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A Culturally Responsive Approach the Mathematics Pedagogy

It is important when educating students to be culturally aware of their needs and to adapt your teaching to fit their learning style. It is important for all our children to be loved, respected and to participate throughout their lives. Inclusive education promotes this, by assessing the way schools, classrooms, programs, and lessons are designed to better benefit all children. Inclusion involves finding ways to better develop friendships, relationships, and mutual respect between all children, despite their disability, race, language, religion, gender, or poverty status. The 21st century schooling has a growing number of diverse groups of people, meaning its time for education to follow in these footsteps. Having a culturally responsive approach to education will assist students who may be different from one another in some way work side by side together in a school environment. It is important in a school for students who are diverse from one another to co-exist as it shows value and the uniqueness of every student. Children have different strengths and weaknesses, and this is even more prominent in diverse settings. Creating greater multicultural awareness and inclusion helps students with different backgrounds and needs succeed, but it also encourages acceptance and helps prepare students to thrive in a diverse world (Drexel University School of Education).

Now, lets discuss a way to be culturally responsive in the classroom through mathematics pedagogy. It is likely that there will be no one single teaching approach that will engage every student at once, but if you consistently deliver culturally responsive teaching lessons will help attract diverse learners will different backgrounds and needs. When teaching to assist all learners, it is important to empower students in class discussions and encourage them to share their thoughts and opinions. This will give students an understanding of different cultures and beliefs. It is also important to integrate diverse study and work practices and understand your students’ learning needs and styles (Guido 2021).

For example, I am teaching a year 8 mathematics lesson. In the classroom I have Aboriginal and non-Aboriginal students, and people will different family structures and backgrounds. I also have a hearing-impaired student and a student that learns English as their additional language. I may not be able to reach all the students at once, but I can evolve different teaching methods throughout the lesson. The subject of the class is the history of mathematics. I would begin the class with a class discussion. This aims for students of different backgrounds sharing their prior knowledge and opinions on the topic. I would write the main point of the whiteboard, so the hearing-impaired student and student that has English as an additional language will be able to pick up on the main points if they are struggling keeping up with the discussion. I then might show a YouTube clip that summarises the main point of the history of education. I would use subtitles so those struggling can read along. I would have an activity, maybe a worksheet where students can reflect on the knowledge learnt. If any students are struggling, I will be able to come over and assist them. In the next lesson, I may have a group activity so those that work better in groups than on their own will excel in that lesson. It is important when teaching a class to mix up the activities and learning methods to have a culturally responsive approach to mathematics pedagogy.

Students should learn of the history of mathematics as a social construct, to better understand its history and development. It should be such an important part of the curriculum, as it will enrich students learning and understanding. A social construct is an idea that has been created by the human mind and been accepted by people in society. As all these prior discussions, mathematics was an idea created by mathematicians and philosophers and used in a way to tell time, create value, understand patterns and make predictions. Mathematics only exists because we needed a way understand patterns and ideas that fit into our world and understandings. The history of mathematics in particularly shows how mathematics was created and how it exactly is a social construct. Mathematics is an idea, and in ways does not really exist. It is something that can not be held or seen, but an idea to understand patterns in the universe. The history of mathematics how this social construct was created, and how it began. Students at school should learn of these events and understand exactly how it was created, the large influencers of mathematics and how it has developed over time as a social construct.

 Below I have created a lesson plan to teach a mathematics class in a culturally appropriate way. 

Year 9 Mathematics  Lesson Plan

Learning  Outcomes/Success Criteria:

LEARNING  OUTCOME: Students will be able to use critical thinking to compare and contrast the history of mathematics and how it has developed into what we learn today

SUCCESS  CRITERIA:

·        Students will identify the main developments of mathematics 

·        Students will understand the history of different cultures 

·        Students will understand influences of mathematics on today 

 Assumed  student knowledge:

·         basic year 9 mathematics 

·      

Lesson  Sequence

 Write  Learning Outcomes/Success Criteria on whiteboard

 Main  Learning Activity

 Watch the YouTube clip as a class, make sure the subtitles are on to help students who English is not their first language and the hearing-impaired. 

https://www.youtube.com/watch?v=cy-8lPVKLIo

 Get students into groups of four, get students to work with students of different gender, race and disability. This will get students thinking differently. 

Get students to answer the following questions as a group:

1. What are the biggest differences between the mathematics in the video, to mathematics now?

2. What are the biggest similarities between mathematics in the video, to mathematics now?

3. Discuss how different countries discovered different theories of mathematics. Do you think these countries had any influences to help these theories become discovered? 

