Life-Long-Learners

When I taught middle years Mathematics, I found myself intrigued by the different ways students solved puzzles. Classic puzzles, such as the following problem, use letters to represent numbers which can be displayed as simple calculation problems in disguise. One must replace each letter by a single 0 to 9 digit. The same digit must be used to represent the same letter. So, if you believe that 4 is being used to represent the letter A, then 4 must be used for all A’s in the same problem. Of course, one must use a different digit for different letters. After one substitutes all the letters for the numbers, a perfectly valid calculation problem will result.

Although some students might approach the problem using a “brute-force” method in which guesswork was employed, I was fascinated by those who approached the problem logically or employed a variety of strategies. I found that it was wise to provide my students with an opportunity to share with the class what assumptions were made and what strategies were used. For example, most would try to solve the above puzzle as shown in its subtraction format. However, some students found this puzzle easier to solve when the problem was rewritten in its corresponding addition format. Such “working backwards” is an effective strategy for solving problems and one that works well in this case. In addition, unlike most mathematical problems where there is only one correct answer, I encouraged students to see if they were able to find more than one series of letter substitutions that would solve each particular puzzle problem.

Excel Spreadsheet Format:
In the January, 2001 issue of “Bits and Bytes”, I wrote an article entitled “Spreadsheets: A Problem Solving Puzzle Creator“. This extensive article, provided the reader with insights into how I designed the spreadsheet component using Microsoft “Works” to create problems such as the above. Recently, I decided to improve and upgrade these same six problems so that they could be used by those readers using the 2007 (or later versions) of Microsoft Office. Educators may download a single Excel 2007 workbook which contains each of the six puzzles as individual worksheets at the end of this blog post.

Word Document Format:
As an educator, I wanted to provide students with an opportunity to identify the hunches and strategies that they used when attempting to solve these problem/puzzles. In order to facilitate this important documentation step, I created a Word document containing each puzzle as an embedded spreadsheet followed by a “What I/we learned” portion at the bottom of the page where students could list the various steps and strategies they took in solving a particular problem. The individual six Word problem/puzzles can be downloaded as “freebies” at the end of this article.

Suggested Lesson Steps:
I would use the following Word puzzle activities in the following manner:

1.  Divide up the classroom into teams consisting of two or three students of similar abilities. I believe that the collaborative interaction in the team approach, as well as a reflective “What I/we learned?” nature of this project gives the best results for learning. Since the puzzles are arranged in order by relative difficulty, I would assign particular puzzles to challenge teams while providing a “best-fit” scenario.

2. Make a backup of all Word document puzzles (and keep them in a safe place) in case student puzzles get saved over the originals.

3. Transfer a copy of each Word document puzzle to a computer server drive location to which the students have access.

4. Open the first Word Puzzle #1 (ONE + ONE = TWO) on a workstation and project the image onto a screen so the entire class can see how the activity will work.

5. Demonstrate where team members will enter their names at the top of the document and stress that student teams must frequently save their progress using a file name format and drive location with which they are familiar.

6. Stress the need to document the team strategies and hunches and have students in class suggest why certain letters can take on certain values. For the initial demonstration, I would only choose values for E within the range 1-4 so that there is no need to carry over a 1 to the adjacent column. You might ask students if E could take on the value of 5 and to explain their rational to support their decision. Likewise, why can E not equal zero?

7. Before attempting to activate the spreadsheet component, enter a few of the class suggestions in the “What I/we learned” area at the bottom of the page and save the Word document (using the agreed upon location and file name convention). Possible sample comments can be viewed by clicking on the image near the end of this article.

8. Demonstrate how the embedded spreadsheet is activated by double-clicking within the yellow frame. Inform students that one will know that the spreadsheet is activated when the Excel column letters and row numbers appear along the top and left hand edge.

9. When the embedded spreadsheet is activated, one can position the mouse over the red-coloured “DIRECTIONS” link to review the puzzle-solving process.

10. Using the suggestions and the strategies listed by the students, enter a value for E in the “Guess & Test Area” and observe the changes in the “Results Area”. Remind students that the <Enter> key must be pressed after inserting any value into the “Guess & Test Area”.

11. Students must regularly update and enter strategies at the bottom of the Word document by deactivating the spreadsheet. To do so, one must click outside the yellow framed embedded spreadsheet. When the spreadsheet column letters and row numbers disappear, one is now in the Word document format.

WARNING: Sometimes when one returns to the Word document, the yellow frame disappears or is not completely displayed. If this happens, students must immediately click on the “Undo Object” (the “reverse arrow”) button or enter the <Ctrl-Z> keystroke combination. This “undo” step will always recover the original Word document display with the complete yellow framed puzzle/problem and team comments at the bottom.

12. Remind students to take turns so that different team members alternate tasks between entering strategies and hunches at the bottom of the Word document and activating the spreadsheet component to enter another letter value to observe the results and progress.

