Category Archives: 3.1 Teaching & Learning

Liping Ma’s Discovery

Liping Ma has undergone research to compare the differences on how mathematics is taught in China and the USA. Her findings were fascinating; even though US students go through more education to become a teacher than those in China, the Chinese teachers have a deeper understanding of mathematics and therefore are able to teach more efficiently. She found that American teachers taught more in a procedural way rather than using the logic of mathematics.

“About 10% of those Chinese teachers, despite their lack of formal education, display a depth of understanding which is extraordinarily rare in the United States.” (Liping Ma, 2010)

I was edger to find out more about Liping Ma’s discover; How do the chinese teachers teach more efficiently? and what can I learn from this for the future?

In Liping Ma’s book ‘Knowing and Teaching Elementary Mathematics’  she explains her theory(Cuarezma, 2013) and suggests how the Chinese teachers understanding how maths contributes to the students success. This is an important theory that i would consider while teaching children mathematics.

so why is it that Asian children consistently outperform American students? there are many factors that researchers have found that contribute to this “learning gap”;

  • Difference in cultural (parential expectations)
  • School organisation (time spent on maths)
  • The content within the curricula.
  • Teachers Knowledge.

Researcher Deborah Ball identified teachers knowledge and understanding of mathematics should be connecting ideas of and about the subject. The concept by the knowledge of mathematics meant; “comprehension of particular topics, procedures, and concepts, and the relationships among these topics, procedures, and concepts.” (Liping Ma, 2010). therefore, understanding all these things and making it clear to the students will assist them reaching success.  The meaning behind the knowledge about mathematics is aiming at the comprehension of the nature and discourse of mathematics. Additionally teachers consistently thinking about the ‘substantive knowledge’; correctness, meaning and connectedness. Mathematics should always be open to more than one way solutions. Students who can solve a problem with a variety of methods will be able to achieve higher, as the skills can be applied to similar situations. I believe this is important for myself and teachers to consider while teaching because if we notice a child struggling to grasp a process, it may be beneficial to teach another method that they could use. Hopefully seeing another method will be the situation clearer for the child rather than becoming frustrated. 

As Liping ma was researching she drew on how teachers taught; subtraction, multiplication, division by fractions and perimeter. I mainly looked into subtraction and found her way of teaching a lot more enlightening. She studied the American the method of borrowing or exchanging in subtraction, so for example, discussing that when subtracting 21-9 that they had to borrow unites from the tens column. she realised that teacher were expecting students to know, based on their knowledge, from a very procedural method of teaching.

Chinese teachers mainly use a regrouping method of subtraction and in contrast with US teachers,  35% of them demonstrate multiple ways to carry out regrouping. Liping Ma states that teachers address the standard algorithm as well as discussing other ways to solve a problem. The main method of regrouping is by decomposing a unit of higher value, so breaking down the hundreds, tens and units number. for example using 21 again, Chinese teachers would decompose the number rather than suggesting to borrow. This highlights that the language a teacher uses is crucial to help students understanding. Using ‘borrowing’ can confuse children as it acts as a metaphor whereas decomposing highlights that the higher digit can be broken down. Linking what happens when the children done addition is also important to help them understand how 10’s are formed and taken away.

An example of the regrouping by a Chinese teacher from Liping Ma’s (2010) book-                             “How come there are not enough ones in 53 to subtract 6? Fifty-three is obviously bigger than 6. Where are the ones in 53? Students will say that the other ones in 53 have been composed into tens. Then I will ask them what can we do to get enough ones to subtract 7. I expect that they will come up with the idea of decomposing a 10. Otherwise, I will propose it. (Tr. P.)” 

An example of borrowing from An American teacher-                                                                 “Where there is a number like 21−9, they would need to know that you cannot subtract 9 from 1, then in turn, you have to borrow a 10 from the tens space, and when you borrow that 1, it equals 10, you cross out the 2 that you had, you turn it into a 10, you now have 11−9, you do that subtraction problem then you have the 1 left and you bring it down.”

Students that understand why higher value units need decomposed is more efficient than borrowing as they can also apply this knowledge when working with three digit equations. Once they’ve learned the facts and the procedure they an apply this to any situation they are in.

What I take away from Liping Ma and Deborah Balls’ theory is that teachers must be able to anticipate children’s response in order to encourage their way of working and not to simply restrict them to one method. Displaying multiple methods of solving a problem is essential as it promotes more independent learning and also a better variety as each child learns differently. I will also be more cautious of the language i use in the classroom to ensure I provide the best learning situation and avoid confusing the children.


Ma, L 2010, Knowing and Teaching Elementary Mathematics : Teachers’ Understanding of Fundamental Mathematics in China and the United States, Taylor and Francis, Abingdon, Oxon. Available from: ProQuest Ebook Central. [4 October 2017].

Cuarezma, A. (2013). Q & A with Liping Ma. The New York Times. [online] Available at: [Accessed 4 Oct. 2017].

First Step in Discovering Maths….


I could honestly say i tried very hard to avoid maths as soon as I walked out of school two years ago. But, stepping back into a module of discovering maths, its brought my realisation that i physically cannot escape the “terrifying fears” that comes with mathematics. No, maths isn’t really that bad. In fact we mainly use maths by doing what we love in our everyday life, playing sports for example, or betting. During our school years we are taught about the simple arithmetic skills all the way up to complex processes of algebra. We may not think we use the complicated formulas in algebra but there are many occasion that we would use the problem solving skills without realising.

