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10 Tips for Teaching with an Interactive Whiteboard

Interactive whiteboard technology can enrich the learning and teaching experience. However, using this technology – and using it well – may seem a little overwhelming. These research-based tips will help make its introduction and ongoing use in your classroom easy and effective.

PractisePractise using the board and the software before you use them in a lesson.Let the students explore the board and software and experiment with the functions.PreparePrepare and save activity files before class to reduce in-lesson preparation time. Keep the files where you can easily find and open them.Check that colours and writing size can be seen from the back of the classroom. Ensure that light (natural and artificial) is not affecting visibility. Clean any smudges and dust from the screen and data projector lens.Recalibrate the board before each lesson. Recalibration aligns the touch screen with the image. If the calibration is out, your writing, for example, will appear in a different position to where you touch the screen.Check that students can comfortably reach most of the board.ProceedUse the touch screen, not the computer, to navigate around the software. When you sit behind the computer you are detached from the students. You can better engage with them when you use the touch screen.Make sure there is a purpose to all student–software interaction. Students really see the mathematics when they manipulate the software tools. However, interaction for the sake of interaction distracts from the learning.Pace yourself. The technology increases efficiency, which means you can present the next step in the lesson more quickly (e.g. a comparison number line). Use this time to focus on the teaching and discussion.Use the board and software to their full potential. Think of them as resources for developing questioning and interactive learning, rather than just as tools for presenting information (e.g. leave “gaps” in activity files for the students to discuss and fill in).Bibliography

Actis Ltd. (n.d.). Interactive whiteboards: An approach to an effective methodology. Retrieved January 18, 2007, from http://www.virtuallearning.org.uk/whiteboards/An_approach_to_an_effective_methodology.pdf

Armstrong, V., Barnes, S., Sutherland, R., Curran, S., Mills, S., & Thompson, I. (2005). Collaborative research methodology for investigating teaching and learning: The use of interactive whiteboard technology. Educational Review, 57, 457–469.

Beauchamp, G. (2004). Teacher use of the interactive whiteboard in primary schools: Towards an effective transition framework. Technology, Pedagogy and Education, 13, 327–348.

Hall, I., & Higgins, S. (2005). Primary school students’ perceptions of interactive whiteboards. Journal of Computer Assisted Learning, 21, 102–117

Higgins, S., Beauchamp, G., & Miller, D. (2007). Reviewing the literature on interactive whiteboards. Learning, Media and Technology, 32, 213–225.

Kent, P. (2006). Using interactive whiteboards to enhance maths teaching. Australian Primary Mathematics Classroom, 11, 23–26.

Levy, P. (2002). Interactive whiteboards in learning and teaching in two Sheffield schools: A developmental study. Retrieved January 17, 2007, from http://dis.shef.ac.uk/eirg/projects/wboards.htm

Smith, H.J., Higgins, S., Wall, K., & Miller, J. (2005). Interactive whiteboards: Boon or bandwagon? A critical review of the literature. Journal of Computer Assisted Learning, 21, 91–101.

Wall, K., Higgins, S., & Smith, H. (2005). “The visual helps me understand the complicated things”: Pupil views of teaching and learning with interactive whiteboards. British Journal of Educational Technology, 36, 851–867.

Algebra: 4 Big Ideas

For many, algebra is a confusing jumble of symbols and equations. Until recently, this abstract area of mathematics was first introduced to students in high school, where it was often approached as a set of procedural rules for solving equations (Kilpatrick & Izsák, 2008). Developing algebraic thinking in the early school years provides a solid foundation for later algebra symbol work (Warren, 2008). Teaching children the big ideas (key concepts) of early algebra (Warren, 2008; explained below) through real-world problems helps them understand its rules and applications.

1 Equivalence and Equations

“Equals” means equivalent sets rather than a place to write an answer. Simple real-world problems with unknowns can be represented as equations. Equations remain true (balanced) if the same change occurs to each side. Unknowns can be found using the balance strategy.

2 Patterns and Functions

Operations almost always change an original number to a new number. Simple real-world problems with variables can be represented as “change situations”. “Backtracking” or reversing a change can be used to find unknowns.

3 Properties

Arithmetic properties apply. The commutative law and associative law apply to addition and multiplication but not to subtraction and division. Addition and subtraction are inverse operations, and multiplication and division are inverse operations. Adding or subtracting zero, and multiplying or dividing by 1, leaves the original number unchanged. In certain circumstances, multiplication and division distribute over addition and subtraction.

4 Representations

Different representations (e.g. graphs, tables of values, equations, drawings, everyday language) help with identifying trends and finding and interpreting solutions to real-world problems.

