Manitoba’s Open Textbooks

Q: Content is accurate, error-free and unbiased

Errors (typographical)

On page x, "How to Use this Book", the text states that you can "... search a specific chapter, open that chapter and use your browser’s search feature by hitting [Cntr] + [f] on your keyboard if using a Windows computer". I think there is an error in that the [Cntr] should be [Ctrl].

Errors in vocabulary
Unless I am missing something, on page 14, writing 53 and 34 on top of one another to align the ones and tens place is not placing them in a "formula". A formula has variables that are substituted out for values. The use of the word "formula" here is misleading, especially since equations are tackled in Maths for Trades: Volume 2. Suggestion: Use the word "format" or better yet, relate to place value, stating that by aligning the ones place we can see whether there is a full group of 10 or not and then regroup any sets of ten to the tens place. "Formula" is used again on page 21 in the same way. Later in the text, the words "format" or "workable form" (page 38) are used.

Bias (conceptual)
There is also some questionable conceptual "bias" that might be misleading and this is a common thread in multiple parts of the text.
Example (excerpted from Introduction): “So, Chapter 1 you can kind of look at as the first step. It’s “Whole Numbers.” And then what we do is once we’ve gone through that, we take a step up to Chapter 2, to “Fractions.” Chapter 3, another step, “Decimals.” And then finally, Chapter 4, which is “Percent.”
Decimals are merely another way to write a fraction, and so I am doubtful that they need to be described as a “step up”! Percentages are, again, merely another way to write a fraction or a decimal, expressed as an amount “out of” 100. The relative difficulty should not be presented in this way as they are merely equal amounts expressed in different ways.
For example: ½ is 50% which is 0.5. Expressing the value in one way (percentages) is not really "a step up" from decimals. The impression that one must convert 1/2 to 0.5 before converting it to 50% is simply not a process that is hierarchial One can convert to any of the three forms of the same number in any order!!
We have to be careful not to assume that maths that we find difficult are not presented as such. In my experience, students can find decimals quite easy compared to fractions!

Content Accuracy Rating: 4 out of 5

Q: Content is up-to-date, but not in a way that will quickly make the text obsolete within a short period of time. The text is written and/or arranged in such a way that necessary updates will be relatively easy and straightforward to implement

The content is up to date, though it does not acknowledge cultural variety in how to do simple math operations, which might be a was to make it more up-to-date. I have noted elsewhere where the procedural focus that does not refer back to the detailed conceptual framing might be the first sight of potential obsoletism I can predict.

The text is arranged such that necessary updates will be implementable with minimal disruption to existing text.

Relevance Rating: 5 out of 5

Q: The text is written in lucid, accessible prose, and provides adequate context for any jargon/technical terminology used

I have scored clarity as 5/5 because I do think the text is clear (with any missing conceptual clarity included in other sections like "consistency").

Lucid, accessible prose
A friendly, supportive tone is used in the opening scenario for each subsection of each of the 4 main sections with tastefully chosen rhetorical questions and straightforward, realistic scenarios to provide a context for the immediate application of each subsection. I think this provides a solid contextualized rationale to learn the topics.

Some phrases might be familiar, local/colloquial (examples below), but depending on the audience, that might/might not work well. For example in "Whole numbers, Place Value System" we see "The purpose of this chapter is to define what a whole number is and then learn to work with those whole numbers, be it by adding, subtracting, multiplying, or dividing". The phrase “be it by…” might be replaced with something like “whether you need to add,…” A second example in "Whole numbers, Place Value System" is that the expression “on the go…” might be too familiar or colloquial odiomatic.

At times, sentences needlessly start with “..and…”
Ex: In the "Introduction" section, the book states “So, Chapter 1 you can kind of look at as the first step. It’s “Whole Numbers.” And then what we do is once we’ve gone through that, we take a step up to Chapter 2, to “Fractions.” Chapter 3, another step, “Decimals.” And then finally, Chapter 4, which is “Percent.”