History of Mathematics…

“The history of mathematics is nearly as old as humanity itself. Since antiquity, mathematics has been fundamental to advances in science, engineering, and philosophy. It has evolved from simple counting, measurement and calculation, and the systematic study of the shapes and motions of physical objects, through the application of abstraction, imagination and logic, to the broad, complex and often abstract discipline we know today” (Luke Maston, 2010). The simplest of maths has grown over the years to create the complex world we live in today. In the beginnings of agriculture, mathematics helped form civilisation as maths was used to measure acres of land. Without it, it would not be clear of whose land is whose, which is crucially for food source back in time.

Mathematics can range from as simple as setting an alarm clock in the morning to as complex as coding a program for electric devices for example. The possibilities of mathematics is endless and I truly believe we should strive to encourage mathematics in all subjects that we teach and not to fall into the trap of fear. Continuously expressing the relevance of maths is crucial while teaching the young minds of children as they are the future and will go on to use maths as an essential tool.


Luke Maston. (2010). The Story of Mathematics – A History of Mathematical Thought from Ancient Times to the Modern Day. [online] Available at: [Accessed 25 Sep. 2017].

Teaching Science

Prior to our input with Richard on science, we were all to prepare a 2-minute science demonstration to show to our group. There were great ideas which can stem great lesson plans for the children in the classroom. This picture shows the “lava-lamp”
experiment, img_7992the oil and water demonstrates to the children that materials don’t always mix due to the oil being less dense than the water, this is called “intermolecular polarity”.  Add food colouring for some colour and a fizzing tablet for the bubbles. You can then take about the creation of gas.


Other experiments included the “Floating egg”. so we got to see that an egg does not float in normal water, however, the egg

img_7995does float in salt water. This can get the children asking why it has happened! children tend to think that its only heavy items that sink but with this experiment you can teach them that it all about the DENSITY of the object compared to the density of the water.

Another experiment shown in my group was the colour chromatography. A simple line drawn by a marker pen on kitchen roll that’s dipped into the water can show the separation of components in a mixture. The mixture separates because its components travel across the paper at different rates, based on their attraction to the paper or solubility in the solvent. You can do this experiment with multicoloured pens and it should show the three priimg_7997mary colours that are built to make that colour.

In another science lesson, we were thinking about highlighting the importance of fair testing to children. that a test cannot be accurate if more that one variable is changed in an experiment. for this lesson, we were linking unfair testing into other curricular subjects. A good one is in PE children can be given different equipment or resources, some children can be given advantages in order to make it easier which promotes unfairness. Timg_8006he children would be able to see it a lot clearer if they can identify how it is unfair to do a sport with more than one variable changed. For example, we created an “unfair lesson” for throwing an object into the target. Each group had a different object (varying weights and sizes), they all had different angles and distances from the target and they had different methods of throwing. The children can quickly identify which team were getting more in and why then you can relate the importance to science.


Learning through Dance

I thoroughly enjoyed our experience of dance on Friday morning. I had always had the idea of having fun exciting lessons with the children but wasn’t exactly sure on how to carry out a lesson effectively. I feel more confident to take a class like this now, I believe dance is important to engage with children’s learning. We started with a warm-up, where the teacher went through a couple of well-known songs and show which one got most of us engaged (tapping our feet, singing etc.) this indicated the most favoured song in the room, which everyone prefers moving to their favourite song! This instantly got us all smiling and laughing before the activity had begun. Next, the teacher had a plan for us, she explained we were going to do a dance routine to jailbird rock by Elvis. The first moves were instructed by the teacher (we were doing the waltz for 11 beats) we were they to create our own moves for the next 8 beats with our partner. This involves creativity and collaborative working. Then the teacher had us split into 4 groups (approx. 6 people in a group) each group were giving a line of the song where we had to create quick dance moves, this allowed us to interrupt the music to influence our dance. At the end, we all came together as a group and danced about for the instrumental part. I found that we felt a lot more comfortable with our peers as we were all acting silly together and it was a good laugh. This would also help promote positive relationships in the classroom.

The teaching tips given to us that lesson have boosted my confidence in delivering a dance lesson in schools. Such as allowing the children to decide which song they would prefer to dance too and listening to what they would like to do. I always find I must have the lesson planned exactly right before constructing a lesson, however, I know feel like if I have a basic plan then it can be improvised to suit the children better. I would like to build my confidence in dance further as I think it would be important for the children to see that the teacher is relaxed and confident in doing some silly, over the top actions as they would then feel comfortable to do the same. If they sense that the teacher feels uneasy or awkward they would be the same and the lesson would not be as effective.

Actions are the most engaging learning methods for children and young people as well as benefitting their physical health. I also believe that dance is an ideal method to use for the cross-curricular lesson. The styles of dance encouraged in the UK schools promotes the diversity of our changing population and other cultures. This can be linked with subjects such as social subjects for example.  It is important as children can understand and celebrate our and other countries cultures.

Dance allows children to use their imagination and creativity as well as boosting their confidence and performing skills- which are essential key skills for life. A small activity including dance encourages children and motivates them to engage with the lesson plan, it can even get them started to work for the day as they see the fun side of learning. It allows them to expressive how they feel and who they are which is positive for their mental health in the classroom too.




The ‘Perciph Center for Arts Education’ declares: “Dance is the art form in which human movement becomes the medium for sensing, understanding, and communicating ideas, feelings, and experiences.”