21st century skills in high school mathematics

As a high school math teacher, there are many ways I can integrate 21st Century student learning experiences in my teaching.

As part of the “Math in the real world” assessment for my 10th grade algebra class, students are required to work in groups and create a word problem based on that week’s lesson content. This allows students to use their creativity and to work collaboratively as the only constraint is to use mathematics studied that week. Students then need to solve the problem, showing all their work, and are encouraged to find different ways to get to the answer. Students then share their solutions on the class’ private forum (Moodle platform) and comment on each other’s work, to ask for clarification, make corrections or offer advice on improving the solution. They can then modify their solution accordingly. As the 10th Commandment of Computer Ethics states (Computer Ethics Institute, 2005), all communication has to be respectful and considerate, and I moderate the forum to ensure the respect of this rule.

conversion between metric and us customary systemsMy students are all Chinese students preparing to attend college in the United States once they graduate from high school. In China, the International System of Units (SI) is used and students have a lot of trouble understanding the United States customary units. To address this difficulty, I introduce American units over the course of one week. As students learn how to relate ounces and pounds, inches and feet, we also focus on the learning outcome “Students analyze how parts of a whole interact with each other in mathematical systems” (Partnership for 21st Century Skills, 2011). One of the activities that week is to find “tricks” to convert quickly between different American units and SI units. Students will also research apps for their smartphone that can convert between SI and customary units, and check their accuracy. To increase their global awareness, students are then look up different measuring systems, historical and current, as well as how they were established and comment on their origin. At the end of the week, we hold a debate to discuss which system is better and why.

11th grade students have a class on obesity and its health impacts each year which coincide with the introduction to statistics. The Partnership for 21st Century Skills provides an excellent cross-disciplinary activity: the 2004 report from the Centers for Disease Control on the yearly number of death due to obesity. While learning about health factors, they study the difference between correlation and causation, and how statistics can be used to mislead people. Students then look for other examples of misuse of statistics and, in groups, create a video explaining how statistical messages can be twisted to influence beliefs and behaviors with numbers used inappropriately. This is also the occasion, in collaboration with the Computer Science class, to address intellectual property, copyright and plagiarism issues. It is very important to teach the 8th Commandment of Computer Ethics, “Thou shalt not appropriate other people’s intellectual output” (Computer Ethics Institute, 2005), as plagiarism is a not considered a problem by most Chinese students.

Financial literacy is an integral part of the 11th grade curriculum. During the first semester, students learn how to calculate prices given discounts or profit margins, IBR_tabledetermine the amount of tax owed or the refund due from a taxable income and regular tax payments, and calculate loan repayment quantities by different methods. Students use spreadsheets and financial functions in their graphing calculators to solve real world problems of interest to them, usually involving repaying student loans. Investment models are also discussed in relation to the Business class, with students comparing different investment options and discussing suitability for their virtual shop model.

The largest cross-discipline project occurs at the end of the 1st semester of grade 11. In a collaborative project between the English Listening & Speaking, English Reading & Writing, Business, Government & Civics, and Mathematics courses, students learn about the Global Financial Crisis of 2007 in Business class. They then focus on systemic risk, propose ways to limit it and discuss the ethical implications of mathematically-based decisions in Math class. In English Reading & Writing class they work in groups to write an argumentative essay presenting and supporting their chosen way to limit systemic risk. Finally, in Government & Civics and English Listening & Speaking, they prepare a “House of Representative” debate of a new federal law on the issue.

rmt64ddThe final example of the integration of 21st Century Skills that I will mention here occurs during the 2nd semester of grade 11. In Calculus class, we study the exponential rate of growth/decay and the Verhulst-Pearl logistic function. We apply these to many health and environmental issues, such as population growth with the notable example of invasive species such as the Nile Perch, or the spread of viruses. Each class ends with a discussion of these issues.

There are many more examples of how I integrate 21st Century student learning experiences in my high school math classes, and these were central to the design of the new grade 10 curriculum which will be used next year, along with the Common Core State Standards.


Computer Ethics Institute. (2005, May). The Ten Commandments of Computer Ethics. Retrieved from http://cpsr.org/issues/ethics/cei/

Partnership for 21st Century Skills. (2011, January). 21st Century Skills Math Map. Retrieved from http://www.p21.org/storage/documents/P21_Math_Map.pdf

Planning for English Language Learners

Every year, I teach a 10th grade class on graphing parabolas. All of my students are English Language Learners with vastly differing English proficiency, and speak Mandarin. Most of them have been in the class for a trimester, but students enroll at all time so some may have just joined. I will use the examples of four students at different proficiency levels describe some of the strategies I use for ELL students in the Mathematics classroom.

