Teaching Strategies
I feel it is important to state once more that each of the following strategies or materials can be incorporated and used together. This incorporation is what allows student to gain a stronger understanding of each concept and in essence provides more instruction time.
Manipulative Materials
The first model used in each step above is the concrete, so I will use a variety of hands on manipulatives for students to hold and move on their own. This will connect with tactile and kinesthetic learners as well as visual students giving even the lowest reader the ability to participate in the lesson, and allowing all students to begin to develop their own understanding of the mathematical concepts. Although I will be using a variety of manipulatives (bears, dinosaurs, tile pieces), base 10 blocks will be my main hands on item. This set consists of one centimeter cubes to represent the ones, a "tens rod", which is a flat rod with makings to denote the ten cubes that make up the rod, and a "hundreds flat" that looks like a hundred cubes connected into a square. Base 10 blocks allow student to easily see the transition into the expanded form of a given number. Each number can be represented using the pieces. To show 243, students would lay our 2 hundreds flats, 4 tens rods and 3 ones cubes. In addition to the common way of grouping base 10 blocks to form squares of 100 units, I will also lay them out long ways like a train to further demonstrate blending of place value, counting and length.
The Number Line to Assist in Computations and Place Value.
By utilizing the number line within my unit I am able to once more teach multiple concepts at once while not overwhelming students. I will begin by using the number line in our addition and subtraction by having students place their base 10 blocks on a pre-printed number line that matches block size. They will be asked to then rearrange their pieces into like trains in order to find the answer to a given problem. For example, to find the answer to the addition problem 23 + 15, students will have 2-tens rods and 3 ones cubes to make 23, and 1 tens rod and 5 ones cubes to make 15. They will lay these out on the number line (in the order above), and will be asked to match "like" values, that is, they will then identify that they have 3 tens rods and 8 ones cubes. At this point student should be able to identify that the answer to this problem is 38. Rods may also be used to illustrate regrouping by simply regrouping 10 ones cubes into 1 tens rod or taking one tens rod and breaking it into ten ones cubes. These types of activities allow for the concrete illustration of a concept. The number line may also be used to pictorially illustrate addition in a similar manner. Students can simply draw the tens rod and ones cubes onto paper, beginning a symbolic process by labeling the rods and cubes and the groups they make. This is illustrated in the figure below:
Place Value Cards
Place value cards are simply cards with place value numbers written on them. For example, the ones cards will be numbered 0 to 9, tens cards numbered 10 to 90, hundreds cards numbered 100 to 900 and so on. These cards will be used throughout the year beginning with the ones to allow once more for a deeper understanding of what each number means and to gain a comfort in using this tool. As we progress through the numbers students will simply lay out the cards in the concrete model to demonstrate a given number. If we are working with 52 bananas for example students can lay out the 50 card and the 2 card. This will lay the groundwork for student to see the connection between a number and its expanded form, as well as the written form they will be working with later. As we attempt to work through to the hundreds and the thousands these cards will become part of our concrete model. For example, rather than having 389 dinosaurs out we can work with the 300 card, the 80 card and the 9 card. Closer to the end of the year, students will create their own set of cards to work with as we delve into hundreds that they can take home at the end of the year to work with over the summer.
Word Problems
With the implementation of the new Core Curriculum Standards students will be required to explain and/or demonstrate their thinking and understanding of math concepts. The use of word problems has the ability to give students the link between reading, writing and math. This encourages students to not only give a numeral for an answer but words as well. By using this combination a teacher can model "thinking" out loud or on paper and teach beyond symbolic "fact" statements like 2+2=4. For example, I have the ability to voice how taking two apples from the tree and putting them with the two apples in my basket now means that I have 4 apples in my basket. This also bridges the various reading levels or gaps students may have. I plan to use the chart of 14 different forms of word problems provided in the Core Curriculum Standards 4 to help develop first one, then two step problems (examples of two step problems and how they can be created can be found in the units referenced below) for my students and teach them to create their own, thus making their knowledge personal and applicable to their everyday lives.
As 2 nd graders my students are still in the early stages of reading and struggle with word problems. Many times I notice long word problems with new or unfamiliar words. This causes a problem for young struggling readers. I will have students work on a daily word problem as we begin our math time each day. They will be posted for students to read each day on a flip chart so we can come back and review problems or look back to work we have already done. Some days students will have the option to work in pairs and some days they will work independently. Students will create word problems based on current classroom vocabulary to assist in recognition and understanding of new vocabulary. As we begin the unit I will begin with simple one step problems that are not focused on regrouping, such as "Timmy has 2 trucks. His dad gives him 2 more trucks. How many trucks does Timmy have?" Word problem types will range from addition, subtraction, comparison, and utilize the missing addend (i.e. solving 2+__= 10). If you would like more information on Word problems in 2007 the Yale National Institute 5 offered a seminar Keeping the Memory in Mathematics: The Craft of Word Problems led by Professor Roger Howe. Some of the units developed for elementary were: Dr. Word Problem – Solving Word Problems With The Four Operations Using Singapore Bar Models, by Valerie Schwarz; Teaching Addition and Subtraction Word Problems to Children, by Tonya M. Shannon; and Crafting Word Problems Even A Child Can Do, by Huwerl Thornton Jr.
Problem solving skills based George Polya's model 6.
I will focus on his step one which is "understand the problem", and step four which is "reflection of work and understanding". These two main steps will teach students to focus on asking questions throughout the problem, discussing their different ideas, and building the foundation that will be critical for them to move onto more difficult concepts and activities. My students come from mostly low-income homes and are lacking in exposure a broad vocabulary and to higher order thinking skills. I will use these skills throughout the year but as we begin to progress to regrouping and multiple step word problems in this unit it will become important for students to have confidence in discussing with their peers what they understand the problem to be and how they solved it. Through the use of class discussions students will improve their ability to understand and reflect on problems as well as how their peers "think".
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