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Using Math Apprentice in the Middle School Classroom

Module by: Laura Rose. E-mail the author

Summary: Math Apprentice is a beautifully tidy and rich website with noble goals. The site connects math to real world careers by allowing students to be apprentices at various companies, applying their math skills to real world challenges. It introduces students to more advanced mathematical ideas as they read about additional math concepts used in each showcased career. The site was created with the belief that it is important for students to interact with math concepts beyond the standards, since this is where the joy of math can often be found.

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Overview

One of the greatest challenges for teachers is to connect their students to their subject matter in a meaningful way. When this is accomplished, interest is piqued and effective learning happens more naturally. Most math teachers are faced with the question, “When are we ever going to use this?!” If this is a burning question on students’ minds, it deserves attention, and the possibilities that are uncovered in the process of exploration may expand students’ thinking in unimaginable ways.

Math Apprentice is a beautifully tidy and rich website with noble goals. The site connects math to real world careers by allowing students to be apprentices at various companies, applying their math skills to real world challenges. It introduces students to more advanced mathematical ideas as they read about additional math concepts used in each showcased career. While the targeted levels are grades 4-6, the content would certainly be stimulating to middle school students. The site creators acknowledge that some of the mathematics in Math Apprentice may seem advanced for its targeted group; concepts include ratios and proportions, functions, scale, symmetry, Pythagorean theorem, and even sine and cosine functions. The site was created with the belief that it is important for students to interact with math concepts beyond the standards, since this is where the joy of math can often be found.

How to Get Started With Math Apprentice

Math Apprentice is extremely easy to navigate, which is a bonus for both teachers and students. Start with “Explore the Math”, then choose your character. Use the arrow keys to move along the city’s street, and click on a building to enter it. You are greeted by an employee from the company who explains the math behind his or her job and presents you with an activity. There are eight companies, each with one activity. It will take you approximately 10 minutes each to preview the activities. Two other pages (“Read About Math Careers” and “Vote for the Next Math Career”) are accessed from any of the pages within the “Explore the Math” section. Each career listed in “Read About Math Careers” corresponds to a company in the city.

Figure 1
Figure 1 (graphics1.jpg)

Figure 2
Figure 2 (graphics2.jpg)

Classroom Examples

A Semester Project on “Math & Me in the Real World”

By engaging students in a semester-long project on this topic, a teacher could set the tone for exploration beyond the material itself. Using Math Apprentice, students would investigate the use of math in a career or hobby related to their interests and hopefully discover some excitement and inspiration along the way. Completing each of the eight activities would give them some insight into applications of math skills, and reading about math in careers would give students some project choices to consider. If none of these choices were attractive to a student, further exploration could be done with the teacher to find something of interest. In addition, the folks at Math Apprentice aim to add a new career to the site each month, and students may access a drop-down list to vote on the next career to be added. Browsing this list or knowing someone who uses math in their career could provide additional project ideas.

Here is what a student sees when he/she visits the bicycle design company, Wheelworks:

Figure 3
Figure 3 (graphics3.jpg)

After listening to the introduction, the student clicks on “Go To Activity”:

Figure 4
Figure 4 (graphics4.jpg)

After solving a problem, the student should then click on “Read About Math Careers” at the bottom of page and choose bicycle designer to read more about the career. (The student may also choose to read about the career before doing the activity.) Each career page gives examples of math concepts used in their discipline:

Figure 5
Figure 5 (graphics5.jpg)

These are written in such a way to make the topic accessible to students, yet as mentioned previously, they purposefully introduce advanced concepts in order to stretch students’ thinking. Ideas which pique a student’s interest can be identified and explored. For example, a student who chose bicycle designer may be most interested in the role of shapes and angles in bicycle design. This short paragraph from the page above provides much to think about [my comments are inserted in brackets]:

Shapes and Angles

Bicycle frames must be carefully constructed to ensure stability, safety, and strength. [Primary considerations of design are introduced.] Frames are often built with a rear triangle and a front quadrilateral. [Why?] The angles formed are also very important. Bigger angles are necessary when speed is required. When comfort is more important, the frame is usually built with smaller, acute angles. [Why?] Recently, there have been some very innovative frames that break all the conventional rules of bike design. [Innovative thinking is important, and there are opportunities for creativity.]

Exploring these ideas could be enough for a student, or it could be a jumping-off point for discovering much more information of interest. Each paragraph of each career page lends itself well to this type of questioning. In addition, students may think of other math-related aspects of a career about which they are curious.