References

Kilpatrick, J., & Izsák, A. (2008). A history of algebra in the school curriculum. In Greenes, C.E. & Rubenstein, R. (Eds.), Algebra and algebraic thinking in school mathematics: Seventieth yearbook (pp. 3–18). Reston, VA: The National Council of Teachers of Mathematics.

Warren, E. (2008). Algebra for all. Brisbane, Australia: ORIGO Education.

Reaction to the Common Core State Standards 1: Carol Findell

In general, this document presents a clear directive for a more consistent, challenging, concise, and connected mathematics curriculum for all students in grades K–12. It does away with the spiraling notion – that if we keep re-teaching the same concept every year, students will eventually “get it”. This is a positive step.While we can debate about the order of topics, or the grade level chosen for any particular topic, the general outline seems sensible and achievable. For example, I was at first upset that I didn’t see algebra as a strand in grades K–5. However, a more careful look found at least four statements about algebraic properties and reasoning in each of these grades.One of the criticisms that I have seen is that the skill development for addition and subtraction is too fast and too short. I maintain that we have not in the past taken time to CAREFULLY develop the concepts needed to maintain skill and fluency. If concepts are developed carefully, AND connected to procedures, procedural fluency will follow.We have consistently underestimated what students can do at early grade levels. I believe that this document sets higher, but achievable goals. It is not perfect, but without something like this, we will not more forward.Carol R. Findell, EdDClinical Associate ProfessorMathematics EducationBoston University

Carol Findell is co-author of two ORIGO series: ZUPELZ and The Think Tank (Problem Solving). You can read reaction to the Common Core standards from co-author Carole Greenes here. These articles are the opinions of the author and do not necessarily reflect the views of ORIGO Education.

Reaction to the Common Core State Standards 2: Carole Greenes

Note: This communication was originally sent to the National Governors Association Center for Best Practices and the Council of Chief State School Officers.

I am in strong support of all efforts to improve the mathematical education of our students, PreK–Grade 12, and endorse many of the ideas in the Common Core. I hope that my comments/suggestions will prompt educators to rethink some of the key ideas, their introduction, and their development across grades.

1. Algebra and Algebraic Reasoning When NCTM released their 2000 Principles and Standards for School Mathematics, I was pleased to see the strengthening and expansion of the algebra strand to Pre-kindergarten. I particularly applauded acknowledgement of the importance of algebra and algebraic reasoning in the PreK–8 sequence as supporting the learning of other domains of mathematics (number, measurement, geometry, probability, and statistics) as well as preparing young learners for the formal study of algebra. The fact that most instructional PreK-8 programs have never offered a well delivered sequence of instruction in algebra is amazing to me. I was hopeful that the Common Core would reinvigorate that important part of mathematics. As I read the Standards, I see no algebra strand, or at the very minimum, a proportional reasoning strand through the early grades.

In the Common Core, the first identification of a major section dealing with algebra is in Grade 6. Before that, there are isolated items that have the special algebra symbol. But the use of that symbol is not consistent. For example, in grades 1, 2, 3 and 4, solving word problems is considered algebra. In other grades, it is considered as part of the problem solving section. Explaining why some of the computational algorithms "work" is considered algebra. But at other times, those same standards are included in sections entitled “work with the base ten system,” “solving problems with addition and subtraction,” or “operations on fractions.” From reading those standards with the algebra symbol, I don’t have a clue about the meaning and goal for instruction in algebra. And I am equally confused about the meaning of and development of problem solving.

We all know that successful completion of Algebra I is the gateway to the study of higher level mathematics and the sciences. We all have heard horror stories about the great numbers of students failing Algebra I. As educators, we recognize that good education builds on earlier learned and mastered concepts and skills. In a couple of years, California will be requiring that all students enroll in Algebra I in Grade 8. I have no doubt that other states will follow suit. How are we educators planning to get students ready for that eighth grade challenge?

2. StatisticsThere is limited attention to this important domain of mathematics in the Common Core Standards in the elementary and middle school grades. Statistics is the primary support of the inquiry cycle in the design and conduct of experiments. It is useful in understanding how to deal with the collection, display and analyses of data in order to identify trends, to make predictions, and so on. It is central to success in the study of the sciences, business, economics, medicine, and of course higher level courses in mathematics. For me, statistics should be up there with algebra as a major strand throughout PreK–12 curriculum.

3. The Presentation of the StandardsI have great difficulty knowing what is expected from students, in terms of knowledge or skill to be demonstrated, when a standard begins with "Understand." I get it when standards require students to explain, draw, construct, organize, measure, compute, or solve. What do we expect students to be able to do with that information? The “Understand” standards should be clarified.

