Teaching Spatial Fractions

[Lucas Timpe]

Good Morning,

I have a question regarding the decision to use a spatial format for fractions. What would be some good determining factors in retaining a spatial layout? I have a book with several examples of fractions that appear to qualify as good candidates for retaining the spatial layout, but I can’t find any guidelines with specific information. Some of the fractions have explanatory notes associated with the numerator/denominator, but some do not. The one example I could find available in the Guidelines for Technical Material is under section 4.1.4, but it doesn’t give much context. I don’t think I need help with the actual transcription of these, but more so in just making the decision of whether or not to retain the spatial format or just do a linear type equation.

Thank you for your help!

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[kdejute]

Thank you for sharing your question! I love the question, "Which fractions should be transcribed as spatial material?"

One good place to start is considering the benefits of spatial layout. (Spoiler: after listing a couple of benefits, we will weigh the benefits against the drawbacks.)

Spatial layout has the benefit of making a direct connection between a label and the specific component that is being labeled.

In addition, spatial layout can pretty closely reproduce the print layout. This can make it easier for a sighted teacher or classmate to discuss content with the braille user.

Now let's talk drawbacks.

Reading a spatial layout can be a challenging proposition, forcing the braille user to recognize and remember connections both horizontally and vertically simultaneously while also traversing some utterly blank space. Another challenge is that if a label applies to multiple components, a spatial layout can make it seem like it applies only to one.

With that, and a few other things in mind, I might use something like the following criteria to identify which fractions should be transcribed as spatial material:

• Each label in print applies to one component ... ... or the components to which any label applies can clearly be indicated with two (or maybe three) tactile graphic lead lines
• The text explicitly discusses the spatial nature of the content.

Lastly, remember you can present a fraction twice – once linearly without labels and then again spatially. (This is like what we do with a poem with scansion marks. Braille Formats 2016 §13.9.3)

Please let us know if you need anything more or different!

–Kyle

[Lucas Timpe]

Thank you so much for your response, you provided some insights that I hadn’t thought of. Presenting the fraction twice was something I hadn’t considered, but the second spatial presentation with the labels would still require some braille ninja skills. Making the connection from the component to the label is definitely the part that I’m having the most difficulty with. I just don’t want to make it harder for the reader to understand what’s going on. Here’s my attempt at a couple of displayed fractions with labels. I did this before receiving your response, but I was also considering using some tactile lead lines. Do you think lead lines would be necessary for this particular example? Also, is it ok to use a few different solutions within the same book? More specifically, in this example if I do retain the spatial layout and maybe include some tactile lead lines, would it confuse the reader if an example later in the book is done differently? I’m including another example from later on in the book that has a few more labels. Do you think both of these examples need to be done the same?

Thanks again for the help.

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[kdejute]

Braille ninja skills! 😍

I do not think lead lines are necessary for any of the examples you shared.

Your attempt at displayed fractions, with a label for the numerators and also a label for the denominators is effective, I think.

Yes, it is ok to use a few different solutions within the same book? Often we need different solutions for different sorts of content, even within one book. (What we should strive for is consistency in transcription of any one sort of content throughout a book.)

–Kyle

[Lucas Timpe]

Perfect, thank you for your guidance on this!

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