Sometimes - not often - the writing could also be more concise. In the same excerpt above,
Suggestion: “…and then what we do is once we’ve gone through that…” can just say “Once we have reviewed whole numbers, we can learn about fractions – that are parts of whole number” (perhaps insert a powerful visual like a number line showing how fractions are inbetween whole numbers).

The text definitely provides adequate context for any jargon/technical terminology used.

Clarity Rating: 5 out of 5

Q: The text is internally consistent in terms of terminology and framework

This was my only real disappointment with the text, but it was a big one and I hope that I have added it to the correct category.

Internal consistency
Overall, if internal consistency refers more to alignment, then I say "bravo"! The alignment between the assessment and the practice examples is strong, and that alignment extends to the carefully worded and concise learning objectives. In other words, what is said to be "taught" is taught and that what is taught aligns with the practice quizzes. I should note that the difficulty of the questions on the quiz is higher than in the practice questions. For example on the Whole Numbers quiz, most questions required multiple operations combined (ie multiply several numbers first, then sum the results). A subsection on making decisions on when to use which operation would make these practice quiz questions more aligned.

Consistent feature of metacognitive coaching/motivation
I appreciated the interspersed cognitive coaching such as that in the example on page 22 (step-by-step). I would recommend a consistent visual layout for this more metacognitive coaching on mathematical conventions and processes. This would avoid having those "coaching sessions" in the middle of an explanation and having to say "now back to the question"! Similarly, the "Brain Break" later in the text is a great idea, but having a consistent visual cue for that "coaching" would help those learners who want it to access it and those who do not to continue reading the explanation, unimpeded. Keeping the coaching alongside but not within the explanation would also serve neurodivergent learners.

Terminology
Using consistent wording might help when defining terminology. For example when defining place value system and digits, the following excerpt from "Whole numbers, Place Value System" uses the word “spots” and “locations” and “place”. Excerpt: “The 9, the 3, and the 1 are all located in different spots in the larger number, and each of them is called a digit. Putting the digits in the wrong locations could result in disaster when dealing with money and in many other situations."
Later in the same subsection “Notice that each of the original values has a specific place in the total.”
The phrase “original values” could be changed to “digit”. The point is that the word digit is introduced but then not utilized in context when the opportunity arises!!

Instructional vocabulary could be more consistent.
For example, in the practice questions, the instructions are “Locate digits in the place value system….Find the place value of each of the following digits:”
However, in the first video of "Whole Numbers, Place Value" (timestamp 0:19) the instructions are: “…and that will tell what position each value places..”.

Framework consistency

I appreciated that the explanations were clearly carefully constructed and indicative of a constructivist approach rather than a "rote memorization of procedures" approach. Yet, I found that the very careful conceptual development of previously defined words/concepts was not consistently carried through to the video explanations or practice examples.

Example 1: Since much time is spent explaining place value, it could be more consistently used as a frame when explaining the operations (add, subtract, multiply, divide). For example, one could write “add up the digits in the ones place.” This would facilitate the discussion of regrouping when the digits in the ones place equal more than 9. Instead, the text writes "Step 2: Add up the ones. In this case, we have 3 and 4. Together, they add up to 7." It is a slight change, but I found this consistently missing in the text - the use of previously defined words/concepts did not always transfer to the explanations.

Example 2: Another clear example of this glaring omission was later on that page, when adding 27 + 45, the idea of regrouping could be used. The idea that 12 is 1 group of 10 (1 in the tens place) and 2 is the digit that remains in the ones place would give a more conceptual explanation (as opposed to “carry the 1”) and that would more closely align with the necessity of explaining place value earlier in “The Place Value System” section. Instead, this excerpt shows a more procedural, mechanistic approach rather than a conceptual one and the wording is also mechanistic rather than tied to the concept of place value.
"Note: In this case, we do not put the number 12 at the bottom of the equation. Instead, we “carry the one” into the next spot (the tens) in the place value system."
The idea of borrowing is insroduced on page 22 without ever referring to regrouping. On page 22, we could specify what we are borrowing - 1 group of ten - to align with the idea of place value. A simple analogy might be to "get change" for a dime in pennies (though I realize pennies are old school).

