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Monday, 26 May 2014

The Influences of Different Number Languages on Numeracy Learning

The Influences of Different Number Languages on Numeracy Learning
Written by:
Ozlem Cankaya, Ph.D., Institute of Cognitive Science, Jo-Anne LeFevre, Ph.D., Departments of Psychology/Cognitive Science and Carla Sowinski, Ph.D. Candidate, Department of Psychology, Carleton University
Published online:
2012-06-09 14:30:25
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Number naming systems connect number words to quantities.  For example, in English, the word eleven is used for the quantity that is also represented as 11 in Arabic digits.  Number naming systems include words for both small (e.g., onethree) and large quantities (e.g., hundredthousand), plus rules for combining them (e.g., 346 is three hundred and forty-six). Because each language has its own number naming system, studying these systems allows us to examine how language and culture affect numerical thinking.  Examining how number languages influence number learning is important because mathematical competencies vary across cultures that have different languages.  For example, children who speak Asian languages that have regular number naming systems (e.g., Chinese, Japanese) appear to acquire counting and place-value knowledge earlier than children who speak languages like English and French, which have irregular number naming systems (see more on irregular versus regular number naming systems below; Aunio, Aubrey, Godfrey, Pan, & Liu, 2008; Dehaene, 1997; Fuson & Kwon, 1992; Geary, Bow-Thomas, Liu, & Siegler, 1996; Miller, Smith, Zhu, & Zhang, 1995).  In this article, we explain how number languages may influence children and adults' numeracy performance. 
Research Questions 
(1) What are the differences among number languages that may influence children's numeracy knowledge acquisition?
(2) Do more regular number naming systems support children's numeracy learning?
(3) What are the long-term effects of number languages on numerical thinking?
Recent Research Results
What are the differences among number languages that may influence children's numeracy knowledge acquisition? 
Counting up to 10 in many languages requires mastering an arbitrary but ordered set of names (e.g., one, two, three … ten in English; yi, er, san … shi in Chinese).  After 10, some languages' number naming systems are regular; they use consistent rules to combine the ten basic number words to indicate quantities.  Other languages' number naming systems are irregular; they have rules, but with exceptions.  For example, in Chinese, 13 (shi-san) translates to ten-three and 34 to three-ten four; thus, counting beyond 10 in Chinese involves learning rules to combine the words from one to ten to create larger number words.  In contrast, many other languages, including English and French, have special words between 11 and 19.  English has rules for producing number words from 20 on, but these are not as predictable as in Asian languages (compare thirty and three-ten, for example).  Some other languages, such as French, use some base-20 rules (e.g., 80 is quatre-vingt or four-twenty).  It seems plausible that learning to count in more regular languages should be easier for children than learning to count in less regular languages.
Beyond the number 10, place-value knowledge helps one know the value of each digit in a multi-digit number.  The visual Arabic number system is completely regular because it combines a limited set of symbols (0 to 9).  Furthermore, this system assigns each number symbol a value depending on the relative position of the digits to indicate quantities. In comparison to the Arabic digit system, many spoken languages have more symbols (i.e., words) and more complex rules for combining the number words to reflect quantities.  Thus, in different number naming systems, the place value assigned to each number word may not be consistent with the spoken position of the numbers.  For example, in languages such as Dutch and German, ones digits and tens digits are reversed such that 45 is named as five-and-forty rather than forty-five.  In English, 16 is named as six-teen whereas in Chinese it is ten-six.  Furthermore, the structure of complex numerals may involve multiplication (e.g., two hundred) and/or addition (e.g., twenty-three; Lonin & Matushansky, 2006).  Thus, mastering place value is difficult, at least for English-speaking North American children (Fuson & Briars, 1990).  It seems reasonable that children will find it easier to learn number naming systems where there is a consistent rule for mapping number words to quantities.  Furthermore, because children ultimately need to make connections among the various symbolic and non-symbolic number codes (number words, digits and quantities), the lack of consistency between the spoken and written number words and the visual Arabic digits may make the ongoing translations among these codes more complex.  As a result, performance differences may exist across languages (Pixner et al., 2011a).
Do more regular number naming systems support children's numeracy learning? 
Children whose languages have regular number naming systems may more easily learn to (a) count (LeFevre, Clarke, & Stringer, 2002; Miller et al., 1995), (b) learn about place value (Ho & Fuson, 1998; Miura, Kim, Chang, & Okamoto, 1988), and (c) acquire number system knowledge (Pixner et al., 2011b; Siegler & Mu, 2008), as compared to children whose number languages are less predictable.In irregular languages, such as English and French, children may have difficulty learning the teen and decade names due to the complex number structure that does not reflect the base-10 system directly.  For instance, 3- to 5-year-old English-speaking children from the U.S. could not count as high as Chinese-speaking children, even though children's performance did not differ in counting small sets of objects or solving problems (Miller et al., 1995).  Similarly,LeFevre et al. (2002) found that 3- to 6-year-old French-speaking children could not count as high as their English-speaking peers.  The differences between children's performance were partially attributed to the structure differences in number languages. However, French children also performed more poorly in object counting and number recognition tasks compared to English-speaking children.  In this study, English-speaking parents reported more frequent teaching of early numeracy skills than French-speaking parents.  Therefore, when evaluating children's early numeracy knowledge, experiential factors should also be considered.             