4. The Developmental SequenceWith regard to the order of skills and "rigor" of demands for performance at the various grade levels, I see several items that I would delete or move to a different grade level because they are developmentally "out of the ballpark.” For example, counting back by ones in K is not a useful skill. Some say that it prepares students for subtraction, when in practice, subtraction defined as removing a subset and identifying the quantity that remains “is left” is much more age appropriate for 5 year-olds. “Understanding the distributive property” in Grade 3 should be moved up a grade to where students may be able to use that skill and gain insight into how and why it works. “Understanding that fractions give meaning to the quotient of any whole number by any non-zero whole number" in Grade 4 is far too complex for 9 year olds. I have teachers who don’t “understand” this.

5. Alternative Instructional ApproachMany students continue to have difficulty with mathematics despite attempts of various groups (NCTM, NCSM, and the various State Frameworks) to suggest new standards for instruction. Some researchers have identified Grade 4 as the beginning of the downturn in math achievement. Others have suggested that the start of declining achievement begins in Grade 2. I suspect that much of the difficulty students have with the learning of mathematics may stem from their lack of enthusiasm for the subject because of the great amount of memorization and lack of application of acquired skills. High school, and even college students tell us that they are often bored with math and don't see the relevance of the subject to their futures. In 2009, the American Association for the Advancement of Science produced their Benchmarks to reiterate and expand on several of the points made in their 1993 document, Science for All Americans: Project 2061. Several of the benchmarks suggest a different approach to teaching mathematics, one that shows the utility of mathematics for solving problems as a way of enhancing understanding.

One of the drawbacks of teaching mathematics entirely as a separate subject is that mathematics is taught before real-world problems are identified, so the related experiences may have mostly to do with learning the procedures rather than solving interesting problems. (AAAS, Chapter 11, p. 5)

Carole E. GreenesAssociate Vice Provost for STEM EducationProfessor, Mathematics EducationArizona State University

Carole Greenes is co-author of two ORIGO series: ZUPELZ and The Think Tank (Problem Solving). You can read reaction to the Common Core standards from co-author Carol Findell here. These articles are the opinions of the author and do not necessarily reflect the views of ORIGO Education.

Dominoes: More Than a Game

Have you ever played with dominoes? As well as being fun, domino games involve calculation and thinking strategies, which makes dominoes an ideal resource for teaching various aspects of mathematics. They can be used to develop number concepts, computation strategies, patterns and algebra, and chance and data. This sample activity shows how double-nine dot dominoes can be used to investigate addition involving three addends.

Sum Snakes

Activity

Have students work in groups. Each student in the group selects nine dominoes. Place one domino in the middle of a table. The students take turns to place their dominoes at either end of the “snake” as shown below (three ends in a section). The sum of the dots in each three-end section must always equal 12. A player who is unable to place a domino to make 12 misses a turn. The winner is the first player to use all of their tiles or have the fewest number of tiles left over in the event that no-one can play.

Variation

Play the game with different target numbers from 8 to 14.

Activity from A Little Book of Big Ideas: Double-Nine Dot Dominoes, 2007, ORIGO Education Bibliography

Irons, C. (2007). A little book of big ideas: Double-nine dot dominoes. Brisbane, Australia: ORIGO Education.

Fingers: A Powerful Representation of Ten

Representations of ten are used for teaching place value, number sense, and computation. However, many of the resources used for representing ten (frames, sticks, cubes, rods, and blocks) do not clearly show the individual ones within the number or effectively demonstrate three- and four-digit numbers. For example, all one thousand smaller cubes are not visible within a one thousand base-10 cube.

Fingers are a ready and powerful resource for representing ten that students already use naturally in mathematics (e.g. for counting). They readily show ten as 10 ones or 1 ten, and so are ideal for further developing understanding of two-, three-, and four-digit numbers. This property also makes them an effective resource for developing mental computation strategies such as bridging to 10 and splitting numbers into places.

Representing 0–10 with fingers

Have each student hold both their hands up palms forward and make fists, then raise their fingers one at a time, starting from the little finger of their right hand (the audience’s left).

Presenting the numbers in this way shows left-to-right reading for the audience. The raised and unraised fingers also represent the two parts that total 10 (e.g. “I’m showing 7 fingers and I need 3 more to make 10.”).

Representing numbers beyond 10 with fingers

Have more than one student show the tens and ones. For example, three students will show 28 like this:

As well as showing the 28 ones, it also shows that there are 2 tens and 8 ones, and that 2 more ones are needed to make 30. Showing the tens and ones simultaneously helps students develop a deep understanding of the place-value system.

Bibliography

Tickle, B. (2007). DecaCards: A real hands-on approach to teaching place value. Brisbane, Australia: ORIGO Education.

