{"id":4874,"date":"2018-02-01T03:40:32","date_gmt":"2018-02-01T10:40:32","guid":{"rendered":"https:\/\/blogs.ubc.ca\/stem2018\/?p=4874"},"modified":"2018-02-01T04:40:44","modified_gmt":"2018-02-01T11:40:44","slug":"grasp-tpack","status":"publish","type":"post","link":"https:\/\/blogs.ubc.ca\/stem2018\/2018\/02\/01\/grasp-tpack\/","title":{"rendered":"GRASP & TPACK"},"content":{"rendered":"

\u201cNew comprehension does not automatically occur, even after evaluation and reflection. Specific strategies for documentation, analysis, and discussion are needed.\u201d (Shulman, 1987, p.19)<\/p><\/blockquote>\n

This quote is crucial to evaluating mathematical word problem solving skills. Students require direct instructions to support the development to skilfully extract information from word problems, identify missing attributes, select most approach analytical method and compute and make sounded conclusions. GRASP is an explicit metacognitive strategy that trains learners to effortlessly process word problems.<\/p>\n

Using the GRASP Method to teach word problem solving skills <\/strong><\/p>\n

What is GRASP? <\/strong><\/p>\n

GRASP is a strategy to solve mathematical word problems. Below is the one of the many definitions of GRASP.<\/p>\n

G<\/strong> – Give Information (i.e. operation signal words\/ phrases)<\/p>\n

Students are to extract information from a given word problem.<\/p>\n

R<\/strong> – Required Information<\/p>\n

Students are to identify parts that need to be solved.<\/p>\n

A<\/strong> \u2013 Analyze (i.e. mathematical strategies)<\/p>\n

Students are to select appropriate strategy (or strategies) to develop an answer.<\/p>\n

S<\/strong> \u2013 Solve the question (i.e. computation)<\/p>\n

Students are to use the select strategy (or strategies) to solve the question.<\/p>\n

P <\/strong>– Paraphrase the answer<\/p>\n

Students are to communicate their answer in a way that solves the problem.<\/p>\n

 <\/p>\n

Pedagogical Knowledge <\/strong><\/p>\n

Pedagogically, the GRASP method is a suitable framework to teach students how to solve word problems because this strategies shows thinking processes. The method helps make thinking visible by asking students to isolate and document components of the word problems. Linn (2000) believes that making thinking visible makes the metacogntive processes inspectable. In the case of GRASP, students can reflect upon their work and inspect the areas that led to an erroneous answer. For example, if it were a computation error, the analysis part would contain mistakes.<\/p>\n

Teachers can clearly insepect how a student comprehends authentic word problems. Since students have to mindfully select appropriate analysis strategies based on given information, it mobilizes an integrated understanding of problem solving strategies. Moreover, authentic word problems make comprehension and problem solving accessible and relatable. Students are also more motivated to solve problems that were created by their peers.<\/p>\n

Additionally, this strategy requires teaching practices such as scaffolding and modeling. Without this pedagogical strategy, students fail to independently apply the GRASP method. It is best to model as a whole class demonstration. Here, one can employ the cognitive apprenticeship. This pedagogical design helps foster problem-solving success by providing independent practice time. Moreover, this pedagogical awareness and experience helps promoting lifelong mathematical learning and success by installing a plausible approach to solve word problems.<\/p>\n

Another pedgagoical consideration is about differentiation. The GRASP method enables all learners to find success in solving word problems. Some students find that advance operations (i.e. multiplication and division) are easy. In contrast, some students require direct operational signals to solve problems. This problem-solving approach allows educators to differentiate for slow or excelling learners. For example, teachers can modify the wording, include computation choices and provide sentence starters to fit the needs of their learners. Nonetheless, this depends on how well educators know about their students\u2019 needs and strategies to support the needs.<\/p>\n

\u00a0<\/strong><\/p>\n

Content knowledge<\/strong><\/p>\n

Shulman (1987) suggests that teachers serve \u201cas the primary source of students understanding of content knowledge\u201d (p.9). In the case of GRASP, teacher\u2019s knowledge of signal words (i.e. math words and phrases that signals operations) and age-appropriate problems solving strategies influence how successful GRASP is. Explicit teaching of math vocabulary and computation strategies is key. Educators should be able to help students develop a strong repertoire of this knowledge. In this instant, educators need to develop content rich anchor charts to supplement students\u2019 understanding of computation strategies and words that signal specific operations. Students also benefit when they are front-loaded with this information. These ideas are consistent with Shulman\u2019s (1987) emphasis on the importance of teacher\u2019s content knowledge. Without building a strong foundation of words and strategies, students fail to employ the GRASP method on more challenging word problems. Learners may also lack skills to develop their own problems.<\/p>\n