Children whose languages have regular rules use place value knowledge earlier and more consistently than children who speak less regular languages (Ho & Fuson, 1998; Miura, Okamoto, Kim, Steere, & Fayol, 1993).  For example, Miura and colleagues (1993) found that Asian born-and-educated children (Chinese, Japanese, and Korean) illustrated numbers such as 23 as collections of blocks and units (e.g., 2 blocks of 10 plus three units), whereas non-Asians (French, English, and Swedish) used a collection of 23 single units and did not use blocks of 10.  These differences in children's representation of numbers were attributed to the transparency of number languages and their correspondence with the base-10 Arabic system. 
Other researchers have argued that the differences that have been attributed to number language could be due to the combined effects of tailored instructions and other cultural differences (Alsawaie, 2004; Dowker, Bala, & Lloyd, 2008; Towse & Saxton, 1997).  For instance, Towse and Saxton (1997) demonstrated thatexperimenters' initial practice demonstration strongly influenced English-speaking children's preference for using only units versus both blocks and units to represent numbers.  Zijuan and Chan (2005)found that, although Chinese preschoolers' could provide the right answers to addition and subtraction problems, their computational strategies did not indicate an understanding of the base-10 system or of place value.  Instead, they performed well because they were adept at using their fingers to count and produce the answers.  Thus, differences in performance between Asian and non-Asian children may be a consequence of differing experiences at home or in school, rather than of differences in number languages (Chen & Uttal, 1988; Göbel, Shaki, & Fischer, 2011; Pan, Gauvain, Liu, & Cheng, 2006; Yang & Cobb, 1995; for review, Ngan Ng & Rao, 2010).
What are the long-term effects of different number languages on numerical thinking?
The structure of number languages may have persistent effects on children and adults' numerical performance.  For example, Czech children learn two, equally common, number word systems: One version has an inverted number-word structure (ones digit + decade; four-and-twenty) and the other version has a non-inverted number-word structure (decade + ones digit; twenty-four).  Pixner et al. (2011b) had 7-year-old Czech children write numbers from spoken dictation. When the numbers were spoken using the inverted number-word system, children made many errors in which they incorrectly ordered the digits; no ordering errors were made when numbers were presented using the non-inverted number-word system.  Furthermore, Brysbaert, Fias, and Noël (1998) showed that the arithmetic performance of Dutch and French speakers was affected by differences in how numbers were named, at least when answers were produced verbally.  In Dutch, multi-digit numbers are inverted, as in three-and-twenty, whereas in French, the decade word precedes the ones digit word as in twenty-three.  Like the Czech children using the inverted system, Dutch speakers were slower to produce the answers to problems like 20 + 3 as compared to 3 + 20.  Interestingly, the linguistic differences disappeared when the answers were typed. 
Similarly, Colomé, Laka, and Sebastián-Gallés (2010) examined the addition performance of adult Basque speakers and found that they responded to addition problems faster if the problem reflected their language structure.  The Basque number language follows a base-20 system, such that 35 is the equivalent of twenty-fifteen.  Therefore, the addition problems that involved multiples of 20 plus a teen (e.g., 20 + 15 = 35) were easier for the Basque speakers than the ones that did not include multiples of 20 but had the same answer (e.g., 25 + 10 = 35).  Such findings suggest that the structure of number languages has long-term implications for processing numbers.
Bilingualism can also affect early numeracy knowledge.  For example, when Chinese-English bilingual children counted in English and Chinese, the proficiency in each language determined how high children could count (Rasmussen, Ho, Nicoladis, Leung, & Bisanz, 2006).  Children who spoke Chinese more fluently than English counted much higher in Chinese whereas children who spoke English more fluently counted much higher in English.  It is possible that children's performance might have been affected by learning to count in two number language systems, as the simultaneous learning may reinforce understanding of the base-10 concept.  Furthermore, bilingual children may have more ways of representing numbers than monolinguals (Miura et al., 1993).
Variation in number languages offer a possible explanation for why speakers of Asian languages are better at grasping the counting sequence and acquiring place-value understanding than are speakers of non-Asian number languages.  Differences in the structure of number languages also seem to have some long-term implications for how adults use number words in mathematical tasks.  However, differences in numeracy skills between, for example, American and Chinese children, have many other potential causes, such as home and school experiences (Huntsinger, Jose, Liaw, & Ching, 1997; Wang & Lin, 2009).  Thus, number language differences are only a partial explanation for observed cultural differences.
Future Directions
Much, if not all, of the existing research comparing regular to less-regular number languages is correlational and thus many other sources could be the causes of differences in mathematical performance.  An alternative approach is use of interventions to teach children early numeracy skills and examine whether children who speak more regular languages learn faster than children who speak less regular languages.  More radically, children could be taught using simplified, regular number languages (e.g., ten-three instead of thirteen) and their learning progress compared to other children using standard languages.  Some number languages have evolved to be simpler.  For example, the French spoken in France uses the complex words soixante-dixquatre-vingt, and quatre-vingt-dix for 70, 80, and 90 (literally, sixty-ten, four-twenty, and four-twenty-ten), whereas the French spoken in the Walloon part of Belgium uses the words septanteoctante, and nonante instead (the equivalent of seventyeighty, and ninety).  Walloon children make fewer errors writing these numbers from spoken dictation than French children (Seron & Fayol, 1994).  Thus, research that establishes exactly how the regularity of the spoken number language influences learning has the potential to improve instruction as well as to advance our understanding of numerical thinking. 

