Conceptua Math is a site designed for teachers and students to help them visualize and understand fractional concepts by using illustrations and clear language to explain them.
This website contains colorful interactive tools to help students understand fractions. They are reasonably easy to use. The relationships are shown clearly. The aim is to facilitate teachers in their ability to help students see the concepts through active participation.
Type of Material:
Models using virtual pattern blocks, number lines, area and set models for fractions. Problems are given that use these tools. This is an animated web-site. There are instructive videos to aid teachers.
As an enhancement to hands on learning in a classroom or for use in online courses for remote learners. The activities address math standards grades 3-7, although could be used by students and teachers of lower or higher grades depending on needs.
This material would be useful in a math methods classroom at the undergraduate or graduate level.
Flash Player (9 or higher); Safari or Firefox browsers
Windows: Firefox, and Internet Explorer 6, 7, and 8
Identify Major Learning Goals:
To help students gain number sense when dealing with fractions. Students should gain a sense of larger and smaller, closeness to benchmarks and equivalence. In addition students should learn to estimate using benchmarks and gain experience with various representations of a whole.
These tools are designed for teacher-facilitated instruction, and include sample problems to give teachers instructional suggestions. Each tool includes a short instructional video, standards alignment (including the recent Common Core State Standards), key vocabulary, and IEP goals.
Target Student Population:
The tools gradually get more difficult. Therefore the first tools would belong with students who are first being introduced to fractions. That varies with school populations and adopted curricula. There are schools that begin basic fractions in kindergarten or first grade while others don't begin until fourth grade. As students need to increase their skills the other tools can be introduced.
Prerequisite Knowledge or Skills:
Students should have a solid understanding of whole number, including the basic facts.
The strengths are the attractiveness of the tools and their ease of use. Many of the problems presented were rich and encouraged higher order thinking. The addition of vocabulary in each tool is helpful.
The material is up to date and approaches the teaching of mathematics from the NCTM perspective.
There were several errors or sources of confusion. When using the area model for mixed numbers a 2 or a 3 was placed on the representation of the whole number with the appropriate model for the fractional part. That is confusing when we are trying to have students learn the approximate size of fractions. Two wholes need to be shown plus the fractional part. The number line showed this appropriately.
When using benchmarks, moving the minimum up ruins the whole purpose of seeing the sizes and distances on the number line. The number line starts at zero. I like the idea of other benchmarks. They can be added in or used on more difficult problems.
In the video on common denominators the speaker made an error saying that 3 is a multiple of 12.
Potential Effectiveness as a Teaching Tool
The tools can be very effective. The pictures are clear. The comparisons are easy to see. In the beginning the questions involve estimations. Once the correct choice is made a model appears to enforce your choice. There are multiple models to use: pies, rectangles, sets, lines, decimals.
If students learned the material well they should have a good sense of what fractions are representing. The material fits well into any curriculum that is teaching fractions.
With the paid subscription (beginning Fall 2010) there are more activities, customization, data collection and activity sharing. These were not reviewed.
There does not seem to be a way to get an answer without doing the problem correctly. That is okay if a teacher or aid is available. However for a person doing it remotely, that could be difficult.
Ease of Use for Both Students and Faculty
The material is easy to use once you have seen the video. A teacher could easily show students how to use the tools. Feedback is basically informing of correctness and errors. If there is more than one part to the problem the wrong parts are indicated. The layout is easy to follow. For example, a checkmark tells you to click on it to check your work.The reset button is clear. In addition little pop-ups present additional information about how to work the buttons. Most of the tools are very attractively laid out.
Ordering of fractions on the number line was technically difficult. Even when a user knows the correct answer, fractions could move if they were close to each other.
Other Issues and Comments:
Students who think spatially will enjoy many of the tools. Some errors need to be adjusted.
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