Collaboration

Collaborative Working

A key concept from this week’s math class was collaborative working. The concept taught me and the other teacher candidates a great resource to use in the classroom. The idea of allowing the students to group themselves together in a way they wanted was a different experience to me. While we as students were given popsicles sticks with colors and numbers on them we were then allowed to divide up in a way in which we wanted to. We could have got into groups based on the color of our popsicle stick or the number we had – all the number 1s together or all different numbers from 1-6. The concept of choice allows the students to feel involved and does not make it seem like they were forced to work with particular peers.

Collaborative work also ensured that everyone was able to take part in the math lesson. Each member of the group was given a clue that they were to read to the rest of the group. That clue was only for that person and they had to read it to the others causing them to be involved. The interaction made sure that all members of the group participated and that the group was not dominated by a student that excels in math. An example of what can come from the collaboration is shown below as my group was able to solve the clues to complete the task given to us.

Assessment

Assessment is an influential part of a student’s learning experience. In the past assessment has been focused on what the student is able to produce on paper. Recently the narrative of assessment has begun to change to better reflect the knowledge and understanding of the student. According to “Teaching and Learning Mathematics,” the use of more informal assessment methods such as discussion or observation allow teachers to provide a mark that better reflects the students understanding. A students understanding should not be based on one test of performance task but should be based on their overall understanding of the math concepts. This week’s class along with the readings taught me that as a teacher we should be making notes about the success of the students. These notes will allow teachers to understand what they need to teach but will also allow them to document the success and understanding of the students.

Technology in the classroom

This week my classmates learning activity presentations examined the use of technology in mathematics. Two of the presentations used the website https://www.explorelearning.com/, which has multiple math activities for students of all ability levels. The ‘Gizmos’ as the activities are called allow the students to interact with the information that they are learning. By being able to interact with the content the students are learning they will be able to better understand and be more interested in the math topics. The Gizmos can be extremely helpful as a reinforcement activity or introduction into new topics. The Gizmos are just another example of the concept of ensuring that students are engaged in mathematics. Just in the past classes, the use of a student’s interest to teach math was reinforced as important and influential tool. 

Measurement

Measurement

I have! Who Has?

A great way to review concepts, be the main activity of the class or even the consolidation this math game creates an engaged and entertained class. This game allows for all students to take part and helps reinforce definitions or specific aspects of the math topic for the unit. A description of the game and some example card decks can be found online at Math Wire. The answers for the game would have to be known before hand and because of this the game would not be a good use for an introduction. The answers should also be simple so that students do not take to long answer and become disengaged. I can see this game easily being used in my practicum. The game does not take long to set up and provides for a fun form of review. Students will be able to have fun while completing math activities and hopefully this will keep them interested in the topics.

Different Area Same Perimeter

In class this week we examined the measurements of perimeter and area in rectangles. The main concept that we looked at was that even if shapes can have the same perimeter the area inside can be vastly different. The area does not stay the same if you change the dimensions of the shape. If asking students to find examples of this try to ensure that they keep track of the dimensions that they have tried. By keeping track of their attempts they will be able to see what has or hasn’t worked and can work more effectively because of this.

How to Measure

Teaching measurement can be a difficult topic especially if the first way to introduce it is by measuring with centimeters. Instead measurement can be introduced through three different ways. As seen below it can be introduced by comparison, non-standard units and standard units.

 

Retrieved from: Making Math Meaningful 472

These different concepts of measurement allow the student to better grasp how to measure. With comparison students should be able to recognize what object is longer by comparing to another. The comparison aspect also allows the student to develop vocabulary such as longer than or shorter than.  Measuring with non-standard units can help the students relate to the object that they are measuring. By using objects that are familiar to them such as a new pencil or popsicle stick the students can form a mental image of how long that object might be. Lastly measuring in standard units should be taught to the students as something that everyone will understand as the same length. Explaining to students that measuring with your feet may be different between two people if they do not have the same size feet. Measuring with standard units allow all people to have the same measurement of objects. Measuring with standard units should be introduced to students so that they see the value in everyone understanding the measurement as the same.

Geometry

Geometry and why it Should Be Physical

Geometry is one aspect of mathematics that should be made as physical as possible for the students. Having physical manipulatives will allow students to become more comfortable with the 2D and 3D shapes and have a better understanding of key concepts such as symmetry, congruency, and similarity. One of the main fundamental aspects of geometry is visualization, a study conducted in 2004 states, “visual reasoning as ‘seeing to think’” (Whiteley 2004). Since visualization is such an important aspect of geometry allowing students to use physical manipulatives will help them improve on their own visual thinking. Below is an example of an activity that presents geometry to the students in a physical form.