Friday, 16 May 2014

Free, online textbooks developed for skills training

Free, online textbooks developed for skills training

 British Columbia is now developing 20 open, online textbooks specifically for post-secondary skills training and technical programs.

"British Columbia's open textbooks are already being used by students all over the province who are studying science, arts and business," said Advanced Education Minister Amrik Virk. "Now students taking skills and technical training programs like electrical, oil and gas, tourism, nursing and others will also be able to get some of their textbooks online for free, saving hundreds of dollars. This is another way we're matching education with jobs, ensuring students are getting affordable, accessible training to move from learner to earner."

The open textbooks for skills training and technical programs support the priorities in B.C.'s Skills for Jobs Blueprint to align training with the labour market, and a total of 20 open textbooks will be developed for:

  • High-demand foundational trades programs, such as carpentry, pipefitting, electrical and plumbing.
  • Oil and gas programs supporting the LNG industry.
  • Tourism and hospitality programs.
  • Adult basic education programs linked to giving students essential skills for trades and technical training.
  • Mining-related programs.
  • Health-care programs, such as health-care assistant, practical nursing and registered nursing.

The online textbooks will be developed based on an open call for proposals, and will be available online starting September 2015.

"The Open Textbooks Project creates another avenue of access to post-secondary education in B.C. by helping to make it more affordable for all students," said Ralph Nilson, chair of the Trades Training Consortium of British Columbia, and president and vice-chancellor of Vancouver Island University. "Expanding the number of textbooks available online and focusing on the area of skills training and technical programs will help post-secondary institutions to achieve B.C.'s Skills for Jobs Blueprint by meeting industry's demand for more skilled workers."

The 20 online textbooks for skills training and technical programs are in addition to the 19 made available in 2013 and the 21 others expected to be ready by September 2014 for 40 highly enrolled first-year and second-year post-secondary subjects.

Thursday, 15 May 2014

Models of First Nations control of education

This article was initially published in Muskrat Magazine  Edited and republished with permission.

While the proposed First Nations education act is on hold, models of First Nations control of education are currently in action across the country, and have been for years.

