Taking the Problem out of Problem Solving?

By Jacques, Laurie | Mathematics Teaching, December 2005 | Go to article overview

Taking the Problem out of Problem Solving?


Jacques, Laurie, Mathematics Teaching


One of the most refreshing and useful resources to have been published by the national numeracy strategy tor primary teachers has been Mathematical challenges for able pupils in key stage 1 and 2 [1]. The national curriculum for mathematics [2] requires teachers to integrate 'Using and applying mathematics' within the other programmes of study (Number, Shape, space and measures and Data handling). However, the Framework for teaching mathematics from YR to Y6 [3], which was published simultaneously with this revised national curriculum (and is a suggested means of implementing it), lacks guidance on how to embed problem solving into its recommended teaching strategies. Working originally as a Leading Mathematics Teacher and presently as an Advanced Skills Teacher, I find that many primary colleagues still view 'school mathematics' as a sequence of procedures and skills to be taught and the Framework document goes some way to perpetuating this by bolting on 'reasoning about mathematics' as a separate teaching unit each term. This creates a tension when attempting to develop practice so that non-specialist primary teachers can begin to view mathematics as a way of thinking rather than a way of doing. When Mathematical challenges for able pupils was published a few years after the Framework, there was at last a starting point for supporting teachers in this change. My only criticism of the book was the title 'for more able pupils' suggesting that thinking mathematically should be reserved for 'clever' pupils.

The recent drive [4] to return 'creativity' to the primary curriculum has meant that the mathematics team from the Primary National Strategy (PNS) have now begun to consider how this can be done in mathematics. In their wisdom they have chosen to use Mathematical challenges in a structured two-part INSET pack [5] which has been available to schools since last year. The pack includes details for a short staff meeting and a set of teaching resources for each year group. Teachers are invited to try out the resources and discuss outcomes and implications at a further staff meeting.

Case study

The school in which I work has a rapidly rising roll and last year three new teachers joined the team so there was scope for reviewing how pupils learn and how mathematics is taught across the school from YR to Y6. From a specialist's point of view I was very worried about the messages being conveyed about problem solving in the INSET pack. Firstly they attempt to classify problems in order to decide which strategies should be used to solve a problem:

* Finding all possibilities;

* Logic problems;

* Finding rules and describing patterns;

* Diagram problems and visual puzzles;

* Word problems.

Secondly, the guidance suggests that 'specific strategies to solve particular types of problem' (pp5-6) need to be taught. They say 'simply giving children problems is not enough' (p12). I intepreted this as meaning that pupils have to be taught strategies to solve a problem rather than develop them from engaging with problems themselves and from this I wonder how the pupil is problem solving? It seems problem solving has also been made into a sequence of skills to be learned rather than a process of mathematical thinking and taking the problem out of problem solving!

The INSET pack tocused specifically on 'finding all possibilities' problems (eg, see image, right)

These were intended to teach pupils systematic strategies for problem solving. The plans stuck to the traditional three-part lesson structure and most problems included two parts with the second extending the number of possibilities. I he plans also modelled the types of questions that teachers should ask and encouraged collaborative working. I wanted to use the INSET materials in my school to try and gauge how non-specialists might change their practice in the light of the guidance. …

The rest of this article is only available to active members of Questia

Sign up now for a free, 1-day trial and receive full access to:

  • Questia's entire collection
  • Automatic bibliography creation
  • More helpful research tools like notes, citations, and highlights
  • A full archive of books and articles related to this one
  • Ad-free environment

Already a member? Log in now.

Notes for this article

Add a new note
If you are trying to select text to create highlights or citations, remember that you must now click or tap on the first word, and then click or tap on the last word.
One moment ...
Default project is now your active project.
Project items

Items saved from this article

This article has been saved
Highlights (0)
Some of your highlights are legacy items.

Highlights saved before July 30, 2012 will not be displayed on their respective source pages.

You can easily re-create the highlights by opening the book page or article, selecting the text, and clicking “Highlight.”

Citations (0)
Some of your citations are legacy items.

Any citation created before July 30, 2012 will labeled as a “Cited page.” New citations will be saved as cited passages, pages or articles.

We also added the ability to view new citations from your projects or the book or article where you created them.

Notes (0)
Bookmarks (0)

You have no saved items from this article

Project items include:
  • Saved book/article
  • Highlights
  • Quotes/citations
  • Notes
  • Bookmarks
Notes
Cite this article

Cited article

Style
Citations are available only to our active members.
Sign up now to cite pages or passages in MLA, APA and Chicago citation styles.

(Einhorn, 1992, p. 25)

(Einhorn 25)

1

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

Cited article

Taking the Problem out of Problem Solving?
Settings

Settings

Typeface
Text size Smaller Larger Reset View mode
Search within

Search within this article

Look up

Look up a word

  • Dictionary
  • Thesaurus
Please submit a word or phrase above.
Print this page

Print this page

Why can't I print more than one page at a time?

Help
Full screen

matching results for page

    Questia reader help

    How to highlight and cite specific passages

    1. Click or tap the first word you want to select.
    2. Click or tap the last word you want to select, and you’ll see everything in between get selected.
    3. You’ll then get a menu of options like creating a highlight or a citation from that passage of text.

    OK, got it!

    Cited passage

    Style
    Citations are available only to our active members.
    Sign up now to cite pages or passages in MLA, APA and Chicago citation styles.

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn, 1992, p. 25).

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn 25)

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences."1

    1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

    Cited passage

    Thanks for trying Questia!

    Please continue trying out our research tools, but please note, full functionality is available only to our active members.

    Your work will be lost once you leave this Web page.

    For full access in an ad-free environment, sign up now for a FREE, 1-day trial.

    Already a member? Log in now.