Example 3: The same missed opportunity is shown on page 21, "...there is only one number in the tens column, and that happens to be the number 1. That makes things easy, as there is no work for us to do. We move the 1 down in to the tens columnof the answer and then we have our final answer." The reason that we mechanistically move the 1 down is because we are taking 0 away from 1 group of ten items. There is 1 group of ten and 7 for a total of 17 items (jobs in this case). "Taking away" five "ones" leave us with the original remaining full group of ten (shown by leaving 1 in the tens place) and 2 in the ones place. Similarly, in that same section, when you borrow a group of 100 for a column that has a "4" in it, then you now essentially have 140 in that column (not 14).

Example 4: pages 36 Step 2: (for the question 90 divided by 5): "Take the 5 and divide it into the first digit in the number to be divided into. In this case this is the 9. We have to figure out how many times 5 goes into 9 without going over." A more place-value focus would emphasize that 5 goes into 90 how many times. 9 is in the tens place and so to think of it as simply 9 counteracts the learning that the students did in the first subsection of this section - place value.

Example 5: For the concept of defining "place value", there was a lack of the use of place value words like "groups of ten” in constructing the definition.
“1” in the “tens” place represents “1” group of ten (rather than saying that we “start again at 0")
“1” in the hundreds place represents 10 groups of ten. The promotes a procedural view, but aims to tackle a conceptual understanding that each location affords a digit a specific value. (1 in the ones place has a value of 1; 1 in the tens place has a value of 10).

Example 6: Excerpt from Whole numbers, Place Value System
“When the value of a digit increases past nine, we start again at zero but add one to the value of the digit in the next highest place value. The simplest way to think about this is to go from 9 to 10: (diagram is here). In this case, the ones place goes back to zero and the tens place increases by one. The ones place has gone from nine to zero. There was no value in the tens place when we started, but now, the tens place has increased by one." Again, because there was a full group of ten, we write "1" in the tens place to represent that group of ten.

Similar departure from pulling the conceptual understanding through to the explanations happen on p. 48 and then in the video for "Mixed fractions to Improper fractions", a procedural method is shown with no integration of why 3 3/8 pizzas is the same as 27/8 pizza.

Consistency Rating: 3 out of 5

Q: The text is easily and readily divisible into smaller reading sections that can be assigned at different points within the course (i.e., enormous blocks of text without subheadings should be avoided). The text should not be overly self-referential, and should be easily reorganized and realigned with various subunits of a course without presenting much disruption to the reader.

Text is chunked extremely well into bite-sized chunks with very clear headings.

Easily reorganized
The four sections of the book could be reorganized, but due to the nature of Maths and the constructivist orientation of the authors, each section could not have its subsections reorganized easily. Each section is its own narrative. I see this as mostly due to the nature of Mathematics and not as a flaw of the book.

Self-referential
There are references to previous contexts because Harpreet and Jamieson are "characters" who have running commentary throughout the text. I also see the references to earlier concepts ars quite necessary and so I don't see the text as "overly self-referential". Editing earlier references out would not be a huge task.

There are specific references to "you may have noticed in this text that..." (see page 22) which assume a linear front-to-back navigation through the text, though this self-reference would not be difficult to delete OR transfer to the "How to Use this Book" section. Another example of this assumption occurs in the following excerpt from "Whole numbers, Place Value System": "All the chapters in this textbook, including this one, will have examples and exercises geared towards the trades. It contains content relevant to all trades, no matter what trade you are in." It assumes that the reader is “digesting” the book in a chronological front-to-back way. The “How to Use this Book” introduction is a better place to explain repeating structural elements of each module.. The introduction explains the examples, and exercises etc and so moving this content to the Introduction would make the book more easily reorganized.