 <\/p>\n

GRASP & Technology<\/strong><\/p>\n

Although GRASP can be used without technology, simple word-processing knowledge would be beneficial. Educators can make set word problems more organized and attractive by printing off typed word problems and adding pictures. Additionally, to demonstrate that some problems are differentiated, teachers can place a picture on the opposite side.<\/p>\n

Another key advantage of using the GRASP method is that educators can analysis the isolated parts of the word-problem solving process. Educators can digitally document students\u2019 area of strength and or weakness. More specifically, teachers require higher digital competency to code an Excel sheet to automatically map student data and the evolving performance trends. For example, after values are imputed, the Excel can use color to highlight consistent errors and populate other visuals to show trends for student performance.<\/p>\n

For learners, the computation part the GRASP can be digitized. For example, as students use GRASP, they can replace writing and drawing via technical means. More specifically, students can use Excel to make a graph or use Google drawing to visualize and manipulate variables to improve computation efficiency and accuracy. This is consistent with Jonassen\u2019s (2000) claim. He believes that \u201cthat the most productive roles for media are as computation and memory tools for off-loading unproductive cognitive task that may interfere with knowledge construction by the learner.\u201d (Jonassen 2000, p.33) Furthermore, students can also discuss their GRASP methods on student forums to extend their and extend their thinking.<\/p>\n

Food for thought<\/strong><\/p>\n

In Mishra & Koehler (2006), although the overlapping circles appeal to be a useful method to talk about integrating these different types of knowledge, it may not accurately represent the extent of each type of knowledge. Rather, a power map may provide more information. In a sense, each example has its own power map. Here is what the GRASP model may look like:<\/p>\n

\"\"<\/p>\n

Visibly, the success of GRASP relies heavily on pedagogical and content knowledge.<\/p>\n

A follow up question is how educators evaluate whether this is a \u2018good\u2019 mix of Msihra & Koehler\u2019s idea of TPACK? Are these variations dependent of content?<\/p>\n

 <\/p>\n

References <\/strong><\/p>\n

Mishra, P., & Koehler, M. J. (2006). Technological pedagogical content knowledge: A framework for teacher knowledge. Teachers college record, 108<\/em>(6), 1017.<\/p>\n

Jonassen, D. H. (2000). Computers as mindtools for schools, 2nd Ed. Upper Saddle River, NJ: Merrill\/ Prentice Hall. Retrieved from Google Scholar:\u00a0http:\/\/scholar.google.com\/scholar?q=Jonassen+mindtools&ie=UTF-8&oe=UTF-8&hl=en&btnG=Search<\/p>\n

Linn, M.C. (2000). Designing the knowledge integration environment.\u00a0International Journal of Science Education, 22<\/em>(8), 781-796.<\/p>\n

Shulman, L.S. (1987). Knowledge and teaching. The foundations of a new reform.\u00a0Harvard Educational Review, 57<\/em>(1)1-23.<\/p>\n","protected":false},"excerpt":{"rendered":"

\u201cNew comprehension does not automatically occur, even after evaluation and reflection. Specific strategies for documentation, analysis, and discussion are needed.\u201d (Shulman, 1987, p.19) This quote is crucial to evaluating mathematical word problem solving skills. Students require direct instructions to support the development to skilfully extract information from word problems, identify missing attributes, select most approach […]<\/p>\n","protected":false},"author":18709,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1669398],"tags":[],"class_list":["post-4874","post","type-post","status-publish","format-standard","hentry","category-b-pck"],"_links":{"self":[{"href":"https:\/\/blogs.ubc.ca\/stem2018\/wp-json\/wp\/v2\/posts\/4874","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.ubc.ca\/stem2018\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.ubc.ca\/stem2018\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.ubc.ca\/stem2018\/wp-json\/wp\/v2\/users\/18709"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.ubc.ca\/stem2018\/wp-json\/wp\/v2\/comments?post=4874"}],"version-history":[{"count":2,"href":"https:\/\/blogs.ubc.ca\/stem2018\/wp-json\/wp\/v2\/posts\/4874\/revisions"}],"predecessor-version":[{"id":4877,"href":"https:\/\/blogs.ubc.ca\/stem2018\/wp-json\/wp\/v2\/posts\/4874\/revisions\/4877"}],"wp:attachment":[{"href":"https:\/\/blogs.ubc.ca\/stem2018\/wp-json\/wp\/v2\/media?parent=4874"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ubc.ca\/stem2018\/wp-json\/wp\/v2\/categories?post=4874"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ubc.ca\/stem2018\/wp-json\/wp\/v2\/tags?post=4874"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}