Chapter 16 - Consistency in Units

Measuring units – it seems so straightforward and simple, doesn’t it?  I mean… where could anyone possibly go wrong? You take a measurement tool and you measure an object.  Simple! No... apparently not.  The text brings up a great concern.  After students develop a concept of an attribute through comparison activities, they can move onto the measurement process.  Common questions can be something like “How long is the pencil?”.  The interesting scenario that the text brings up is that young children oftentimes don’t understand that units have to be equal size.  For example, they might measure something with pencils of different sizes and report that the object was three pencils long.  The problem would be the inconsistencies in the different sizes of pencils used to measure.  They are correct – the object is three pencils long… but three different sized pencils long.  I would imagine explaining that they have to use a constant unit for measurement would be difficult.  Besides telling them they have to use one unit, I wouldn’t really know how to explain further.

Chapter 5 - Three Connections

       Making connections is vital to learning.  People wouldn’t understand the significance of learning content if they didn’t realize the connections involved.  The text explains three important types of connections that are important when learning mathematics.  First, is the idea that math is connected within itself.  For example, students can learn about fractions, decimals and percentages and how they can be converted to equal each other.  Secondly, is the connection between symbols and procedures of mathematics.  For example, the text shows that three squared should be shown as a drawing of nine dots so that students can see why x to the second power is x squared.  And finally, I think the third connection that the text explains is the most important – the connection between mathematics and the real world.  As adults we now understand that we use math on a daily basis.  To help encourage learning in the area, it would be beneficial to explain why math is so helpful and how it is used on a daily basis in all of our lives.

Chapter 9 - Talking and Writing about Mathematical Ideas

     When most of us hear the term math, or if we were to be asked about activities concerning mathematics, not many of us will think of interactive activities.  The text however, suggests otherwise.  Children “need to talk and write about mathematics”.  The importance of basic interpersonal communicative skills being  incorporated into mathematics is that it will help the students make connections to the content.  Similarly, they can get feedback as well as help from one another by communicating to each other about the content.  Ultimately talking and writing about mathematics will help them make meaning to the content.

Chapter 8 - Ungrouped and Pre-Grouped

      When it comes to place value, many students may initially come across difficulty understanding the concept.  Two types of materials the text explains that can help children learn this concept are ungrouped materials and pre-grouped materials.  Some examples of ungrouped materials are beans, straws or more commonly seen are cubes.  These individually are ungrouped.  However, once these items are pout together in clumps such as a pack of ten beans or a bundle of ten straws or a pile of ten cubes, then they are called pre-grouped materials.  I have seen these manipulatives used in classrooms before and I’d like to use them in my classroom as well if I were to teach this concept.  Being able to actually see items and count out the objects in front of you has been found to be very beneficial.  The use of pre-grouped materials in particular gives the students a better grasp on place values for clumps of numbers.

Chapter 17 – What Do You Call Those Lines and Bars… Oh Yeah, a Graph!

            Classic conditioning.  That’s what happened to me at least.  When I see a graph – pie graphs, line graphs, bar graphs – you name it, I fear it.  These visual tools are only meant to help you understand and analyze data.  For example, let’s take a look at bar graphs and histograms.  Bar graphs are used to display separate and distinct data.  The text gives an example where they graph the “number of children’s birthdays in each month or the number of students who travel to school by bus, by car, or on foot.”  If a student were to be given a word problem and had a bar graph displaying this information, the child would have been able to utilize the graph as a quick visual comparison of the data, which would obviously be beneficial to the student in solving the problem.  Reading the explanation for the text of the function of a bar graph really makes sense to me as a helpful tool. However intimidating the concept may be to me, I know one thing’s for certain – I need to strive to show students as the text has shown me, just how helpful these visual aids can be.

Chapter 15 – Geometry

            An interesting point the text made was that children are taught the names of geometric shapes, “but they do not develop the discriminating power they need to use the names with meaning”.  I really enjoyed some of the beginning activities the text suggested.  For example, a very simple and activity that most instructors already use would be “Who am I” activity.  This is where you put out three different objects and describe one of them (it is round all over) and have the children explain their reasoning.  Another activity, the “How are we alike or different” was a nice way to have children learn shapes.  However, instead of simply holding up two solids and have the children tell how they are alike or different, I would incorporate  Basic Interpersonal Communication Skills by having a pair of objects per pair of students have them discuss how they are alike or different to each other.

Chapter 14 - Patterns

            I don’t recall coming across too many pattern questions in the past.  I now know the importance of patterns – it can help children ‘organize their world and understand mathematics’.  There are several kinds of patterns.  One of them is the classic repeating pattern.  My question is, how do you explain a pattern to someone?  Isn’t it self explanatory – you see the repetition in something and there you have it! A pattern!  Let’s say there are objects that follow as such: red blue, red, blue  and it asks what is the color of the following object.  Some children might say red (which is correct) and some might say blue.  Instead of just telling them the answer is red, the text suggests that children have minds that are difficult to get so it is important to have them explain their ideas to you.  Sharing ideas help the kids consider alternative ways to look at patterns.  Studies show that kids should start by recognizing patterns and thinking about them and then eventually encouraged to look at patterns in different ways.