Amy is a new students. She transferred in this week and is in the early pre-production stage of English language acquisition. At this point, she cannot understand instruction in English and should focus  on learning basic English, rather than math vocabulary. To make sure she still receives the math instruction, I asked Camille to sit next to her and assist her throughout the lesson. Camille studied in Canada for a year before joining the program and is at the intermediate fluency stage of language acquisition. She has agreed to translate instructions for Amy. John, my teaching assistant, will also be there to translate explanations and answer questions in Chinese.

David is also new. He is at the speech emergent stage of English acquisition and understands most of the general English instructions. However, he has never attended an English math class and doesn’t know the specific vocabulary. John and I prepared a vocabulary list with Chinese translations for him. Other students are supposed to prepare their own translations based on their preview and are assisted by teaching assistants during independent study hours. John and I will make sure to check that he understands the instructions by asking him to explain what he needs to do and how he will do it, in English or in Chinese. He is also paired with a more proficient partner.

Jerry is at the beginning fluency stage and has been in the class since the beginning. He needs to ask and answer questions in English, but sometimes he doesn’t know how to say a word. He then asks for the translation, before saying the full answer or question in English. His classmates are encouraged to provide the translation. If they don’t know, John or I will answer. Any word that he asks a translation for is added to his logbooks. Other students need to add the word too, if they don’t know it.

At this stage, I start pointing out grammatical mistakes and eliciting the correct sentence. Before that, I focus on encouraging students’ participation in whatever form they choose: Chinese for the pre-production students, a mix of Chinese and English, or broken English.

As this is an ELL class, several procedures are in place for all students and incorporated in the lesson design. I act out instructions a lot, showing the textbook and opening it as I say “open your textbook”, writing the page number on the white board, providing detailed, written instructions for each task… Time for translations in Chinese is also included for lessons that are difficult and include a lot of new vocabulary, though this is phased out throughout the year as there are no teaching assistants in grade 11 and 12.

Students are required to preview the lessons and look up any word they don’t know. Vocabulary lists are also provided and included in the morning preview, a one hour class each day, where the teaching assistants can check the translations and help the students prepare. The review hour, each day, is also a time where students can check their understanding and ask questions about the content of the daily lessons.

These are just a few of the strategies used for ELL instruction in my math class.

Personalized learning in special education

Personalized learning has become the motto of education in recent years, particularly in special education. While I consider this to be excellent on many levels, it’s not without danger.

What is personalized learning?

It’s actually a very difficult question to answer because definitions vary a lot. One that many agree on, is that learning should be student centered, and not teacher centered. In its most conservative form, it means shifting the focus from lecturing to student activities. Where it starts becoming personalized is when students are allowed different options to demonstrate their knowledge and gain credit for the class. After that the field is open and interpretations vary. Examples include:

  • Catering to different learning styles (School of One, 2010);
  • Providing material adapted for the students disability;
  • Allowing students to advance at their own pace through the material and providing enrichment material for the advanced students;
  • Letting students choose their homework;
  • Allowing students to choose how to demonstrate their knowledge; and
  • Letting students choose what they learn

Personalized learning and special education

In special education, personalized learning is essential. Students have extremely varied needs requiring diverse adaptations or modifications of the curriculum and assessments (A Day in the Life – Special Education Teacher, 2008). Providing subtitles to blind students would be useless. Asking deaf students to write comments based on an audio recording with no transcript would be equally meaningless. There are obvious needs for personalized learning when it comes to sensory impairments.

Less obvious maybe but no less essential are personalization for students with learning disabilities. I tutored a little girl ten years ago. She was in third grade at the time and the school wanted to send her to a CLIS (special education class in French primary schools), in another school because they didn’t have one adapted to their needs. The family was firmly opposed to this, as CLIS were a dump for children with disabilities at the time, where education was sub-par, and it would cause them many hardship due to the distance. I could talk about this case for hours, but to keep it short I’ll just say this. Yes, this little girl suffered from disability(ies), I don’t know which one(s), but it was obvious that she had at least a speech impairment and difficulties with any abstract concepts. And at the time I met her she was failing in math and French. With 3 months and 2 hours a week of tutoring, she passed. What happened? Personalized instruction. She probably isn’t majoring in math in college, but without it, she wouldn’t have graduated from primary school…

With the move toward inclusive education, personalized learning is bound to gain in importance, and not only for special education students. As it is believed in Finland, every student is special and all deserve personalized learning (Finland’s Formula for Success, 2012). If all students receive personalized learning, it de-stigmatizes special education, on top of being beneficial for all students. Finland consistently ranks very high on PISA, though not as much as in the past (Taylor, 2013).

