An effective teaching of mathematics establishes clear goals for students to accomplish. It also allows room for growth and involves learning progression to eventually let the student make final decisions and have a solid understanding of the material. These practices implement tasks that promote students to use reasoning and problem solving as they find meaning behind the math they are involved with. Students can build procedural fluency and develop more of a conceptual understand the material.
On our visit to Peach Plains Elementary School, the students were introduced to the problem-solving technique the most with the activity we performed with them. Students watched a video of numerous bags of skittles being poured into a large jar. They were then given the task of making an educated estimate of how many packages of skittles and single skittles they believed it would take to completely fill that jar. There were various ways the children were considering as possible solutions to the problem and they all discussed their ideas with one another.
When the thought process began, not all students were thinking mathematically. Two students at my table said that they would replay the video of skittles being poured into the jar and record it on their phones such that they can slow it down and count the number of packages used. I then proposed the thought that maybe they should consider how to do it without a phone in case it is dead, or you did not have one with you. However, they did not like this idea and simply argued that they would just charge it or ask someone else for a phone to use. They did not want to do physically or mentally do any real math and were just looking for a quick and easy way out of the situation.
As we continued exploring ways to problem solve, one girl had the bright idea to multiply the number of skittles we saw at the bottom of the jar for one package (14/15) by how many packages they believed it would take to fill it. This would then give them the approximate number of how many total skittles there may be in the jar. Two of her tablemates agreed with this thought process and communicated their opinions on how many Skittles they calculated. The one member of the table, the one who wanted to cheat the system of not doing math, took a bit longer to understand that method. He believed it would have been easier to just count the skittles individually as they get poured into the jar and still felt math would not be necessary. It was a bit difficult working with him while he was still deciding on what solution he wanted to use, but he eventually came around to the multiplication idea previously announced.
Throughout the activity, we passed around a tray of 1 pack of opened skittles and a jar with one pack of open skittles in it as well. This gave the students a better view of what can fit into the container and how many can be in a single pack. At this point, they had small numbers thinking that there are 15 skittles in one pack and only around 20 packs. However, when they say the image of all the packages used in a pile after being poured into the jar, the students increased their amount of skittle packs used. By the end, my group of students had varying answers between 250 to 450 skittles necessary to fill the jar. When they saw the results, they correctly counted 853 skittles as shown in the video, but they did not believe that there were that many in the jar. They seemed a bit baffled and explained to me that they have never seen so many skittles before to really know they would need that many packs.
Overall, I really enjoyed my time visiting Peach Plains and working with the students because I truly feel that the experience of working with them has bettered both them as students and learners and myself as a future educator. I got a better look at what children think, how they process critical thinking questions, and how they attempt to problem solve. They were able to find the meaning in the activity and developed questions to ask us in return regarding their ideas and math. When teaching math, one must be open to varying ideas, no matter how out of the box they may be. Everyone has a different view and understanding of mathematics and always bring a fresh pair of eyes to any given problem. Students work well and can develop new ideas or better understandings of concepts when they share their thought processes with peers. Conducting these activities with elementary schools has been beneficial in many ways to my overall learning of how children work and has given me hands on experience with them.
For the Family Math Nights that we attended, Claire and I created our own counting BINGO game. We visited two schools where we set up our game and allowed children to visit each of our different tables to learn about and play the games we had to offer. Our game seemed well-liked by many parents and students. They got to show off their counting abilities and mathematic skills such as addition, subtraction, and multiplication. We managed to bring out this math by asking them questions throughout about how they are counting quickly and what it means to add or multiply groups of shapes together. Here is the idea of our game:
Materials Needed: white paper (to make the BINGO sheets), crayons or markers (we used the colors of the rainbow to add a pop of color to the boards and star chips), a ruler (to make straight lines on the cards and chips), sharpie (to darken numbers and words), scissors (to cut out the chips and boards), and two to four young students willing to participate in the activity.