13. Continue with the demonstration on Puzzle #1 until the spreadsheet feedback area finally displays “CORRECT!”

14. Return to the Word document (using the Undo process) to re-draw the Word document and finish entering any additional strategies or hunches that the class agrees upon. Remind the class that it is important that students not only document strategies that worked but also hunches that need more refinement. Stress that we often learn more from our failures than our successes.

15. Invite students to suggest whether Puzzle #1 can have other solutions. Discuss such possibilities, without demonstration, particularly if you wish to use this puzzle with a team as an easier entry into this activity.

16. Save the Word document, one last time, and demonstrate how you wish this completed Word puzzle file to be submitted to the teacher.

17. Now ask the students to arrange themselves into the teams that you have chosen and advise each team which puzzle is their responsibility. Select a particular member of each team to open their assigned Word document puzzle.

18. Instruct another team member to enter their team or individual names at the top of the Word document puzzle and save this named document in an appropriate location using their student names as a file identifier.

19. If one of your teams is working on Puzzle #1 (which was used during the demonstration) tell these team members that they have to find a different solution than the one that was demonstrated.

20. Direct team members to examine their puzzle (in the word processing format) and discuss any beginning steps or strategies that they think might be used to help solve the puzzle. Have a new team member type their initial strategies/thoughts  in the “What I/we learned” area at the bottom and save their team Word puzzle document before proceeding.

21. Ask a new team member, to start the puzzle by double-clicking within the yellow frame to activate the embedded spreadsheet. Remind the teams that the spreadsheet is “activated” when the Excel column letters and row numbers appear along the top and left side boundaries.

22. If necessary, team members can move the mouse over the red-coloured “DIRECTIONS” link, when the spreadsheet is activated.

23. Have each student, in turn, enter a value in the “Guess & Test Area” and observe the results in the “Results Area”.

24. Frequently remind teams, to return to update their strategies at the bottom of the Word document. To do so, one must click outside the yellow frame to deactivate the spreadsheet. Once the spreadsheet column letters and row numbers disappear, one may update the strategies and hunches at the bottom of the Word document. Remind students that if they return to the Word format (where no Excel column or row indicators are displayed) and the yellow frame spreadsheet does not display properly, one must immediately click the “Undo Object” (reverse arrow) or enter the <Ctrl-Z> keystroke combination to recover the Word document without any distortion.

25. Have students alternate between activating the spreadsheet, entering the next number, observing the results, returning to the Word document (using the “Undo” process to re-draw the Word document) and refining or typing in the new hunch or strategy to be tested.

26. Once the problem/puzzle feedback indicates that the team is “CORRECT!”, have the team complete the “What I/we learned … Area”, save the final version of the Word document, and transfer the resulting Word document to the teacher.

27. After finding their first solution, suggest that student teams, re-open the same puzzle, repeat the same steps to see if they can find more than one solution to their particular problem or to determine if their solution unique.

28. This problem solving activity could be used again by ensuring that different puzzles were assigned to different teams.

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Sample Team Word Document

< Click the above image to view the display in a larger format. >

Freebie Downloads:

• EXCEL PUZZLES (#1- #6) WORKBOOK (Excel format)
• PUZZLE #1 ~ ONE + ONE = TWO (Word format)
• PUZZLE #2 ~ TWO – ONE = ONE (Word format)
• PUZZLE #3 ~ SEND + MORE = MONEY (Word format)
• PUZZLE #4 ~ SPEND – MORE = MONEY (Word format)
• PUZZLE #5 ~ SANTA – CLAUS = XMAS (Word format)
• PUZZLE #6 ~ THIS + IS +VERY = EASY (Word format)
  

Take care & keep smiling

At this time of year, many educators are looking for review projects or activities that will really engage their students. In addition, many teachers know that using technology can help students review concepts in all subjects as well as meet the descriptors that are identified in Manitoba Education’s Literacy with Information and Communication Technology (LwICT) developmental continuum.

I thought that I might challenge students to demonstrate, through the LwICT “Produce to Show Understanding” Big Idea that they really understand a particular concept or unit of study. However, rather than write the traditional essay or report, I want students to exercise their brain and use the Audacity (open source, free audio editor and recorder) application to create personal “review song” lyrics. In order to demonstrate this process, I decided to summarize and review Manitoba Education’s LwICT Across the Curriculum by creating a poem set to music. On-line readers can hear my “ICT-Rap” and view the lyrics by clicking on the appropriate hyper-links. I am sure that with the basic steps below, students will be soon generating exceptional musical compositions as a review mechanism.

The basic steps begin with finding a freeware background music track which can be, optionally, loaded into Audacity. One can then play this background loop while using a microphone to record the lyrics to your song. Although one can spend more time experimenting with the various effects in Audacity, one can simply save the lyrics and background musical loop as a blended MP3 file and celebrate your learning.