Quiz Question that require conventions that are explored in other sections
For the following question on the Whole Numbers Quiz - "Fill in the missing value: On a 124-foot length of pipe, 32 supports are used. The supports are equally spaced. If one support is placed at the beginning and one at the end of the pipe..."
This question demands that a decimal answer be rounded. The conventions for rounding answers has not yet been given (the first mention of rounding is in the decimals section). If a whole number answer is desired, that should be specified. The answer would have to be 5 feet because rounding down (ie 4 feet apart) will not span the full 124 m. (answer is 4.14 feet)

Modularity Rating: 4 out of 5

Q: The topics in the text are presented in a logical, clear fashion

Clarity is a selling point for this text. I found great clarity of the presentation of the topics. (I have commented on conceptual consistency section and so I will not include that in this rating).

Strengths related to the logical presentation of concepts include adequate scaffolding. For example: In the "Adding whole numbers" section
o first two 2 – digit numbers involve no regrouping (53 + 34)
o the second set of 2-digit numbers include 1 regrouping (27 + 45)

One suggestion: I was disappointed that throughout the text, the two types of questions (separated as Question 1 and Question 2 in the practice section) are not labelled with the corresponding scaffolding! Recognizing question types is a HUGE part of everyday mathematical literacy.
For example, in that same section, Question 1 could be labelled as "no regrouping" (or even "ones place does not exceed 9")
Question 2 could be labelled as "regrouping" (or even "ones place exceeds 9). Carrying that identification of the types of questions through to the quiz as well, further helps students understand which types of questions they get correct and which they get incorrect. Without this labelling, they don't realize that the questions that they may be getting incorrect are ones involving regrouping. This also helps students mathematical vocabulary and helps them self-assess.

Organization Rating: 4 out of 5

Q: The text is free of significant interface issues, including navigation problems, distortion of images/charts, and any other display features that may distract or confuse the reader

I experienced no navigation issues, no distortion of images or tables. In fact, I appreciated that some formats linked to the external h5p formats to allow for full functionality and a parity between experiences with the book in different formats. I did not review all of the formats, however. In some cases, images contribute to cognitive load and some applications of Richard Mayer's Principles of Multimedia (https://waterbearlearning.com/mayers-principles-multimedia-learning/) would alleviate any images causing this extra cognitive load.

For example, many of the diagrams/images can be educative rather than just decorative. On page 15, (according to Richard Mayer’s Multimedia Principles) having the word “sum” instead of the word “note” in the callout box would reduces cognitive load, allowing the learner to have more "brain space" to work with the content. This change could be carried through the other modules of the text as well. This is not an error in content, I should note, but in design.

Interface Rating: 5 out of 5

Q: The text contains no grammatical errors

Spelling
No spelling errors found.

Punctuation
There are minor punctuation errors, likely incurred by the familiar, conversational tone of the writing. They do not detract from the flow of the text. However, the adding of punctuation would not detract from the meaning or tone and so I see no reason not to add/remediate punctuation.

While the tone of the writing might suggest that punctuation rules be bent, my personal opinion is to model correct punctuation so that it becomes normative. In the example below, the adding of punctuation doesn’t seem to detract from the tone and thus, there is no loss to adding it. Such attempts at tasteful humor (which were effective for me!) are effective so a better option might be to add captions that are visually separated from the text for this “running commentary” as in the example below.

Ex: Whole numbers, Place Value System
"Harpreet had to order one toilet, two sets of taps, three fittings, four braided hoses, and five chocolate bars (it seems like Harpreet has a bit of a sweet tooth)."
Suggestion: “…five chocolate bars. It seems like Harpreet has a bit of a sweet tooth!”

Grammar Rating: 4 out of 5

Q: The text is not culturally insensitive or offensive in any way. It should make use of examples that are inclusive of a variety of races, ethnicities, and backgrounds

Names of people include an effective mix of representation in my view. Harpreet is a ‘main character' in the Whole numbers, Place Value System subsection and Harpreet is later joined by Jamieson, representing a different population, with various employees hired throughout the text and their names varied in ethnicity and perhaps (difficult to tell), gender (Abigail, Hannah & Naomi on page 45). I do question the utility of the character on p.27 who is dressed in a pink dress, attire that would not likely be practical for work in trades.

