PBL

Improving Math Problem Solving Skills: Anchored Instruction

ANCHORED INSTRUCTION

Anchored instruction is an idea that purportes the necessity to “anchor” learned ideas, especially in the realm of mathematics, to real-world ideas. Students and teachers “engage [in] problem-rich environments that allow sustained exploration” (Cognition and Technology Group at Vanderbilt, 1992). The idea behind anchored instruction stems from constructivist pedagogy, and is intended not to increase computational skills in students but rather to improve problem solving skills in real world situations. It’s the difference between

25 x 3

and

Frederick has 25 potatoes on his farm. He grows his potatoes for 4 more months and triples his number of potatoes. How many potatoes does he have now?

The first is computational, and the second is problem solving.




Is Anchored Instruction a Good Thing?

Anchored instruction necessitates a change in pedagogical style, and with it, a change in the way that we assess and teach. Anchored instruction is a part of the “Guide on the Side” vs. “Sage on the Stage” movement popularized by Alison King (1993). Rather than instructing up front in a lecture style, anchored instruction puts students into “real world”, or at the least certainly more authentic, problems than if students were to complete worksheet upon worksheet of math problems. Complex, real world problems are not overly difficult to create for students either. Anchored instruction methods are highly collaborative, problem-solving based, and have more than one “right” answer.

Jasper Adventures: An Anchored Instruction Example

Up until now, we have only talked about how amazing anchored instruction can be, without much evidence to back up these claims. Let’s take a look at Hickey, Moore, and Pellegrino’s study of the “Jasper Adventures”, a video anchored instructional mathematics series from the 80’s (more information here).

The long and short, Jasper had 12 video “adventures” that students would watch. While watching, students would hear facts and figures as a part of the story that they would need to use to solve a final problem posed at the end of the video. Jasper was based on the idea that students needed to become independent thinkers, rather than only being able to regurgitate mathematics proofs and formulas (Cognition and Technology Group at Vanderbilt, 1992). Jasper seeks to make learning relevant, instead of creating inert knowledge.

Inert Knowledge: Knowledge that is not used spontaneously, even though it is relevant
— Bransford et. al., 1986; Gick & Holyoak, 1980, 1983; Scardamalia & Bereiter, 1985)
 

Overview of Hickey, Moore, and Pellegrino

  • A quasi-experimental design in which the authors studied 19, fifth grade classrooms from two well-matched schools.

  • One school was higher in socioeconomic status (SES), the other in low.

  • Half the classes used Jasper materials, half did not.

  • Classes were split into “more consistent” use of new reform mathematics curriculum encouraging research based practices, or “less consistent” to the new reformed curriculum. (USA National Council of Teachers of Mathematics (NCTM) curricular standards)

  • Had 4 groupings to study:

    1. High SES and more consistent classrooms using Jasper

    2. High SES and less consistent classrooms

    3. Low SES and more consistent classrooms using Jasper

    4. Low SES and less consistent classrooms

  • I found their research parameters and practices sufficiently rigorous in its methods. However, as always, be sure to check out the research for yourself. The research generalizability should be relatively high for other high and low SES classrooms in the united states and similar countries, and provides strong support for using constructivist style practices in mathematics education.

Research Goals

(a) consider student subjective motivational experiences,

(b) study a large-scale implementation that was initiated and carried out by the school system

(c) using newer ostensibly more appropriate standardized achievement measures

d) comparing consequences in classrooms that are more consistent and less consistent with the broader curricular reforms [NCTM & Jasper]

(e) comparing consequences in higher-achieving, high-socioeconomic status (SES) classrooms and lower achieving, low-SES classrooms (2001. pp. 615)

Main Findings

  • Teachers using Jasper materials had goals to use mathematics to solve real world problems, but did not define using collaborative methods as a goal (despite allowing for more collaboration in their classes).

“ All six of these Jasper teachers listed their first (or only) goal for the activities as something like "showing students how math problem solving is useful in the real world." Meanwhile, none alluded to the broader goal of supporting extended collaborative investigation around complex problems” (p. 634)

  • Increased Problem solving skills in students using anchored instructional methods.

“The mathematical achievement results in the area of problem solving and data interpretation clearly showed that the Jasper instructional implementation had very desirable consequences, with no evidence of negative consequences.” (2001, p. 648)

“ In other words, the scores in every Jasper classroom increased while the scores in every non-Jasper classroom stayed the same or went down slightly” (p. 638)

  • Improved conceptual knowledge and estimation skills were limited to high SES Jasper classrooms, not low SES classrooms.

  • High SES students using Jasper report lower subjective competence in mathematics than non-Jasper students. The researchers note that this is most likely this is due to the highly complex, challenging, and novel ideas of the Jasper activities. Low SES students reported increased subjective competence in mathematics.

  • Low SES students had more positive outlooks on mathematics education.

  • High SES students perceived the Jasper activities as “effectively delay[ing] their progress through [the] levels of curriculum” (p. 637).

  • Support against the idea that lower achieving students will not be able to handle high levels of complexity in problem solving style mathematics problems and are better served with traditional mathematics teaching methods. Using Jasper materials with lower SES students:

“supports the argument that academically disadvantaged students can profit from the complex problem-solving activities associated with the Jasper materials and that such students do not suffer negative academic or motivational consequence".” (2001, p. 648)

Conclusion

Given the above evidence, it seems clear, at least in the continental USA, that there is strong support for the idea that anchored instruction improves mathematics abilities in grade 5 students. The question now becomes, how can we, as educators, best incorporate anchored styles of instruction into our own practice, and how much time should we spend teaching a skill before sending students off to problem solve? Should we teach the skill parallel as students need for the skill arises, or should we front load this instruction?

REFERENCES

Cognition and Technology Group at Vanderbilt, (1992). The Jasper Experiment: An Exploration of Issues in Learning and Instructional Design, Educational Technology Research and Development, Vol. 40, No. 1, pp. 65-80. Retrieved from: http://www.jstor.org/stable/30219998

Daniel T. Hickey, Allison L. Moore and James W. Pellegrino, (2001). The Motivational and Academic Consequences of Elementary Mathematics Environments: Do Constructivist Innovations and Reforms Make a Difference? American Educational Research Journal, Vol. 38, No. 3 (Autumn, 2001), pp. 611-652. Retrieved from: http://www.jstor.org/stable/3202494

King, A., (1993). From Sage on the Stage to Guide on the Side, college Teaching, Vol 41, No. 1 (Winter, 1993). pp. 30-35. Retrieved from: http://www.jstor.org/stable/27558571?origin=JSTOR-pdf