Class closers allow for a quick assessment to see what students have learned and the teacher can connect the ideas back to the stated objectives from the start of the class to review if the objectives were met. Below are some basic examples and following that are some more creative ideas to mix things up every now and then.
Of all the fourth graders at Fairview Elementary the twins, Tony and Tina, were known for their ability to make friends. They enjoyed school but struggled with mathematics. After learning more about the importance of mathematics, Tony and Tina strive to help their classmates have the right mindset. Find out how Tony and Tina's ideas lead to mathematical success for themselves and their classmates!
“You teach math? Oh I never got math.” I have heard the following comment so often, that I decided I would try to do as much as possible to change this sentiment. Mathematics is a subject that has the stigma that some people are “just not math people”. This is a dangerous idea that needs to change. While everyone will not go into a math heavy career, everyone is capable of doing mathematics. The life skills including teamwork, communication, and being synthesizers of information that students can develop from mathematics will help in any career as well.
Mathematics education can be improved with little things that could cause a tipping point. A tipping point is the moment at which ideas and messages can spread very quickly to cause change. Eliminating the phrase, “I never got mathematics” and replacing it with the phrase, “You can do math. I can do math” is a good start to improving mathematics education for all. Beliefs are the best indicators of the decisions that people make over their life-time. By giving children the right mindset at an early age, they will be set up for success!
Mathematics and exercise, what a great combination! The title of this book has two meanings. Children can learn effective ways to group and add numbers through this book. Also, the book extols the benefits of exercise throughout one's life. This wonderful book is fun for children and adults!
Pluses of Pilates encourages students to combine numbers in groups of 5’s and 10’s for easier adding. Children need experiences to see how to count things quicker than just counting by one’s and can work on number facts through reasoning while doing this.
My view on the teaching and learning of mathematics is based on the points below and should be encouraged and instilled in children at a young age.
· Everyone can do math!
· Emphasize reasoning over memorization
· Encourage multiple strategies and ways of thinking
· Math is not about how quick problems can be done but shortcuts with understanding are great!
· Encourage discussion and exploration
· Math should foster curiosity
· Math should be relevant and realistic
Exercise is important for your whole life. Keep in mind the basics below for continuing to exercise and be healthy.
· Find an exercise routine that you enjoy
· Incorporate variety in your routine
· Eat healthy and drink plenty of water in addition to exercise
· Do not go 3 days without exercising
Ben and Julie's parents have some questions for them before they will be able to get a dog. Meanwhile, Hesed, the husky, also has questions about his new home. Will Ben and Julie pass the dog interview? The mathematics of area, perimeter, and geometry are incorporated in this wonderful book.
The relationship between area and perimeter
Area, the two-dimensional space inside a region, and perimeter, the distance around a region, are continually a source of confusion for students. This is in part because students may simply be given formulas to use and not understand the concept of area and perimeter. The two activities below are useful to help students understand area and perimeter.
Give students a loop of non-stretching string that is exactly 24 centimeters in circumference. The task is to decide what different-sized rectangles can be made with a perimeter of 24 cm. Students can be given 1 cm grid paper to place their string on. Each different rectangle can be recorded by students with the area calculated. Students can also do this activity with just the grid paper by being asked to find rectangles with perimeters of 24 cm.
Provide students with centimeter grid paper. The task is to see how many rectangles can be made with an area of 36 cm squared. Each new rectangle should be recorded by sketching the outline and the dimensions on grid paper. For each rectangle, students should determine and record the perimeter as well.
An escape room is a game in which teams solve multiple puzzles using clues, hints, and strategy in order to figure out how to escape from a locked room. It has been found that the use of puzzles and gamification in mathematics increases students’ participation and engagement. The prevalence of escape room businesses has increased in recent years. Escape rooms used in the classroom can provide an enjoyable and memorable challenge for students as they work together in teams. Incorporating escape rooms is one way to engage students, encourage productive struggle, and foster teamwork.
In designing and classroom testing escape rooms I have developed important principles for preparing escape rooms to be used in the mathematics classroom. These include a unifying theme and a brief backstory, structures to help students persevere in problem solving, and a compelling twist. The backstory provides information on the context of the problem and what students must do to finish the escape room (Stohlmann, 2020).
Students that participated in the escape rooms have enjoyed the mathematical work situated in a fun challenge and they were able to persevere in problem solving by demonstrating many characteristics associated with a growth mindset. Students commented that the time went by quickly as they stayed focused on completing the escape room. As groups worked on the problems they shared their mathematical thinking and developed their knowledge (Stohlmann, 2020).
Students also felt a sense of pride in the work and effort that they put forth. For example, a student at the conclusion of one of the escape rooms commented, “I feel so accomplished!” I have also written a book based on the Michael's Movie Moves escape room with example student responses that highlight a variety of strategies that students can use to solve ratio and proportional thinking problems. Included in the book is useful information for teachers and students on proportional thinking strategies including scale factors, tables, unit rates, tape or strip diagrams, double number lines, pictures, equations, and graphs (Stohlmann, 2019). An example from the book is below.