Humor is a tricky device in content that is consumed via text. I did not find any humor inappropriate, but I am also not 100% I can detect any possible negative impact of any of the humor. For example, would there be any negative impact from the humor below? in "Whole numbers, Place Value System" when the text reads: "Harpreet had to order one toilet, two sets of taps, three fittings, four braided hoses, and five chocolate bars (it seems like Harpreet has a bit of a sweet tooth). I don't detect any, but perhaps someone else would! In

There might be a hint of maths anxiety or a tone of acceptance for the idea that everyone dislikes maths woven into the text. For example, on page 115, "Remember the last time you wrote a test? What percentage did you receive? If you got 30 out of 35, could you calculate the percentage? How about finding out the percentage of students who like math? How would you calculate that number? Percentages are used in many different areas of our lives. For example, we hear about the interest rate or unemployment rate, the percentage of people who prefer hockey over football or the percentage of people who prefer science over math. "

There are also undertones that math is difficult. For example, I found that the idea that decimals are merely another way to write a fraction, and so I am doubtful that they need to be described as a “step up” as they are presented in the Introduction of the text! Percentages are, again, merely another way to write a fraction or a decimal, expressed as an amount “out of” 100. The relative difficulty should not be presented in this way as they are merely equal amounts expressed in different ways. Stating that these topics are an increase in difficulty might be an appeal for empathy, but also might cause unecessary angst.

One example of a missed opportunity for embracing diversity, was found in "Whole numbers, Place Value System" in which the text reads: “The discovery of the number zero was a big step in the history of mathematics. Don’t ask me why, but apparently it was.” This would be a great way to educate about Arabic/Chinese origins of numbers. The “big step” referred to was a big deal - it was the idea of place value (positionality of the numbers). It is succinctly summarized in many online YouTube videos. Could a short video be linked to existing text for those interested? Notably, a chance to integrate Latin roots of many mathematical terms was taken advatage of on page 115 "The word cent is actually Latin for 100". This can be seen as positive or exclusionary because it is a dominant ancient language often associated with academia.

Stereotype
I found, ironically, that there was a sense of “maths is for geeks” sentiment, but that might be because I am sensitive to this. It is such a pervasive attitude, that we use this humor as an assumption that Maths is too geeky to actually be interesting. Since the age group is an impressionable group (I remember feeling that I lived on the geeky side of life as a woman in maths/science) and it really doesn’t help to reinforce the stereotypes in this way, especially since I think we still strive to engage women in trades education.

Cultural Relevance Rating: 4 out of 5

Q: Are there any other comments you would like to make about this book, for example, its appropriateness in a Canadian context or specific updates you think need to be made?

Yes, with a caveat, I recommend this book, particularly for the target audience, due to its clarity; well-edited text; friendly, supportive tone; and realistic opening scenarios for each subsection within the four main sections - Whole Numbers, Fractions, Decimals and Percentages. Tastefully chosen rhetorical questions and scenarios provide a context for the immediate application of each subsection. Learners are guided carefully toward conceptual understanding in a scaffolded way, often in a simple to complex trajectory. For example, adding fractions with common denominators is followed by adding fractions with dissimilar denominators. This lends a sense of logic to the text. I would recommend that future adaptations carry through that strong scaffodling to the other main features of the text - the labelling of the practice questions, the procedural steps delineated in the videos, and the practice quizzes.

The interface and variety of images, practice opportunities and chunked text are generally conducive to learning, and the running commentary on the "main characters" (Harpreet and Jamieson) keeps the conceptual parts of the text closely married to practical applications. At times, decorative images might be substituted for more meaningful, educative images. Once such example is expressing a mixed numeral as an improper fraction such that the equivalence between the two representations can be visually verified.

Thus, my one caveat is that the strong conceptual base that is clearly communicated at the beginning of each subsection needs to be more consistently interwoven into the procedural explanations (practice examples, videos).

Future adaptations may also want to emphasize that fractions, decimals and percents as merely different ways to express the same values throughout the text. Example: 0.5 is 1/2 is 50%. The idea that one of these different ways to express the same values are more or less difficult than the other could be deleted as it might be unnecessarily confounding.

Adapting the text, due to its modularity, would be achievable and would be worth it as the essential content will not likely become irrelevant anytime soon!