#### Mathematical Concepts

**Concepts** are the mathematical operations and concepts that students should be able to understand. We can assess our

students' abilities in these Concepts through the Actions that they perform.

The first two categories contain concepts that are widely considered to be crucial for quantitative literacy. **If you are new to QL, start here.**

The next three categories include some concepts that go beyond the middle grades. I include them because I find them particularly useful for thinking through issues in the humanities--and because the humanities can help us to develop the habits of mind that these concepts require.

These two categories are perhaps more geared to mathematics than to QL, but the kinds of thinking they encourage are useful and may inspire creative connections with the humanities:

- Algebraic thinking
- Geometric thinking

Finally, one category is strictly speaking not quantitative at all*, but its emphasis on rational thought makes it worth mentioning here:

- Logical thinking

* Formal logic can be thought of as quantitative, as it involves binaries and algorithms

Not every concept will be easily incorporated into every discipline; personally, I am not yet sure how to incorporate algebraic and geometric thinking, and I haven't developed logical thinking here, but I welcome suggestions and encourage your own development of these categories in relation to the humanities.

### Sources

In keeping with the notion that quantitative literacy is rooted in relatively elementary mathematics, the Concepts come from the Common Core State Standards recently adopted by forty-five states, including Ohio, Kentucky and Indiana, and from the Quantway pathway developed by the Carnegie Foundation (particularly from the course Quantway 2), along with concepts and examples from a number of popular mathematics and statistics books. Therefore, many concepts that are important to more mathematically-oriented disciplines are not included.

At the end of each Concepts section are questions that integrate them with the values, experiences and judgment fostered in the humanities. My hope is that these questions will inspire classroom discussion and spur new ways of thinking.

### Quantitative Concepts and Bloom's Taxonomy

Because the quantitative concepts in QL should have been learned in middle school, **humanities faculty are not expected to introduce them** so much as help students identify when these insights are useful, and demonstrate how to use them.

It may be useful to think about quantitative concepts in relation to Bloom's Taxonomy (the new version):

Although the level of mathematical skill may be at the middle-school level, we expect that students will be able to use these skills for higher-level learning--we expect them to apply, analyze, evaluate and create using quantitative concepts and knowledge and skills from their discipline.

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