Stohlmann, M., & Kim, Y.R. (In press). Game-based learning: Robotics and escape rooms. The Australian Mathematics Education Journal.
Stohlmann, M. (2020). Escape room math: Luna’s lines. Mathematics Teacher: Learning and Teaching PK-12, 113(5), 383-389.
Stohlmann, M. (2019). Escape room: Michael’s movie moves. Seattle, WA: KDP.
There are several important things to keep in mind when selecting an integrated STEM lesson and preparing to engage students in integrated STEM education. When selecting an activity keep the mathematical objectives in mind. It is important that grade level mathematical topics can be used and that they are aligned to the mathematical objectives. This can be done by anticipating possible student solutions to the tasks. If students do not use the all the intended mathematics, teachers can share additional ways of thinking about the task and make connections to students’ ideas.
It is also important to consider if students will understand the problem context. If the problem involves an unfamiliar realistic context, this could hinder students’ work. If teachers are new to integrated steM education, another important point is to select classroom-tested lessons. These may also include possible student solutions to help with anticipating.
Students can be supported to productively engage in integrated STEM education with messages before participating, while participating, and after participating in integrated steM. Teachers can share the following messages with students to prepare them for the work they will do.
While students are working, teachers can monitor the groups to see what ideas groups are using. Teachers can also provide feedback to ensure groups work well together. The following messages are important to reinforce while groups work.
When the time for groups to work is complete, students will be interested in hearing how other groups solved the problem. Teachers can let students know to listen for connections between the ideas. Students can also be given time to reflect on what mathematics they used, how well they understand it, and how well they did working in a group. In summary, it is important to carefully select tasks by anticipating possible student ideas, utilizing cooperative learning, supporting students with important messages about integrated steM education, and having whole class discussion on students’ ideas
Technology can allow for new tasks or improved tasks that help students make connections between representations and preserve in problem solving; as well as enables teachers to elicit and use evidence of student thinking in new ways. Recent technology has the potential to enable students to work on higher-demand tasks as delineated by Smith & Stein (1998).
These tasks make use of multiple representations and focus on mathematical concepts, processes, or relationships. Technology can aid in students being able to make connections between representations. This is done through analysis of real life videos and pictures as well as explorations through dynamic geometric constructions. Students are able to quickly explore different ideas and receive feedback on the results of their actions. Productive struggle has the potential to be enhanced as students progress through technology based activities and receive immediate feedback. Scaffolding can also be incorporated through important questions that focus students’ thinking and also through the incorporation of making other students’ thinking visible to all students. This allows teachers and students to elicit and use evidence of student thinking. When students are able to easily view others’ ideas it can lead to richer discussion and understanding. Mathematical knowledge is then not viewed as solely residing in the teacher but as a shared collaborative knowledge building.
Stohlmann, M., & Acquah, A. (2020). New directions for technology integration in K-12 mathematics. The International Journal for Technology in Mathematics Education, 27(2), 99-112.
“I’ve learned that people will forget what you said, people will forget what you did, but people will never forget how you made them feel.”
The quote above from poet Maya Angelou can be connected to integrated Science, Technology, Engineering, and Mathematics (STEM) education. If students learn mathematics passively by only listening, taking notes and practice, then this can lead to less retention and understanding. Students learn best by being actively involved in mathematics. It is important that students know that mathematics is not a spectator sport! When students are able to participate in integrated STEM education they see mathematics as applicable and engaging. These good feelings can stay with students and motivate them to put forth continued effort in mathematics. Mathematics teachers can implement integrated STEM education in order to ensure that the M in STEM is given focus.
There are three ways that mathematics teachers can implement integrated steM education: engineering design challenges, mathematical modeling, and technology game-based learning (Stohlmann, 2019). Integrated steM education is the integration of STEM subjects through open-ended problems with an explicit focus on mathematics (Stohlmann, 2019).
Technology game-based learning
The technologically based data driven world in which we live in has made STEM (Science, Technology, Engineering, and Mathematics) education and STEM careers of great importance. There are certain STEM fields and occupations where the need for workers is expected to be greatest. The fastest growing jobs include statisticians, operations research analysts, forensic science technicians, biomedical engineers, mathematicians, computer systems analysts, actuaries, software developers, and information security analysts.
Because there is such a high need for skilled professionals at all educational levels there is a shortage of STEM workers who have either associate degrees or attended trade school (Xue & Larson, 2014). There are two careers which usually require an associate degree, one is a computer user support specialist, which is expected to grow by 12.8% and the other is a web developer which is predicted
to grow by 26.6% from 2014 to 2024 (Fayer et al., 2017).
