

Q T E

1 -1 -1 -1

2 1 -1 -1

3 -1 1 -1

4 1 1 -1

5 -1 -1 1

6 1 -1 1

7 -1 1 1

8 1 1 1


Appendix E Example of the Survey to Evaluate Teaching Strategies and Techniques

Name of strategy of learning math:

Circle the number you agree with. 1 is low, 5 is high.

Not at

all

Somehow A little Most

of the

time

Significan

t

This strategy is interesting 1 2 3 4 5

This strategy is easy to do. 1 2 3 4 5

This strategy is fun. 1 2 3 4 5

This strategy is useful. 1 2 3 4 5

This strategy helps me understand

math.

1 2 3 4 5

This strategy helps me remember. 1 2 3 4 5

This strategy helps me talk about

math.

1 2 3 4 5

Note: This is an example of the type of surveys to be developed to assess the two factors,

Inadequate Teaching Techniques (T) and Evaluation System (E).


Figure 1 Quantitative Problem Statement Draft (Conceptual Flow Chart)

Figure 1. Quantitative Problem Statement Draft

Government Educational Policies

Mathematical Skills Enhancement

Government Technology Policies

Innovation Capacity Strengthening

R&D Intensity Increase (Granted Patents Increase)

Economic Growth

Corruption Minimization

Figure 1. This is the so-called virtuous circle (Rodriguez, 2013) the draft quantitative problem statement is expected to address and validate. Lack of corruption generates better leadership, better leadership promote the right policies, right policies produced higher educated and skilled inhabitants, higher educated and skilled inhabitants will produce more patents, more patents will increase the innovation capacity of a country, innovation capacity of a country will increase its odds for economic growth, and economic growth will minimize the corruption patterns and behaviors.

mathematics proficiency, innovation capacity, and government effectiveness (concept paper)

Documents