The format of the project can be somewhat flexible; some students may be very excited about creating a digital presentation, while others may not have access to the resources necessary or may prefer to create a stand-up poster. Either way, scaffolding should be provided for creating effective presentations/posters with graphics and explanatory text, and students could present their projects to the class.

The attributes of this use of Math Apprentice are numerous. Students engage their problem-solving skills, higher-order thinking skills, and potentially even venture into the affective domain by responding to and valuing real world examples. They connect math to their own interests and get a taste of the interdisciplinary nature of math. Hopefully, the creative and open-ended aspects of the project would make it enjoyable, and students would certainly benefit from practicing project design. They would also learn from each other by sharing their knowledge, and they would practice their presentation skills.

Reading and Writing to Learn with Math Apprentice

Over the course of the semester, each student could rotate through each of the eight activities and career pages. They would then answer the following questions for each activity/career in a journal:

  • Math Activity: Describe what you did in the activity.
  • Was it too hard, too easy, or the right challenge for you?
  • Did you know this activity was part of this job?
  • Did you enjoy the activity? Why or why not?
  • Career Page: Which career and which math concepts interested you the most?
  • Did anything interest you enough to want to find out more about it?
  • Do you know anyone with this career? If so, consider asking them about it.
  • Other subjects that were mentioned besides math:
  • New vocabulary:

This use of Math Apprentice still engages problem-solving skills, higher-order thinking skills, and the affective domain. Connections between math, their own interests, and other subjects are drawn. Students think about how math is used in the real world, although a deeper level of exploration (as with the semester project) is left up to the student. There is a greater focus, however, on reading and writing about math, which are very important skills for improving comprehension and communicating mathematics concepts. Sharing in small groups could be incorporated after each journal entry is completed.

Short Activity & Report

If you are not looking for a semester-long project, or if you feel time constraints would make the Reading and Writing to Learn project difficult, you could consider using Math Apprentice for a Short Activity and Report, either in the computer lab at school or as homework. Each student would choose the apprenticeship which sounds most interesting to them and complete the activity. They would then read the corresponding career page and write a short report, guided by the same questions above. Sharing in small groups could be incorporated. Students could potentially be interested enough in this site that they may spend more time exploring it at home.

This is a scaled-down version of the Reading and Writing to Learn project, but the attributes remain the same.

Assessing Math Apprentice for the Classroom

Pro’s

This is a very user-friendly resource which requires little to no navigational learning time. The selected math activities represent real-world tasks, and the math concepts described within the career profiles are well-designed to pique students’ interests and stretch their thinking. The resource lends itself well to varying depths of exploration.

Con’s

Since I found no apparent difficulties or shortcomings with the resource itself, I will simply mention the challenges inherent in the proposed classroom uses of the site. The primary challenge is that students may need a “guide on the side” to help them focus in on the concept of each activity rather than simply the wonderful graphics and interactivity. And, as mentioned previously, some of these concepts may be too advanced to completely understand, but students can probably begin to understand them on a certain level with some guidance.

Semester Project: The potential benefits to students are numerous; however, you will certainly need to ensure that you can devote time to project planning and development, from topic choice all the way through presentations. Scaffolding will be required with various project-related skills (research, drafting, editing, layout, presenting, etc.), and assistance will be needed along the way.

Reading and Writing to Learn Project: Students would hopefully benefit from interacting with all eight of the activities and career pages on Math Apprentice, but be aware of whether or not the activity is losing its value as time goes on. Perhaps the journal questions need to be varied, or perhaps students would choose four of the eight careers to investigate.

Short Activity and Report: A single short exposure to the theme of math in the real world certainly would not be as effective as longer projects in connecting students to this important topic. Nevertheless, any time spent on this exploration should be considered valuable.

Considerations for Teachers

Semester Project:

  1. Students can easily feel bogged down by projects and presentations. Emphasize the creative, open-ended, and personal interest aspects of the project.
  2. Time management will be important. Suggest dates and goals for project development.
  3. Check in with students on their progress, and make yourself available to help with issues that arise.

Reading and Writing to Learn Project & Short Activity and Report:

  1. If group sharing is incorporated, some scaffolding may be useful to ensure that group discussions are productive.
  • For the Short Activity and Report, groups could be designed so that repetition of career choices would be minimized.

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