The danger of personalized learning

Personalized learning seem awesome when you look at it from the perspective of what it could bring to students, but not all is perfect. What makes personalized learning dangerous is that it can be used to dumb-down education for struggling students, pushing them toward lower standards of achievement and vocational teaching.

France’s services for students with disabilities are far below that of the United States. Despite some great improvements since the beginning of personalized learning plans and educational reforms of 2005 – in 2014, 260,000 attended regular schools, twice as many as in 2006 –  76,000 do so in special education classes, and the number of students with disability attending secondary schools is half of those enrolled in primary schools, despite it lasting two years longer than primary school. Those special education classes, the government is proud to mention, are being created at a fast pace mostly in vocational schools (Ministère de l’Education Nationale, 2015).

All of this is in accordance with the students’ personalized learning plans. As we can see, personalized learning doesn’t necessary lead to access to proper education…

Personalized learning, great but be careful

In conclusion, I would still say that personalized learning is an incredible opportunity for students and this effort needs to be continued and promoted. It also need to be carefully monitored to ensure that it leads to equal opportunities and better learning, not a lowering of standards or delivery of a sub-par education.


Ministère de l’Education Nationale, de l’Enseignement Supérieur et de la Recherche. (2015, February). La scolarisation des élèves handicapés. Retrieved from http://www.education.gouv.fr/cid207/la-scolarisation-des-eleves-handicapes.html

Taylor, Adam. (2013, December 3). Finland used to have the best education system in the world – What happened? Retrieved from http://www.businessinsider.com/why-finland-fell-in-the-pisa-rankings-2013-12

Youtube. (2008, August 5). A Day in the Life – Special Education Teacher. Retrieved from https://www.youtube.com/watch?v=tcWtAmVB9-o

Youtube. (2010, November 30). School of One. Retrieved from https://www.youtube.com/watch?v=HSTrI6nj5xU

Youtube. (2012, January 25). Finland’s Formula for Success. Retrieved from https://www.youtube.com/watch?v=HsdFi8zMrYI

Gifted students – Forgotten?

Many talk about the implementation of the Common Core State Standards. Every new educational policy is the cause for much debate. Special education programs are receiving a lot of attention. But there is a group of students that we hear very little about: the gifted. Have they been forgotten? Let us examine what professional organizations and recent educational policies say about them.

Gifted students and the common core

The Standards do not define the nature of advanced work for students who meet the Standards prior to the end of high school.

The Common Core State Standards have been the subject of much talk lately: their content, their cost of implementation… One particular thing they have been used for – and that is often swept under the rug – is to reduce, sometimes even remove, gifted education services. However, as stated in the standards themselves, the Common Core State Standards are not meant for students whose level differs a lot from the “norm”.

The Standards do not define the nature of advanced work for students who meet the Standards prior to the end of high school.” (CCSS, n.d., “What is not covered by the Standards, para. 3)

The Standards set grade-specific standards but do not define the intervention methods or materials necessary to support students who are well below or well above grade-level expectations. No set of grade-specific standards can fully reflect the great variety in abilities, needs, learning rates, and achievement levels of students in any given classroom.” (CCSS, n.d., “What is not covered by the Standards, para. 4)

The math standards have a more roundabout way to say this.

What students can learn at any particular grade level depends upon what they have learned before. Ideally then, each standard in this document might have been phrased in the form, “Students who already know A should next come to learn B.” But at present this approach is unrealistic—not least because existing education research cannot specify all such learning pathways.” (CCSS, n.d.)

What this means is that the math standards define what should be taught at a grade level according to the “norm”, as a base target level for students in that grade, but it admits that these standards may not be adapted to the students in that grade depending on what they have learned before. What we do with students whose prior learning is above or below standard level is left for others to figure out on their own.

Gifted students and misconceptions

Like most gifted students, C.J. is a straight “A” student with a soaring I.Q.