Have a class  discussion on the students’ findings.

  Get students to write down their main findings of the day. 

“What have you learnt today? Write down individually what you learnt and how that has influenced your thoughts on the history of mathematics.”

Having a class discussion along with a individual learning task will assist different types of learners, along with those that work well in groups and those that would rather work individually. 

References:

Drexel University School of Education, ‘The Importance of Diversity and Cultural Awareness in the Classroom,’ Drexel University School of Education, viewed 22nd October 2021, <https://drexel.edu/soe/resources/student-teaching/advice/importance-of-cultural-diversity-in-classroom/>

Guido, M 2021 ‘Culturally Responsive Teaching: Examples, Strategies & Activities for Success’, Prodigy, viewed 22nd October 2021, < https://www.prodigygame.com/main-en/blog/culturally-responsive-teaching/>

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Development of the Number Zero

Our whole number system revolves around 0. It is the first whole number in our system, and this single number has changed the way we perceive maths and science. Without this number, we would have no financial accounting or calculus. But where does it come from?

It is often said that the discovery of the number 0 has resulted into the technology we have today. The reason for this is that 0 and 1 make up the binary code, which denotes text, computer processor instructions and any other data that’s uses a two-symbol system. This is also used when storing data onto CD’s and DVD’s along with long-distance telephone calls over different mobile networks (Jana 2021).

Many civilisations discovered 0 independently, although the first people to have it documented was in Mesopotamia around 5000 years ago, in 3 B.C. This occurred through a pair of angled wedges inserted between cuneiform symbols for numbers. Following was the Egyptian’s, Sumerian’s and Chinese, although these people only used 0 as a placeholder, to determine the difference between 10 to 100. It was also used to signify an empty column. From what he has discovered, there is no true way to record who discovered 0 first (Jana 2021). This event being taught in schools would be highly important and beneficial to students. It would assist students in learning the value and importance of the number zero and how much it has progressed into what they know as the number zero being used for today. It would be great for teachers to create an activity to compare and contrast how zero was used to how it is used today. Students could analyse how a pair of angles wedges influenced the number zero, how it was only a placeholder, and how these simple discoveries began the great development of zero. This would enrich their learning of not only mathematics but its history. 

The symbol changed over time, as the development made its way to the Babylonian empire, then to India and Greece. The Greeks for one had a late development of the number 0, as there is no trace of it with the Romans. There was thought of ‘nothingness’ echoing around the colonies, although this thought and 0 are similar but not the same. The thought of nothingness was a large influence in India which was called sunya (Kaplan 2007).  Along with this, India was the founder of the first modern equivalent of the numeral zero. A Hindu astronomer and mathematician Brahmagupta created a symbol to represent the numeral was a dot underneath the number. Following this, he wrote standard rules for reaching zero through addition and subtraction. In Gwalior India, a circle was inscribed on a temple wall which dates to the ninth century. According to the University of Oxford, this is the oldest example of zero. This number was also shown on an ancient Indian scroll called Bhakehali Manuscript which was discovered in 1881. Due to these findings, many scientists argue that India was the true first created of the number zero (Jana 2021).

From the discoveries In India, it was then transported by the Arabian voyagers to their home cities and towns. After time, the number reached Baghdad by 773 AD. In the ninth century a Persian mathematician, Mohammed ibn-Musa al-Khowarizmi, created equations that equalled to zero, referring to zero as ‘sifr’. This was the beginning of the invention of Algebra. He also developed methods for multiplying and dividing numbers which is known as algorithms. By 878 AD, the dot had transformed and taken an oval shape, which is closely to what we know now as the number 0.  After the Moorish conquest in Spain, Al-Khowarizmi’s work made its way to England. Fibonacci, an Italian mathematician, developed the number further, using it to do equations without an abacus. By the 1600’s, zero was widely spread through Europe (Jana 2021).

There is no real way to first discovered zero as there are many different recordings, beliefs, and opinions. Although, there are many recordings on how it was developed. Without this number being founded and developed the way it has been, it is not far fetched to say we would live a very different world today.

