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Review of Carnegie Learning's Cognitive Tutor Algebra 1

Carnegie Learning's Algebra 1 curriculum consists of two parts: textbook and software. It is truly a unique curriculum, and unlike anything I've seen before. You can see that a lot of work has gone into creating this product (yet it only costs $99 for home users).

The software is the most innovative part in this curriculum; however the textbook also follows somewhat different ideas and principles than standard algebra textbooks.

The software component is called Cognitive Tutor. It provides the student intelligent practice with everything in Algebra 1 curriculum. The problems that the electronic tutor gives you range from simple simplifying of expressions and equation solvings to modeling of real-world like situations.

It is a "tutor": the software has on-demand hints for all problems that advance from general hints to more specific ones. It is cognitive: the software adapts the problems to the student's performance, and sometimes provides hints for the student ("just-in-time help").

I especially liked the grapher problems in the software. The student is presented with a problem situation from the real world. The questions involve choosing the variables, building an algebraic equation to model the situation, answering questions about specific values of the variables, and making a graph using the Grapher.

The problems require the STUDENT to think what are the quantities that should be chosen as variables, and those are linked to each other (via an algebraic expression). The situations were from the real world, such as work hours/pay or time/distance or packages/price. In each case, the student then makes a graph, thus building his understanding of linear equations and graphs even before the formal chapter about them.


Screenshots from the program

The student either fills in empty boxes, chooses from multiple possible choices, or makes graphs etc. The problems are quite varied. The problems advance step-by-step towards more open-ended ones. For example, when learning equation solving, at first the student only chooses which transformation to do, and the program does it. Then in later problems, the student has to choose the transformation, and do it (type in the transformed equation).

The problems in the software cover the whole scope of an algebra 1 curriculum. See below a few examples. Click the images to enlarge them.

solving linear equations in Carnegie Learning Algebra 1 Cognitive Tutor software
The student chooses which transformation or simplification to apply to the equation. The first step was to use distributive property, which is under "Simplification" menu.
Graphing inequalities in Carnegie Learning Algebra 1 Cognitive Tutor software
The student first chooses which graphing method to use for the boundary lines of each inequality, and the grapher program allows him to graph the lines. That is already done here. Then, the student chooses how the shading is done.
proportion solving in Carnegie Learning Algebra 1 Cognitive Tutor software
The student fills in the boxes to build the proportion from the word problem.
solve linear systems in Carnegie Learning Algebra 1 Cognitive Tutor software
The student chooses a graphing method and graphs the two lines, then the intersection is found.
solving squares and square roots in Carnegie Learning Algebra 1 Cognitive Tutor software
The student finds and models squares and square roots.
height versus time parabola problem in Carnegie Learning Algebra 1 Cognitive Tutor software
This is a real-life situation about shooting a bottle rocket up, but it is a dud and falls back to the ground. The height versus time graph is a parabola.
Learning Pythagorean theorem in Carnegie Learning Algebra 1 Cognitive Tutor software
The student carefully fills in the table the parts of the triangle to study Pythagorean theorem.
Exponential functions in Carnegie Learning Algebra 1 Cognitive Tutor software
A scenario of exponential growth - lilies in a pond that double in area very day.

The textbook

The student is supposed to spend about 40% of learning time with the software, and the rest with problem-solving activities from the textbook, so while reading all the above it might appear to you that the software is the most important part, it is just about equally important with the textbook.

I only saw the first chapter of the printed textbook. It contains extended investigations or problem situations in which the student learns by guided exploration. The problems use real-world situations and they are designed so as to emphasize connections between verbal, numeric, graphic and algebraic representations.

The textbook would be better described as a worktext. It presents you with a scenario, and then problems and questions follow. In between all that are short teaching boxes that explain terms, notation, or concepts. In fact, the explanations may even be in the end of the lesson. In short, all learning is occurring within a context of a real-life problem.

Please click on this link to see a sample lesson from the textbook (PDF).


Considerations when implementing Carnegie Learning Algebra 1 in a homeschool situation

While the program is excellent, I am a bit hesitant to recommend it if the parent does not already know some algebra.

It is different from your "standard" algebra curriculum in two main aspects: because of the software, and because the textbook is based upon investigations instead of plain "lecturing".

These features do make the curriculum excellent and highly commendable! In fact, a parent and a homeschooled student can probably study together and the parent is likely to learn a bunch as well.

However, a parent with weak math background might not be able to guide the student through the explorations. When using open-ended investigations in teaching, the teacher needs to understand beforehand what the investigation is coming to and what are the goals of such instruction. School teachers using this receive several days of training so they understand how to best implement this curriculum.

If you feel you need help in these aspects, consider buying the teacher's guide as well.


What I didn't like

The program makes the student to go through the problems in order, and automatically advances him to the next level when the software determines he is ready. This is good for most students, but can be a constraint as well. However, the teacher can change the student placement manually.

Sometimes I had to stop and think to figure out what the program wanted in which box, or in which order I needed to do things before the program would let me proceed.

In one instance I did not like the mathematical approach: the chapter about proportions. In another place (simplifying rational expressions), I thought the placing of text and of the empty boxes to fill made the whole problem to look very confusing. But the program is in constant development, and little things like that are likely to be changed based on user feedback.



Carnegie Learning Cognitive Tutor Algebra 1. Price: $99 for home users — but you get 10% off with the coupon code HSMNET-10. Teacher's guides $85.
Website: Carnegie Learning Algebra 1.

Review by Maria Miller, MSc, author of HomeschoolMath.net

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