Mental Computation Strategies: Addition

It is essential that all students are able to calculate mentally as well as with paper and pencil. Students can make mental calculations quickly and easily with the help of strategies. There are mental computation strategies for each of the four operations: addition, subtraction, multiplication, and division. Strategies for addition are explained here.

Adding the places

Start with one addend, then add the value of the digits of the other addend(s).

See 35 + 23

Think 35 + 20 + 3

Bridging to ten

Start with one addend, count up to the next multiple of 10 (100, 1000 etc.), then add the balance of the second addend.

See 17 + 8

Think 17 + 3 + 5

Synonyms: bridge the decades; bridge to ten; make a ten; make to ten; use ten

Compensating

Round one or both addends before adding. Then adjust the answer to compensate for the rounding.

See 28 + 36

Think (30 + 36) – 2

Synonyms: compensation; round and adjust; round or adjust; use a nearby number

Counting on

Start with one addend, then count on parts (not places) of the other addend.

See 58 + 24

Think 58 + 10 + 10 + 4

Synonym: jump

Sub-strategies: count on 1; count on 2; count on 3; count on 0

Using compatible addends

Choose pairs of addends to make the calculation more manageable. This strategy applies only when there are three or more addends.

See 14 + 23 + 16

Think 14 + 16 + 23

Synonym: use compatible pairs

Using doubles

Use a known nearby double.

See 7 + 8 = ___

Think 7 + 8 = 15 because 7 + 7 = 14

Synonym: near doubles

Sub-strategies: double plus 1; double plus 2

Using place value

Expand the addends into places before adding the value of the digits in each place.

See 56 + 17

Think 50 + 10 + 6 + 7 or 6 + 7 + 50 + 10

Synonym: split

(For doubling)

Split one of the addends into places, double the value of the digits in each place, then add the doubled values.

See 12 + 12

Think double 10 + double 2

From The ORIGO Handbook of Mathematics Education, 2007, ORIGO Education

These addition strategies, as well as strategies for subtraction, multiplication, and division, are explained in The ORIGO Handbook of Mathematics Education.

Bibliography

Burnett, J. (2001). Mastering mental maths: Addition. Brisbane, Australia: Prime Education.

Burnett, J., & Irons, C. (2005). GO maths teacher sourcebook: Level 2B. Brisbane, Australia: ORIGO Education.

Irons, C., Burnett, J., & Turton, A. (2007). The book of facts: Addition. Brisbane, Australia: ORIGO Education.

The ORIGO handbook of mathematics education. (2007). Brisbane, Australia: ORIGO Education.

Number Sense: What It Is and How It Is Developed

Number sense. Students need it to develop their mathematical skills and understanding. It is a key part of mathematics curricula. But what exactly is it? And how is it developed?

Number sense is an attribute that a person has. It is a feel for or natural intuition about numbers that includes an understanding of all the different representations that numbers can have. A good sense of number is developed by discussing students’ understanding of numbers, encouraging them to think about numbers and use operations in new ways, exposing them to different representations of numbers, and linking mathematics they use every day to the mathematics they are learning in the classroom. Two examples of activities that promote the development of number sense are shown below.

Speedy Starters Card 1

Trace this number line onto another sheet of paper.

If the arrow is pointing to 50, mark where you think these numbers are located.

651001045110Activity from The Think Tank: Computation and Number Sense Green (Age 10), 2005, ORIGO EducationSpeedy Starters Card 16

Write a short story problem about the data in this graph.

Activity from The Think Tank: Computation and Number Sense Green (Age 10), 2005, ORIGO Education Bibliography

Irons, C., Burnett, J., & Turton, A. (2007). The book of facts series. Brisbane, Australia: ORIGO Education.

The ORIGO handbook of mathematics education. (2007). Brisbane, Australia: ORIGO Education.

Classification Charts: 2D Shapes

Classification charts show hierarchical relationships between categories of items, such as objects or concepts. As you move from the top of the chart to the bottom, the categories become more specific. What is true for an item at the top of the chart is also true for all connected objects or concepts below it. However, what is true for an item at the bottom of the chart may be, but is not necessarily, true for the higher concept.

For an example, look at the classification chart for two-dimensional shapes below. Following the connections towards the top of the chart, you can see that a rhombus is also a kite, a convex quadrilateral, a polygon, and ultimately a simple, closed two-dimensional shape. Each of these categories of shapes can also be thought of as a family.

From The ORIGO Handbook of Mathematics Education, 2007, ORIGO Education Bibliography

The ORIGO handbook of mathematics education. (2007). Brisbane, Australia: ORIGO Education.

Usiskin, Z., Hirschhorn, D., Coxford, A., Highstone, V., Lewellen, H., Oppong, N., et al. (2002). Geometry (2nd ed.). Upper Saddle River, NJ: Prentice-Hall.