  References

Jana, S 2021 ‘Who Discovered Zero? The Truth Might Be Closer To Home’, Orchids The International School, viewed 17th October 2021, < https://www.orchidsinternationalschool.com/blog/child-learning/invention-of-zero/>

Kaplan, R 2007 ‘What is the origin of zero? How did we indicate nothingness before zero?’ Scientific American, viewed 19th October 2021, < https://www.scientificamerican.com/article/what-is-the-origin-of-zer/>

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Interview with a Teacher

To better understand the influence of the history of mathematics has on education, I had a meeting with a high school teacher, Miss Carlsson. She teaches mathematics and science and was a perfect candidate to reflect on this topic. Carlsson is new to teaching, graduating in her Master of Education in 2019 and has been teaching high school Maths and Science for almost two years. A script of the interview is as below:

What is your favourite part of teaching mathematics?

My favourite part of teaching mathematics is when students who say they struggle with mathematics and the content eventually make those connections that help them understand. I love encouraging students to take risks but also differentiating each student’s skillset to create classroom activities that fit all students’ strengths and weaknesses. I try to create an environment where students feel welcome to come to class and express their learning abilities and make connections.

What have been some of the challenges teaching this subject?

Connecting mathematics such as algebra to real life scenarios can be a challenge. It can be hard to relate the learning material to their real life and when students have questions regarding subjects such as Algeria it can be a challenge helping them understand when there is no simple way to explain the method.

Do you know much about the history of mathematics?

I am aware it stems back a long time ago, and it was used to navigate real world issues. For example, Pythagoras and trigonometry was used to measure the distance from the sun to earth the navigate time. These simple discoveries have been adapted to the mathematics we know today. My knowledge on it isn’t strong but I know the basics.

Do you feel confident teaching it?

I’m intrigued by the idea, but I feel that I don’t have the current knowledge to teach it but I believe students will get a lot of benefit learning it. Students knowing the origin of what they are learning could help their understanding.

Is it in the school curriculum?

Not really, sometimes briefly

What are the benefits of teaching history of mathematics?

I think students understanding why it was initially created and discovered is important and valuable to their learning. It will help them understand the topic if they know where it came from.

Do you think it should be present in the school curriculum?

Yes I think it should be in the school curriculum.

In my blog, I have written about the history of mathematics in education. What are your thoughts on this article? Do you agree for disagree with the survey’s results?

Depends, I think a lot of teachers teach it without realising. You always draw on real life context is where mathematics has come from, for example, budgeting etc. you probably are learning it without realising. I think the survey results are accurate because of this.  

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History of Mathematics in Education

It is often discussed whether the history of mathematics is important to incorporate in education. This idea has been considered for decades, and it is difficult to answer the question, why should the history of mathematics have a place in school mathematics? Rather than answering it, it is beneficial to discuss its benefits and the reason that this is such a big topic in education. Fauvel (1991) conducted a list of fifteen reasons for including the history of mathematics into the classroom. These reasons included cognitive, affective, and sociocultural aspects. From Fauvel’s list and other scholarly arguments, Po-Hung Liu (2003), proposed five reasons for using the history of mathematics in school curriculums, which is as follows:

- History can help increase motivation and helps develop a positive attitude toward learning

- Past obstacles in the development of mathematics can help explain what today’s students find difficult

-  Historical problems can help develop students’ mathematical thinking

-  History reveals the humanistic facets of mathematical knowledge

- History gives teachers a guide for teaching (Liu 2003).

Studying mathematics helps students develop deeper understanding of the knowledge they already studied by seeing how it has been developed over time. It encourages students to think creatively and interpret historical evidence. It is believed by a majority that learning the history of mathematics should be apart of every mathematics program (Tattersall, Beery, Bradley, Rickey and Shirley 2011).

A comprehensive survey was taken by Panasuk and Horton in 2013, which aimed to understand teachers’ point of view when integrating the history of mathematics in schools. The survey was taken on one of the New England states which included 372 public schools which approximately 3,000 mathematics teachers. After invitations being sent out, 367 teachers responded and completed the on-line survey, which resulted in 12% of all high school mathematics teachers being participants of the study.  The survey consisted of 110 statements; some of the statements being formed by the researchers and some were adopted with substantial modification from previous studies. It was founded that 39% of the teachers in the study do not include the history of mathematics in their teaching, while 61% do. Other discoveries of this survey found that of those teachers that teach the history of mathematics, enjoy doing so and they believe their students enjoy the topic as well. It was acknowledged that the learning of history and mathematics can assist in the development of their students understanding and interpreting mathematics (Panasuk and Horton 2013).

It can be agreed than from this survey, the learning and teaching of the history of mathematics benefits both the teacher and the student. There seemed to be a lack of confidence when teaching the subject which can be blamed upon the education teachers are provided with prior to teaching and a lack of presence it has in the school curriculum. Supporting teachers’ confidence to teach this in the classroom would be widely productive and improve the education of mathematics in schools.