STAR BINGO: There will be various 4x4 BINGO sheets with possible numbers up to 25 listed in the 16 spaces. The space marked with a star is a free space. While playing, there will be cards lying face-down across the table. The students will take turns selecting two cards at a time. These two cards have a different number of shapes on it and students will individually count how many shapes are on each card they select. After deciding on the amount, they will share it with the group, and anyone can place a star bingo chip on their corresponding space. The cards will all have different shapes and values and the students will have to use math solve or count what each value is and find it on his or her sheet (if it is applicable). For example, on some cards the students will have to solve for the correct amount by using addition and subtraction. Other cards will be straightforward, and the children will have to count how many shapes they see on them. It is possible to use multiplication to solve for some values when shown groupings of shapes. Students must also keep in mind that they may not always have the card value selected on their bingo board The objective of the game is to visualize what values they need on their own board compared to their opponents and think strategically to count and pick their own lineup for a BINGO.
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While we were attending the first Family Math Night, we were a bit overwhelmed with the setup of the tables and it was a bit too crowded. It was difficult to hear the students right in front of me because there were too many other children roaming about trying to join in the middle of different games just to get the sticker faster. I feel like the reason for this was partly because the school was also an early childhood education building, so there were more younger children there than expected. Anyways, our Star BINGO game went quite well with these younger kids because it only really required counting for them. There were a few students who could do multiplication of row x column and understood groupings of 5 shapes. There was one boy who loved the game because his mother told us how much he loves counting. Not only did he quickly get a BINGO, but he also spent time going through and counting extra, unused cards for the fun of it. When we asked him how he managed to count so quickly, he explained that his brain grouped up shapes near each other and he knew things such as: “5x3 is 15 and then there are 3 left so that’s 18”. He used his fingers to count occasionally and had a good understanding of the objective of the game. Out of all the students who played our game here, I feel that he had the best comprehension and reaction.
At the second event, we liked the setup of everyone’s tables going down the hallway more than the first location. It allowed easy access for students and families to walk down the line and see all the games there were to offer. During this visit, I met a pair of siblings who played our game together with parental supervision. They did not exactly follow the rules of the game, but they were at least taking turns, and both showed their counting skills. The eldest sibling kept trying to help his little brother count the shapes on the cards when he did not even get the chance to start counting yet. The eldest seemed to really enjoy counting and tried to see how quickly he could do it. The youngest was just trying to process the numbers and correctly count the cards at his own pace. The father that accompanied them tried to assist the young boy in pointing to the shapes while he verbally numbered them off. He also tried to question the other son about how he looked at cards so quickly and new without counting one by on. The son replied that he just new his multiplication that 4x4 is 16 so it was easy for him to do. When it came to cards where the shapes were scattered, he often grouped them up by 2s, 3s, or 4s my pointing and covering them with his fingers to count them quickly. This boy was more concerned in seeing how many numbers he can count than trying to get a BINGO first. In fact, he helped his brother win the game because he took enough pride in being able to count accurately.
Overall, I believe that our game was suitable for all elementary school students. The cards were designed so that students can use any form of mathematics: addition, subtraction, multiplication, or even just normal counting. The game also had a competitive aspect to add intensity, excitement, and got them to think strategically. We witnessed students counting the shapes one by one, using addition or multiplication when faced with groupings of shapes, and using subtraction when they counted all shapes and eliminated the ones that were crossed off in the end. After doing these activities for a couple of nights, we recognized varying ways students can perceive a problem and what their different solutions or methods may be. It was interesting to hear them explain their thinking processes sometimes because they would count in ways which I may find more complicated or unnecessary. Nevertheless, it was enjoyable to be a part of and to be able to leave a positive lookout on using math outside of the classroom.