1. Mi'kmaw Kina'matnewey — Sydney, N.S., with authority for 13 Mi'kmaw communities across Nova Scotia.

In 1999, the Mi'kmaw community won a legal battle for the rights of full management of the education of Mi'kmaw children, and the Mi'kmawKina'matnewey is the educational authority doing just that. Mi'kmawKina'matnewey has various programs, including the First Nation School Success Program (FNSSP).

Thanks to FNSSP, Mi'kmaq language courses are offered in all high schools in Nova Scotia, both on- and off-reserve. In Eskasoni, Chief Allison Bernard Memorial High School will see its first generation graduate this year after completing junior high to high school in the Mi'kmaw immersion program.

According to the executive director of Mi'kmaw Kina'matnewey, Eleanor Bernard, the graduation numbers have grown substantially since students moved out of the provincial system and into the Mi'kmaw Kina'matnewey system.

"In the provincial system we might have had nine or 10 graduate. In the first year of the Eskasoni school, we had 40 graduate," said Bernard

Overall, the First Nation high school student graduation rate in Nova Scotia has increased to 88 per cent, compared with the national average of 35 per cent. Last year, more than 500 First Nations students from Nova Scotia were enrolled in post-secondary institutions.

2. Chief Atahm School/ T'selcéwtqenClleqmél'ten — Adams Lake band near Chase, B.C.

Established in 1991 as a Secwepemc language immersion school, this school has graduated hundreds of immersion students and holds an annual conference to share its resources and strategies with other communities.

3. Seven Generations Education Institute — Fort Frances, Kenora & Thunder Bay, Ont.

Ten bands got together in 1985 to form an educational authority to maintain traditional, cultural and linguistic values as well as improve the economic status of band members. The institute partners with colleges and universities and recently made Academia Group's top 10 in indigenous education.

4. Onion Lake Cree Education System — Onion Lake, Treaty 6 Territory, Sask.

The Onion Lake Cree Education System was established in 1981, first at the elementary and secondary school levels, and then in 1984 at the post-secondary level as well. In addition to standard curriculum, the goal is to promote culture, the teaching of elders, knowledge of treaties and language.

5. The Kahnawake Education Centre — Kahnawake, Kanienke'ha:ka Territory, outside of Montreal.

Established in 1980 and gaining complete administrative control between 1983 and 1988 from the Department of Indian Affairs, the centre runs three community schools on reserve and extends services and tuition for many students at both elementary, secondary and post-secondary levels outside of Kahnawake.

Infamous White Paper served as a catalyst

Many of these examples were organized by indigenous communities following the 1969 "White Paper."

In 1969, Pierre Trudeau's government released an extremely contentious document, the Statement of the Government of Canada on Indian Policy, also known as the infamous White Paper.

It was viewed by many as an attempt to assimilate indigenous people. The White Paper backfired and instead became the catalyst for a significant resistance movement from grassroots indigenous peoples.

In fact, the name of Bill C-33, "First Nations Control over First Nations Education," is a direct reference to the critical 1972 report called "Indian Control of Indian Education." It was published by the National Indian Brotherhood, which later became the Assembly of First Nations.

However, the likeness of Bill C-33 to the original report stops abruptly at the name.

"Indian parents must have full responsibility and control of education," the 1972 report states in part.

"The federal government must adjust its policy and practices to make possible the full participation and partnership of Indian people in all decisions and activities connected with the education of Indian children."

Since that report was first published, First Nations across Turtle Island have developed and implemented community-controlled education models that reflect their cultural diversity, with language inclusion often at its core.

First Nations leaders continue to assert that one of the most pressing issues for First Nations schools is a lack of adequate funding levels, which are significantly less than in non-First Nations communities.

Tuesday, 13 May 2014

Library skills still essential to adult literacy

Likely driven by the economic recession, patrons take advantage of affordable entertainment, Internet access, job-search assistance and educational resources, all at less than retail price and in a relatively peaceful environment.

This renaissance in public library usage might be due in part to the very technology that was expected to threaten the existence of community libraries.

All of which reinforces what both elementary and secondary school librarians have been saying for years: that the early and continued development of a full range of library skills and attitudes is the key to the continued development of adult literacy.


Geoff Johnson is a retired superintendent of schools.

