An Introduction to the Developmental Mathematics

Collection: A Collection of Teaching Resources for the

Mathematics Pathway of the National Science Digital Library

LACCD Math Summit, March 11th

Bohdan Rhodehamel, bohdanr561@yahoo.com

Overview

The Developmental Mathematics Collection, National Science Digital Library, and the MathDL

Knowledge Exchange vs. Library

A Tour of the DMC

Reviewing Resources

What is the National Science Digital Library (NSDL)?

NSDL is the Nation's online library for education and research inScience, Technology, Engineering, Mathematics. (NSDL.org)

What is the National Science Digital Library (NSDL)?

The NSDL contains pathways which are projects that provide audience-specific NSDL resources and services to broad categories of users. Each Pathway may contain various collections. The Developmental Mathematics Collection (DMC) is a collection of the MathDL Pathway.

NSDLPathways

MathDL

DMCOther Collections:• MathDL Loci• National

Curve Bank• Etc.

http://mathdl.maa.org/

Perceptuomotor learning as a process of integrating perceptual and motor aspects of experience into a unified whole

Perceptuomotor integration is a key aspect of fluency in many other domains, including playing a musical instrument and participating in sports

We argue that, just as perceptuomotor integration is needed to fluently play a musical instrument, it is also an important – but neglected - element in playing mathematical instruments (compass and straight-edge, pencil and paper, an interactive museum exhibit, and so on)

The DMC is not a typical collection The DMC is supported and “fed” by Knowledge Exchange

Networks

KEN vs. Library

A library tends to be more static than a KEN. A place for storage and retrieval of resources.

A KEN stores resources, but the emphasis is on dynamic interaction and sharing of knowledge among users. Users don’t just retrieve resources and leave.

• They contribute to the adaptation and refinement of resources as an iterative process

• Provide feedback about successful (and unsuccessful) implementations of activities

• Collaborate on projects (across physical spaces teachers might not ordinarily interact)

What Knowledge Exchange activities do faculty find valuable?

Hosted on the open source platform, Curriki.org(curriculum + wiki)

A Tour of the DMC

A central site for the DMC is coming in May…For now we’ll visit the San Diego site (tinyurl.com/sakedevmath)

• Welcome page• Curriculum tab• Course folders

• Activities for students• Topic teaching plans• Technology enhanced learning and teaching• Course and curriculum designs

Promoting Resources From Regional Exchanges to the National Collection

Reviews are one mechanism by which a resource may be promoted.

• What do you think of the criteria in the review rubric?

• What would you add, remove, change?

• What, if any, information would you be interested in seeing as an instructor looking for activities to use in class?

NotesThis instructor-guided activity is used as a review of linear equations as well as an introduction (or re-introduction in Math 96) to systems of equations. It assumes some knowledge of graphing, slope, y-intercept, etc..I find it more meaningful to use actual values and let the students use calculators (if they need them) instead of using integers and losing the realism.

Procedure:Students will be presented with two different gas stations, and will have to come up with equations to determine the price of gas at each. They will do this by first calculating a few values, then using that process to come up with a general equation for each. The equations will be graphed in order to see the “break-even point”, and this will be followed by a discussion of methods for finding solutions to systems of equations.

Modeling Gas PricesYou stop at the next intersection to get gas and find two gas stations across the street from each other. At the Valero station, the cheap stuff is $2.93 per gallon. Across the way at the Arco station, you see that it is $2.79 per gallon, but you remember that they also charge a $0.45 convenience fee for using your debit card. In groups of 3-4, your job will be to figure out which gas station would give you a cheaper fill-up. To help with this, calculate how much it would be for different gallon amounts. Start with 1, 2, and 5 gallons. Suppose we wanted to find out the price at each gas station for any amount of gas, g. Come up with an equation for Valero and one for Arco. To help with this, think about how you calculated the dollar amount in the chart above. To complete the picture, let’s graph each equation on the same set of axes. What information will the x-axis represent? What information will the y-axis represent? Identify the slope and y-intercept of each equation, then graph eachone. Don’t forget to label each line so you can tell which is which.

NAME: Modeling Gas PricesDONE_IN_CLASSROOM: NoENGAGE: Very effectiveENGAGE_COMMENT: This seems to have the potential to interest students. It has relevancy: this is a situation they have most likely encountered and might be curious to see how it is approached in the classroom.CURIOSITY: Somewhat EffectiveCURIOSITY_COMMENTS: Again, I think the potential is there. The teacher could prompt the students to think about what other situations they have encountered outside of the classroom that may be modeled/ made-sense-of using linear modeling.MASTERY: Somewhat EffectiveMASTERY_COMMENTS: I would raise this score if students were asked explicitly to interpret the slopes and y-intercepts in terms of the context, and if there were prompts to generalize this process to other contexts.PROGRESSIVE_DIFFICULTY: Somewhat EffectiveDIFFICULTY_COMMENTS:CRITICAL_THINKING: Somewhat EffectiveCRITICAL_THINKING_COMMENTS: As mentioned above, I'd like slope and intercepts to be discussed in terms of the context.DIFFICULTY_LEVEL: Very appropriateDECISION: yesGENERAL_COMMENTS: I like this activity, and with a few quick changes (like those I mentioned above) it could be improved more.

Feedback

What topics and content would you like to see?

Have a look around: tinyurl.com/lakedevmath (LA) tinyurl.com/sakedevmath (San

Diego) tinyurl.com/bakedevmath (Bay Area)