**Lesson 22:**

**4 divided 2/3.**

We discussed the importance of assessment. According to Richard Skemp there are three levels in the understanding of mathematics:

**Procedural**– Teachers may assess procedure

**Conceptual**– Teachers may assess conceptual knowledge

**Conventional**– Teachers may assess method

The lesson started out with a paper-and-pencil test where we first created story problems (do not use the term problem sum because this indicates “sum” as in addition) and then do the actual computation. It is important to assess to see how much the child has understood…maybe they can only do the computation but does not have a conceptual understanding. Also, teacher assesses in order to see what the child does not understand from which they may assist the child (what are the implications for teaching). Teachers should not rely only on paper and pencil test but also, do oral tests (interviews). If the child writes down the answer without any working but can explain how he or she arrived at the answer that means that the child understands. We also looked at how children conduct a count. For example, some count all, others may skip count, or count in twos, or in repeated addition etc. We should observe to see what strategies it is that they are using. Do the children have good meta-cognition strategies to overcome their weaknesses? It is important that the test is realistic in nature. Do not ask children to tell time by testing them with drawing the clock and time. Telling time means being able to “read” the clock; it does not mean drawing the hour hand and minute hand on the clock. Ask ourselves, “What are we actually assessing the children for? Equally important is that the results of assessment are reliable. Equality in performance should attract the same score.

We also discussed that something per something is called rate and when there is a constant rate, we should apply multiplication, e.g. how many petals are there per flower?

**Lesson 23:**

**“How big is a foot?” by Rolf Myller**

I found this story an excellent introduction to measurement. It was very entertaining. We discussed the right terminology for measurement. For example, 1 meter is actually compared to a wave length up to a certain light (frequency), which is more precise than a physical meter. Also, I learnt that I should say my mass is 52 kilograms and not my weight is 52 kilograms. This is because weight is a force that is pulling me down to earth and if I want to lose weight I should go to the moon…

I also learnt about how to introduce time to young children. It should be concrete (what to Jerome Bruner is called an “enactive representation") which means relating time to every day events. For example, now at three o’clock is our tea break. Young children learn about qualitative time (such as day, night, morning and afternoon). We also discussed distance being length and also location (displacement). As young children measure in non-standard units, we say it is ABOUT five sticks long.

**Lesson 24:**

**MRT Station**

Problem of the evening: We went down to the MRT station to measure the height Level 1 and Basement 1 of the station. There were 62 steps in total and each step was 14cm high. Thus, the total height is 62x14 = 868cm. The first thought of Group Members and I was…we know that each flight has 16 steps times 14cm and there are three flights with 16 steps and 1 flight with 14 steps. Let’s just multiply each flight and then the steps (14cm) but then that would have given us more steps which we think would be an inaccurate measurement. Math is all around us and I believe that math trails is an excellent way of learning mathematics rather than doing paper-and-pencil tasks. It is interactive, engaging and interesting. I think it is especially good for young children because math trails offer concrete learning experiences.

Here are some thoughts...Zero is never shown becasue you do not need to measure nothing....Zero never appears on the ruler itself, however, the first point of measure could be considered as a zero. Often times the very left side of a ruler actually starts at a point that could be considered to be less than zero – so that it would take in account for the inaccuracies of the making of a ruler. Especially useful when measuring from corners of a wall for instance, but then you need to measure the start of the ruler to the start of the first long mark, which distance have to be included when using the very left side of the rule to measure.

Another answer found on Yahoo (retrieved on September 3, 2011 from http://answers.yahoo.com/question/index?qid=20090901213239AAxO4mT) Wooden rulers do not start at 0 because the cut of the wood alters the length of the first measure. Many carpenters usually measure from unit 2 to avoid the distortion in caused by the termination.

**Question:****Why does a ruler not start with a zero?**Here are some thoughts...Zero is never shown becasue you do not need to measure nothing....Zero never appears on the ruler itself, however, the first point of measure could be considered as a zero. Often times the very left side of a ruler actually starts at a point that could be considered to be less than zero – so that it would take in account for the inaccuracies of the making of a ruler. Especially useful when measuring from corners of a wall for instance, but then you need to measure the start of the ruler to the start of the first long mark, which distance have to be included when using the very left side of the rule to measure.

Another answer found on Yahoo (retrieved on September 3, 2011 from http://answers.yahoo.com/question/index?qid=20090901213239AAxO4mT) Wooden rulers do not start at 0 because the cut of the wood alters the length of the first measure. Many carpenters usually measure from unit 2 to avoid the distortion in caused by the termination.

**Lesson 25:****Make a container to fill 15 beans.**

We did a practical assessment at the end of this lesson. We created a small box out of paper and the box should fit 15 kidney beans….Wow, we thought our box was tiny but still we could fit in about 100 beans inside…I learnt that practical test can also be a formal assessment and tests may be conducted with individuals or in groups.

Another interesting discussion we had was about volume and capacity. The capacity of the swimming pool is…and the volume of water needed for the pool is…However, in the U.S. they do not separate these two terms. “

Another interesting discussion we had was about volume and capacity. The capacity of the swimming pool is…and the volume of water needed for the pool is…However, in the U.S. they do not separate these two terms. “

*Volume and capacity are both term for measures of the size of three dimensional regions*.” (Van De Walle, Karp and Bay-Williams, 2010, p. 380).**Lesson 26:**

**Make a graph to show how we get to school.**

This was an interactive lesson on graphs and data collection. E.g. how we can make it interesting for children by a simple questions such as, “How we came to school” and then each person had to stick a colored square piece of paper…we found out that in our class most of the students came to school by MRT. I learn about bar graphs (the width is equal), histograms (area that counts), pie graph and line graph (used for time and not categorical data).

Thank you Dr. Yeap! It has been an interesting and entertaining learning journey!

In summary, this math course has been an invaluable experience for me. Mathematics is not just doing computations but it is all about thinking. "

*Reflection using prior knowledge, social interaction and solving problems in a variety of ways, among other strategies, are essential to learning and therefore becoming mathematically proficient*(Van De Walle et. al, 2010, p. 25). This is what we have done throughout the math course and it worked! I have learnt so much and it made me realize that math can be fun!**"**

**The essence of mathematics is not to make simple things complicated, but to make complicated things simple.****"**S. Gudder (Retrieved on September 3, 2011 from http://www.quotegarden.com/math.html).