Struggle Leads To Growth

Math Can Create Stress

"People who feel math anxious are unable to prevent their stress and worry about doing math from interfering with their ability to perform. Their worry about math so occupies their thoughts, it is hard for them to actually think about math" (Marian Small, Making Math Meaningful). Math is a subject that students struggle with because they are presented with concepts that they might not understand right away. Math is a process where there is a right and wrong answer, requiring hard work and understanding to get the right answer. Students may find math stressful because they know that if they do not get the right answer, they get the wrong answer. This thought is always present while in school, but I would argue is most prominent in a math class. 

How Can I Reduce Stress in a Math Class?

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One of the biggest ways to reduce stress in a math class is to focus on an understanding of math as opposed to following a rigorous set of rules and formulas. Memorization can be extremely problematic in a math class because there are exceptions to rules and not all problems can be solved in the same way. Another way to reduce stress is to remove as many time restrictions as possible. Providing enough time to write a quiz or test is essential to a student's success and allows them to think about questions more clearly and not in a rush. Mistakes are not problematic; they are beneficial. They identify the area of learning that a student needs to focus on and can help in teaching math. It shouldn't be expected of students to learn math concepts immediately. Creating questions where students can approach multiple answers in multiple ways isn't just encouraged, it is necessary for learning. Stress due to math can be minimized by teachers who can identify their students' needs and act upon opportunities that present themselves within the math class.

Patterns and Math

There are several types of patterns in math and are seen on a daily basis. Students start working with patterns in elementary school and will continue working with them as they work their way through high school. A pattern represents an identified regularity. Within a pattern, there is always some element of repetition. The three types of patterns we looked at in class are Repeating Patterns, Growing and Shrinking Patterns, and Recursive Patterns.

Repeating Patterns - In this type of pattern, the shortest part of the pattern is called the core and it repeats itself. Repeating patterns can take on numerous forms and can be used by students to help predict what will happen next.

Growing and Shrinking Patterns - In this type of pattern, growing means the numbers increase in size and shrinking means they decrease in size. Along with number patterns, there can be growing and shrinking shape patterns. 

Recursive Patterns - In this type of pattern, each element in the pattern is defined based on the previous element or elements. The Growing Pattern shown in the picture to the right is an example of a recursive pattern as each element is one square greater then the element before it on the left. 

The Three-part Lesson in Mathematics

We also discussed the concept of a three-part lesson in class. A lesson can be broken up into three parts: Before, During, and After. An important aspect of this lesson is the reflection phase, which takes place between the During part and After part. This type of lesson works in conjunction with assessments and is an effective way to teach students.

Before - In this part of the lesson, students engage in work that draws upon their prior knowledge and what misconceptions they may have. Activating this knowledge helps teachers determine what students know and where to go with their lesson. Allowing students to activate this prior knowledge helps prepare them for the lesson and gets them thinking.

During - In this part of the lesson, students are presented with a problem to solve. Powerful problems allow for a range of solutions or strategies and provide students with choices. During this part of the lesson, students interact with the teacher and themselves to determine what is being asked in the question and how they can go about solving the question. Students can work in pairs or small groups to work collaboratively and reach joint-solutions. During this part, teachers should make sure that all students are working within their zone of proximal development.

Reflection on Student Solutions - The reflection process takes place between part two and three of the lesson. During this process, teachers reflect upon their students' learning process and look at the types of solutions that they presented to the problem. Teachers choose which solutions will be discussed in the After part of the lesson, determining how the solutions are linked and what mathematical language to use/focus on. 

After - This part is often called the consolidation and practice phase of the lesson. In this part of the lesson, the class consolidates through the summary/highlights of the lesson and students learn the big concepts within the lesson. Allowing students to present their solutions to the class helps them to understand their process and allows the class to learn. As a class, students have the opportunity to explain and respond to questions about the ideas found in their own solutions and listen to and question other solutions. Teachers should also allow for independent practice to ensure that students understand concepts outside of working collaboratively.

Growing Patterns: Group Activity

In this weeks class, we looked at an activity aimed towards understanding growing patterns. Working in small groups, we looked at a serious of graphs, formulas, charts, and visual patterns. There were four different patterns and each one aligned itself with one graph, formula, and chart. There was one graph, formula, chart, and pattern that was blank, however, and we were supposed to determine what the missing element looked like. 

Working collaboratively within the group allowed us to solve these blank cards and determine a relationship between the graph, formula, chart, and visual pattern. We also used building blocks to help visually determine what patterns were being used. 

This activity allowed every member of our group to jump in. Some members were more comfortable with the charts while others were comfortable using the formulas. Using each other's strengths allowed us as a group to understand the relationship between the cards and determine which patterns were at play. 

Gizmos

Here are some Gizmos to help teach students the concept of patterns. My favourite Gizmo from this list is Pattern Finder and I think it would be the most effective because of the visuals. Unlike the other two Gizmos, a pattern is not laid out in front of you. Instead, you must follow the frogs to see which lily pads they are jumping to and determine a pattern. 

 

Finding Patterns - Build a pattern to complete a sequence of patterns. Study a sequence of three patterns of squares in a grid and build the fourth pattern of the sequence in the grid.

Pattern Finder - Observe frogs jumping around on coloured lily pads. Find, test, and reason about patterns you see in their jumping

Pattern Flip- In the Pattern Flip carnival game, you are shown a pattern of cards. The first cards are face-up so you can see the pattern, and the rest are face-down. The object of the game is to determine which animals are on the face-down cards.