1. I went to the “loops” section of the Flash Kit web site at: http://www.flashkit.com/loops/

2. I searched for “free loops” and scrolled down the resulting pages and listened to the various samples by pressing the “play” button in the Flashtrak Console.

3. Once I found a free loop, that I thought would provide my song with an appropriate background, I downloaded it in an MP3 format. For example, on-line readers can click on “What_You_Gonna_do” to hear the free loop created by PlayaJayCee. I downloaded this MP3 background loop as the start of my ICT rap.

4. Next I started Audacity. I clicked on Audacity’s File > Open menu items and navigated to the folder where I had previously stored my “What_You_Gonna_do” MP3 loop. When this 8 beat loop is opened in Audacity, it appears on the top track with a 10 second duration. Next, one has to repeat the background loop to accommodate the number of verses in the “review song”. To do so, click the Edit > Select > All menu items to highlight the entire loop and the click Edit > Copy to store the loop in memory. Next one must place the cursor at the end of the selection and press the Edit > Paste menu items to extend the background audio track. The instructions in this previous sentence must be repeated as necessary to accommodate the lyrics or verses that are to be included. The newer version of Audacity (1.2.6) has a special “Play” feature as shown. One can hold down the <Shift> key while pressing the “Play” button to have the loop or song automatically repeat. However, one cannot record any additional narration while this “Shift/Play” button is depressed or in “loop play” mode.

5. Now press the File > Save Project As menu items and store this “work in progress” file (e.g. audio-track.aup) in an appropriate folder as an Audacity’s AUP program file.

6. At this point you will want to create lyrics or a series of verses which summarize the project or concept that you are reviewing. I find that because my background audio track is an 8 beat loop, I type my lyrics into Word making certain that the words adhere to this 8 beat timing structure. Save and print up the lyrics for the up-coming “voice over” narration portion.

7. Next we need to set a preference in Audacity. Click on the Edit > Preferences menu items. On the Audacity Preferences display, click the “Audio I/O” tab, and click to place a checkmark to the left of “Play other tracks while recording new one”. Click the “OK” button to proceed.

8. Insert the microphone into the computer and position your lyrics printed page so that you can begin the “voice over” narration. Press the left-most “Skip to Start” button to make certain that the cursor is positioned at the start of the background loop. Press the reddish “Record” button and begin listening to the background loop. Let the loop play though once before adding you own lyrics to the mix. You will note that your “voice over” narration automatically is displayed as an additional audio track below the loop background music. Adjust the speaker and microphone sliders, immediately located below Audacity’s buttons, as appropriate.

9. Press the File > Save Project As menu terms and store this “work in progress” in an appropriate folder with “version number” filenames ending in V1.AUP, V2.AUP, V3.AUP (e.g. History-Review-V1.AUP) to keep track of various attempts.

10. Undoubtedly you will not be able to record your entire “review song” at one sitting. Make certain that you save any “work in progress” as an Audacity project as noted above. Later, when you return to work, start Audacity. Select the File > Open menu items, navigate to the appropriate folder where you last stored your Audacity AUP project file, select it and click the “Open” button.

11. If you have time, you can explore the various effects that can be applied to your “review song”.  Audacity has an extensive “Help” file and the addtitional resources identified at the end of this article may be helpful as well.

12. When satisfied that the creation is finished, save the project one last time. Before exiting, make certain that one selects the File > Export as MP3 menu items and save the “review song” in a compressed MP3 format which will automatically blend all the tracks together.

12. After all students have played their “review songs” for their peers, provide a process where all students’ review projects can be accessed and listened to for studying purposes. Students who are aural learners may benefit from their colleagues’ “review songs” and find such a depository of audio files quite helpful.

13. Lastly, I encourage you, the reader, to provide feedback to this article by sharing your experience using Audacity to produce a “review song” as another mechanism for students to demonstrate understanding of a concept or unit of study.

Take care & keep smiling

Resources:

• Audacity Tip Sheet at: http://www.scribd.com/doc/28905901/Audacity-Tip-Sheet
• 21st Century School Teacher Tips Sheets (Audacity Tips & Recording in Audacity) at: http://www.21stcenturyschoolteacher.com/tip-sheets.html
• Technology Integration – New Prague Schools – Audacity Tip Sheet at: http://www.np.k12.mn.us/TechIntegration/tipsheets/Software/Audacity/Audacity.doc
• “Super Fast Guide to Audio Editing” by Mindy McAdams at: http://www.jtoolkit.com/audio/Audacity_Guide.pdf

Credit: This blog entry is an updated version of an earlier article entitled “An ICT Christmas gift with lots of rappin’” which was first published in my “Bits and Bytes” educational newsletter in December, 2006.