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Friday, 9 May 2014

Bringing the Outreach IN: The West Chicago Public Library District Summer Lunch Program

Bringing the Outreach IN: The West Chicago Public Library District Summer Lunch Program

Posted on May 2, 2014 by

Summer Lunch - Tuesday, June 18 006-2As part of its continuing efforts to reach out and serve community needs, the West Chicago Public Library District (WCPLD) has created a unique service opportunity that literally brings outreach IN. Throughout the summer, the library participates in the Northern Illinois Food Bank's (NFIB) Summer Food Service Program (SFSP), serving over 2,800 free lunches last year alone to children up to age 18, weekdays over a 10-week period.

The SFSP is designed to fill the gap that occurs when school lets out for summer vacation and children who received free or reduced-price meals during the school year do not have access to those meal programs. So the WCPLD sought out a partnership with the school district and the NIFB last summer to serve as an additional SFSP site, bolstering the school district's two existing sites. To date, we are the only public library in the NIFB service area, covering the northern half of Illinois, to provide this service.

Programs like this represent a great opportunity to reach out and serve the community in a non-traditional way. While the financial commitment is limited to the staff time needed for the mandatory training and the time spent implementing the program, the entire library has taken on the commitment to help solve the problem of food insecurity in the community. Through our partnership with the school district, every child qualifies for free lunch without registration or proof of income.

The additional stream of families utilizing our services has resulted in some great benefits for the library. The SFSP has not only contributed to increased summer reading registrations and participation, but last summer we suddenly noticed programs were filling up, especially on weekdays around the lunch hour. In serving 60 lunches on weekdays last summer, we had over a hundred parents and kids go through our program room every day where, while enjoying lunch, we were able to distribute information about the library and its services to families we may never have seen before. A total of 112 library card registrations last summer were a direct result of offering daily rewards to those children who had their library cards with them at lunch.

The rewards to the library, however, were overshadowed by the benefits to participating families. As the summer wore on, we began to notice kids making new friends. Parents, both moms and dads, started conversations that led to information and resource sharing. Those little wiggle worms, who couldn't sit still for a meal in June, by July were enjoying the relaxed atmosphere and shared time with family and friends.

Summer is the busiest time of year in the public library, and this service model may not fit every library. But the need to demonstrate the essential role libraries play in the life of their communities is universal. The SFSP was a perfect addition to our community outreach activities, fulfilling our mission while providing opportunities for us to reach more children and families with literacy promotion and enriching programs.

Thursday, 8 May 2014

Media Literacy Week (November 3-7, 2014) will focus on Youth and Social Networking: Creative, Connected and Collaborative

Canada NewsWire

OTTAWA, May 7, 2014

OTTAWAMay 7, 2014 /CNW/ - MediaSmarts and the Canadian Teachers' Federation (CTF) are pleased to announce that the theme for Canada's ninth annual Media Literacy Week (November 3-7, 2014) will focus on the positive uses of social networking by young people.

The official theme of the week – Youth and Social Networking: Creative, connected and collaborative – will encourage teachers and parents to work with young people to promote the wide range of activities they use daily on social platforms.

"Youth are using social networks in all kinds of interesting ways that allow them to build communities and connect to the world," said Cathy Wing, Co-Executive Director, MediaSmarts. "We want adults to join with young people in exploring the opportunities these powerful tools provide for contributing positively to society and building digital skills for the future."

"Media Literacy Week is an opportunity for teachers to dialogue and engage with their students on ways to become responsible digital citizens and creative learners thanks to the use of social media," said CTF President Dianne Woloschuk.

MediaSmarts' 2013 survey of 5,436 students in grades 4-11, showed there is a high use of social networking by young Canadians. Sites for posting and sharing content such as YouTube, Facebook, Instagram, Twitter and Tumblr were among the top sites, across all age groups. While a primary focus for these platforms is their social lives, students are also using them for learning, creative expression, peer support and advocacy.

MediaSmarts and the CTF are very pleased to welcome back YouTube as the 2014 Gold Sponsor of Media Literacy Week.

During Media Literacy Week, a variety of activities take place in homes, schools and communities across Canada and internationally, with the goal of promoting the importance of digital and media literacy for children and teens.

To find out how to get involved or become a sponsor of the week, visit:  

MediaSmarts is a Canadian not-for-profit centre for digital and media literacy. Its vision is that young people have the critical thinking skills to engage with media as active and informed digital citizens.

Canadian Teachers' Federation (CTF) represents nearly 200,000 teachers as their national voice on education and related social issues. @CanTeachersFed

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