Important Terms

When learning about geometry this week three key terms became apparent. These terms are essential to teaching geometry and if the student is unable to understand these terms then they will have a difficult time throughout the geometry unity.

Similar: A shape is described as similar if they have the same shape with sides in proportion to another. Similar shapes are an enlargement or reduction of the other

Congruent: shapes are said to be congruent if one can be transformed into the other through a series of flips slides and/or turns. Congruence can also be used to describe specific components of shapes. An example of this is if the angle or side length are the same then the shapes are said to have congruent sides or angles. Congruency can be explained as a shape having equal properties, which could be the whole shape is equal to another or just a side or angle.

Symmetry: There are two types of symmetry, reflective and rotational. Reflective is when a shape is divided by a line or plane and the opposite side are mirror images of each other. Reflective symmetry is easily explained as being the same on both sides of the shape. Reflective symmetry is how many times a shape can fit over itself when it is rotated.

These terms should be a starting point for teachers who are introducing geometry to their students. With these words students will be able to have a foundation for the geometry unit. For more definitions in the geometry strand of mathematics, Geometry definitions  is a great resource that students can utilize to help them remember some more important terms.

The Use of Children’s literature

The story that was used to introduce shapes to our class this week was ‘The Greedy Triangle.’ This book was not only an overview of the properties of shapes and what they are called but also gave real life scenarios for what the shapes are used for. The story was about a triangle who was not happy and always wanted another side which transformed it into another shape. The story then told of all the different jobs that this shape could do in the world. I felt that this story was a great way to present the information for students. The storyline allowed the students a refresher on what certain shapes are called and how many sides they have. Most importantly this story allowed students to visualize how shapes are used in real life. By being able to have concrete examples of the use of shapes students can better relate to the geometry strand in mathematics.

It was yet another great week in math class. I was able to learn valuable lessons to how to teach geometry and even gained another children’s literature resource that can be used within mathematics. 

Patterning and Algebra

Class Overview

            This week in math class we covered the topics patterning and algebra. As a student I thought patterning was just the repetition of images or the continuous increase or decrease of a number of items. I also thought that algebra was the use of letters in math which was truthfully a little frightening. While enduring my math education I always thought that these units were two separate entities that had no relation to each other. In the class this week I quickly found out that I was wrong and that the connection between patterning and algebra is very strong and easy to see.

Matching Patterns

           We started out the week with a matching patterns exercise that had the students match a block pattern with a corresponding t-chart, an algebraic equation, and a graph. The exercise in completion is shown above. I was able to understand the relation between the t-chart and block pattern quickly as the t-chart just stated the stage and how many blocks were present in the pattern. From this chart I was also able to understand the graphing aspect, the left side of the t-chart was the x-axis number and the right side was the y-axis. Using the graphs and t-charts can help the student move from patterning to algebra easily. The organizational tools will help the student clearly see the pattern help them create an equation. Where I was confused was to how to write this relation as an algebraic equation. It was not until a later side that I was fully able to understand the relation. The slide that made it clear how patterns and algebra are related is shown below.

This picture easily explains how to relate a pattern to algebra. The ‘t’ stands for total number of blocks or output. The ‘n’ stands for the input or stage number. With a few input and output numbers given to the student they should be able to realize the pattern and quickly create an equation. The equation is simply put together by the pattern number or what the pattern increases multiplied by the input number and then adding an extra number to get the total output. This picture explains it clearly that that the number that increases the pattern will always be multiplied by the stage number.

Another Week, Another Teaching Tool

            This week showed me another tool that can be used in the classroom to enhance math education. The resource, Explore Learning, Gizmos, allows for a teacher to create a class and invite students in order to teach them more about a certain subject. The resource covers a large variety of topics and can help the students understand mathematics in a fun learning environment. The resource that I viewed in depth was the function machine as it went along with the topic of patterning and algebra. The function machine allows for the student to pick a number and drop it into the machine as it generates a pattern. The resource even has an assessment that the students can use to test their knowledge on the patterns and view how they are doing.

This week was a great one in math because it showed me the relation that patterning and algebra have. This week also provided me with another resource that I can introduce into the math curriculum in placement or when I am teaching in my own classroom.