The history of mathematics can enrich school education and student learning. For students to learn the origin of a theory or discovery, will assist them in their understanding. For example, when students are learning of Pythagoras Theorem discussing with students the history of it well enrich their understanding of the topic. This theorem is named after the Greek mathematician and philosopher, Pythagoras, who founded the Pythagorean School of Mathematics in Cortona, a Greek seaport in Southern Italy. To learn of his background and how he discovered this theory would help students in their understanding, especially in mathematics where students can struggle with the understanding and concepts (Morris 2010). 

 References:

Liu, P 2003, ‘Do teachers need to incorporate the history of mathematics in their teaching’, Connecting Researching to Teaching, viewed 14th October 2021, <https://www.researchgate.net/publication/281223989_Do_teachers_need_to_incorporate_the_history_of_mathematics_in_their_teaching>

Tattersall, J, Beery, J, Bradley, R, Rickey, F, Shirley, L 2011, ‘History of Mathematics’, History Math Courses, viewed 14th October 2021, <https://www.maa.org/sites/default/files/HistoryMathCourses.pdf>

Panasuk, R, Horton, L 2013, ‘Integrating History of Mathematics into the Classroom: Was Aristotle Wrong?’ Journal of Curriculum and Teaching, Vol. 2 No. 2 pp. 37 – 44.

Morris, S 2010, ‘ The Pythagorean Theorem’,  Department of Mathematics Education, viewed 1st November 2021, <http://jwilson.coe.uga.edu/emt669/student.folders/morris.stephanie/emt.669/essay.1/pythagorean.html> 

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History of Mathematics

Without mathematics today, we would live an entirely different world. A way to truly be grateful of how mathematics has impacted our world is to understand how it effects our everyday lives. For a moment, imagine our world without it. What would that look like? We would have no concept of time, calendars, buildings, technology, transportation, recipes, and the list goes on. Take even one of these discoveries out of our lives and it would alter the world we live in dramatically.

The first examples of mathematics date back to 1750 BC from the Babylonians and Egyptians who used geometrical and algebraic equations. Of the two, the Babylonians were much more advanced. They used a base of 60 and calculations depending largely on tables. A whole papyrus of calculations exists of the Egyptian early mathematics. Mathematics is a science of structure order and relation that contributes to the evolution of counting and measuring. It has been made largely aware that mathematics has developed greatly from the 15th century. From this time to the late 20th century, developments in mathematics were largely situated in Europe and North America (Gray, J, Folkerts, M , Berggren, J, Knorr, W, Fraser, C, 2020).

One of the largest influences on mathematics was Archimedes, who was a Greek mathematician born in 287 BC. He developed many theories we learn today and was the foundation of many discoveries. He was born into an astronomer family, so from a young age he took a strong interest into studying science, mathematics, and politics. He was fascinated with mathematical equations and problem-solving. He is considered to be the father of mathematics as he made some great inventions regarding mathematics and science. He created a pulley system which was designed to help sailors move objects up and down that are heavy. He also created diverse mathematical ideas to solve problems along with the ��method of exhaustion’ which assists in measuring the area of shapes. This assisted in the ability to quantify the value of PI. Although, out of all Archimedes achievements, his by far most outstanding discovery would be calculating the measurement of a circle. This method created a relationship between cylinders and spheres. Over his lifetimes he discovered various concepts, methods, and techniques. It is often said that today’s modern world would not be so developed without Archimedes (Toomer 2021).

There are many other great discoveries made by people in history such as Thales, Pythagoras of Samos, Zeno Democritus and many more. Pythagoras of Samons was a Greek philosopher and mathematician. He is well known for the discovery of Pythagoras’ Theorem, although have made other mathematical breakthroughs (Huffman 2005). The history of mathematics is important to understand as it details where our world began and what discoveries have been made to make the society we like in today. Without these people creating the mathematical breakthroughs they have, we would not have the life and resources we have today.

 References

Gray, J, Folkerts, M , Berggren, J, Knorr, W, Fraser, C, 2020 ‘Mathematics’, Encyclopedia Britannica, viewed 20th October 2021, <https://www.britannica.com/science/mathematics>

Toomer, G 2021, ‘Mathematics’ Encyclopedia Britannica, viewed 20th October 2021, < https://www.britannica.com/biography/Archimedes>

Huffman, C 2005 ‘Pythagoras’, Stanford Encyclopedia of Philosophy, viewed 21st October 2021 <https://plato.stanford.edu/entries/pythagoras/>