Many of the problems faced by gifted students are misconceptions on the part of governments, individuals, but most of all teachers. Two years ago, the National Education Association (NEA) questioned whether education in the USA is failing gifted students. They then proceeded to take the example of a highly successful gifted student and used it to argue (though it’s not stated clearly, in fact, the article doesn’t conclude on the question) that education is not failing gifted students. No sources are cited, no proper research seems to have been conducted. One case study seems to be sufficient to conclude on the state of education for gifted students in the entire country.

Worse than the apparent lack of evidence and research from a professional teaching body, wide misconceptions are stated as fact, helping cement them in the collective mind. According to Cindy Long (2013),

Like most gifted students, C.J. is a straight “A” student with a soaring I.Q. He’s also three grades ahead in math, he consistently scores in the top percentile on state assessments, and he took a college-level Astrobiology class online “just for fun” back in seventh grade. He started reading Dr. Seuss at age three, graduated to chapter books like The Magic Tree House series by five, and at six progressed to Harry Potter novels and The Washington Post.

Besides the fact that not all gifted students are the same and resemble this certainly amazing child, it overlooks some fundamental facts like the specific state, district, school this child is studying in, and his social background. This child has had support from his school and teachers through most of his student life (except for one science teacher). He also comes from a family that supported his giftedness and had the means to do so, as is obvious from the enrichment he received at home. The shocking underlying, unstated, assumption of the NEA is that “most gifted students” are attending schools that support them and are from families who will supplement their learning.

The National Education Association is the largest organization representing school professionals, with over 3 millions members across the USA. (NEA, n.d.) As such, they have the most power to influence educational policies. With views such as these, no wonder gifted students are ignored in educational policies.

Gifted students and national policies

The American Federation of Teachers support education programs which will allow children identified as gifted and talented to develop their abilities to the fullest extent possible.

So what about other organizations that weight in the development of new policies? Sadly, they hardly have anything to say about gifted students. The Council of Chief State School Officers does its best by providing a few links to documents written by other organizations, sometimes containing inaccurate information, though it proved better than others. But what do we expect? After all, the CCSSO’s goal is to provide “leadership, advocacy, and technical assistance on major educational issues“… (CCSSO, n.d.)

The American Federation of Teachers (AFT) found the time, once, to consider the question. In a resolution from 1977, it stated that “the American Federation of Teachers support education programs which will allow children identified as gifted and talented to develop their abilities to the fullest extent possible.” (AFT, 1977, para. 6) What became of it since 1977, it’s up to each one of us to judge from our neighboring schools.

Major international organizations, while taking notes of countries’ efforts to support gifted and disabled children alike, usually have more pressing concern, like promoting access to basic education to children from all origins.

Have gifted students truly been forgotten then?

Despite the obliviousness of major organizations, there are those who remember that gifted children have specific needs and should not be ignored. The two most important ones are Mensa and the National Association for Gifted Children (NAGC). The NAGC is focused on school aged gifted individuals and provides a wealth of information to any interested: educators, administrators, university professionals and parents. Their page on “Myths about gifted students” is one that every education professional should read. Mensa caters to gifted individuals of all ages, but also has specific resources for gifted youth.

Sadly, the two organizations mentioned above have far less reach than the NEA or the AFT. As such it seems that gifted students are doomed to remain ignored by educational policy makers.


American Federation of Teachers. (1977). GIFTED AND TALENTED STUDENTS. Retrieved from http://www.aft.org/resolution/gifted-and-talented-students

American Mensa, Ltd. (n.d.). About Mensa. Retrieved from http://www.us.mensa.org/learn/about/

Common Core State Standards. (n.d.). Key Design Consideration. Retrieved from http://www.corestandards.org/ELA-Literacy/introduction/key-design-consideration/

Common Core State Standards. (n.d.). How to read the grade level standards. Retrieved from http://www.corestandards.org/Math/Content/introduction/how-to-read-the-grade-level-standards/

Council of Chief State School Officers. (n.d.). Who We Are. Retrieved from http://www.ccsso.org/Who_We_Are.html

Long, C. (2013, September 18). Are We Failing Gifted Students? NEA Today. Retrieved from http://neatoday.org/2013/09/18/are-we-failing-gifted-students-2/

National Association for Gifted Children. (n.d.). Myths about Gifted Students. Retrieved from http://www.nagc.org/resources-publications/resources/myths-about-gifted-students

National Education Association. (n.d.). About NEA. Retrieved from http://www.nea.org/home/2580.htm