The government and government-related sector has shortages in specific areas such as nuclear engineering, materials science, electrical engineering, cybersecurity, and intelligence. This is not necessarily because of lack of STEM professionals but due to the lack of STEM professionals who are U.S. citizens (Xue & Larson, 2014). This is often criteria for employment that requires certain security clearances.
The private sector has shortages with petroleum engineers in certain geographic locations, data scientists, and software developers (Xue & Larson, 2014).
There is also demand for STEM skills below the bachelor’s level. A 2011 survey of manufacturers found that as many as 600,000 jobs remain unfilled due to lack of qualified candidates for technical positions requiring STEM skills, primarily in production (machinists, operators, craft workers, distributors, and technicians) (The Manufacturing Institute and Deloitte, 2011). While the
number of job openings in this sector has decreased since 2011, there were still 264,00 opening in 2014 (BLS, 2014).
Maiorca, C., Stohlmann, M., & Driessen, M. (2019). Getting to the bottom of the truth: STEM shortage or STEM surplus? In A. Sahin & M. Mohr-Schroeder (Eds.). Myths and Truths: What Has Years of K-12 STEM Education Research Taught Us? (pp.22-35). Boston, MA: Brill.
To introduce the crowd estimation problem play the video below up to the 1 minute 30 second mark.
Estimating Crowd Size
Thousands of people are on the Las Vegas Strip and in downtown Las Vegas each year to celebrate the birth of the new year. A massive fireworks show begins at midnight. According to the Las Vegas Convention and Visitors Authority, more than 318,000 visitors were in Las Vegas for New Year's Eve in 2019. This is the number of people that visited Las Vegas on New Year’s Eve but not the number of people that are out on the street of the Las Vegas Strip. Las Vegas Boulevard is closed for car traffic on New Year’s Eve so people can walk on the Boulevard.
Is it possible to get an accurate count of the number of people on the street of the Las Vegas Strip on New Year’s Eve? What do you need to do this?
Let’s look at just the crowd on Las Vegas Boulevard in front of the Bellagio.
-What is your estimate of the crowd in front of the Bellagio?
-What is your estimate for the lowest possible number of people?
- What is your estimate for the highest possible number of people?
Problem statement: Consider just the area from Flamingo Road to the Cosmopolitan. Determine a mathematical estimate of the number of people on Las Vegas Boulevard on New Year’s Eve.
Follow up question: The Las Vegas strip is about 4.2 miles long. How many people are on the complete strip on New Year’s Eve?
New Year’s Eve on the Las Vegas Strip is an exciting time and attracts large crowds. In this activity students estimate the number of people that are on Las Vegas Boulevard on New Year’s Eve. This is an engaging and relevant activity with multiple possible solutions and methods. Students can use a variety of mathematics in their solutions including area, measurement, proportional thinking, conversions, estimation, and mathematical operations. Students can also use the Internet as a resource to research information. Given the current COVID-19 pandemic teachers can decide whether students will solve the problem based on past crowds on New Year’s Eve in Las Vegas or with social distancing guidelines in place.
Elementary students may measure off a grid on the floor and see how many people could fit in the grid. They could then use the measure distance feature on google maps to calculate the area on the Las Vegas Strip. Students could divide the area of the strip by the area of the grid they used on the floor. This would provide the number of same-sized grids the students used that would fit on the strip. Students could use this number to multiply by the number of people they fit in their grid.
At the middle school level students may make use of the scale on the provided map to help calculate the area on the strip. They might use the Internet to help determine how many people fit into a certain square footage. They could then determine an estimate of the number of people on the strip.
While using similar methods as above high school students may consider more factors in their estimate. They may adjust their estimate so there is space for people to walk along the strip and then space for people who are staying in one place. They might also consider that there are barriers, trees, and a median where people could not stand. High school students may also come up with a formula for people per square foot based on the type of event or the density of a crowd. The follow-up question would require students to convert measurement units to solve. Limiting the number of people allowed to walk on the street would allow for social distancing to be followed. This would adjust the crowd estimate by just considering the maximum number of people who could safely be on the boulevard at one time.
After teachers have facilitated a discussion of students’ ideas, teachers can also share information about the Jacobs Crowd Formula. Herbert Jacobs, who was a journalism professor at the University of California, Berkeley in the 1960s came up with general guidelines for estimating crowds. He determined that generally a light crowd has one person per 10 square feet, a dense crowd has one person per 4.5 square feet, and a mosh pit like crowed has 1 person per 2.5 square feet. Jacobs became interested in investigating crowd estimation after looking out his office window and noticing crowds of students on the plaza below. The plaza’s concrete was poured in a grid so he used the grid and the number of students in each grid to begin to thinking through a way to estimate crowd size. Students can be asked what are the limitations of this method and the methods that they came up with. Students can also be asked in what situations estimating crowd size is used.