Based on my experience in Mrs. Ratke’s fourth grade classroom, I really enjoyed working with the children doing our measuring activity. Of my group of kids, they were very excited initially and enjoyed doing the manual measuring using their footprints. Three-quarters of the students in our group would round up regardless of how much of their footprint was required to complete the length, so we tried to have them round to a quarter or half inch to make it more accurate. They were taking charge and jumped into measuring the objects however they felt was correct and we tried to correct them and offer other ways to measure the objects. The children also noticed how their foot sizes compared to the others in their group. For example, two of them seemed to have the same foot size and said the reasoning was that they were also the same height. I also noticed that when converting their footprint sizes to real inches, however, they did not quite understand the concept yet. This was because they were still getting introduced to multiplying larger numbers together. They were also unfamiliar with fractions and decimals, so then I realized that we should have rounded to half and whole numbers instead of a quarter inch. Next time, I would like to know ahead of time where the students are at in their learning to make sure we can challenge them but not confuse them with the activity expectations. On the bright side, this was good practice for the students to try the smaller, more accurate measurements and allowed us to bust out our own handwritten math abilities and try to help them with their multiplication.
In my upcoming teaching career, I would love to have students come in from a college or university and partake in these kinds of activities because I feel that the learning process and activity will stick better with the children because it was an exciting experience. Memory is linked to emotions and I truly feel that by having them engaged and thrilled in an activity will get them even more excited to learn math and participate in class discussions. Math can be difficult for higher grades to have fun learning and their creativity is not quite as active as when they are at younger ages, hence having an stimulating experience will force them to be engrossed in the activity and will have their creative brain gears turning a bit more. The measuring activity we planned out would be a good learning style to try with other large topics in other classes too because it is linking their objectives and standards to something fun that they can remember and reflect upon. I can only hope my students will get to be involved in such an interesting experience and I would love to be able to work with other classrooms as well and have even larger group discussions to improve their learning and social abilities with other students.
In Mathematics for Elementary Teachers, we have been covering the general topic of shapes and how young students can interpret them while engaged in games designed to help them learn and understand the basic attributes of each accordingly. I have conducted a hunt for various educational activities for children to gain insight on various shapes. I have decided that the best way to teach them about the attributes would be to have each student create their own booklet.
For my lesson plan, called Basic Shapes & Attributes, each individual student will get to make a flipbook of the qualities and characteristics of varying shapes. I plan on working with 1st, 2nd, or 3rd grade students, so the level of difficulty will be low. If working with 1st graders, the booklet will contain the easy characteristics of basic shapes.
Example: a square has 4 equal straight sides, this shape is big/large,
this shape is small/tiny, there are 7 shapes in total, a triangle has 3
straight sides, a circle has no sides and is round, etc.
This allows the kids to grasp the concepts of what the shapes are and describes something about each one. I could also have different sizes (small, medium, large) to let them see how when enlarging or shrinking a shape it remains the same. The higher levels of education would require more advances attributes of the shape cards. For instance, we are no longer focused on just how many sides a shape has, but rather its congruent sides, angles, and whether or not it has parallel sides.
Example: a square has 4 congruent sides and 4 90° angles, and a rectangle
has 2 sets of congruent sides that are parallel from each other and has 4
90° angles, etc.
At this point, we are now challenging the students to be able to identify attributes or varying shapes such as rhombi, squares, quadrilaterals, triangles, rectangles, circles, kites, and so many more. In class, we mainly covered the attributes of quadrilaterals and what defines each of the qualifying shapes, however, lower elementary students may need more focus on what these shapes look like to begin with in order to further identify characteristics of them. I enjoyed the thought of making a flipbook as it was somewhat suggest in class as a thoughtful homework assignment. I would make a full lesson plan from this so I can work with the students to help them visualize and understand these basic shapes and attributes. The students will be able to identify various shapes and the mathematical properties / qualities of it which makes it different from others. Below I have attached my personal attribute flipbook cards as a demonstration to show what my plan is for this lesson plan. The best thing about this activity is that it can easily be incorporated into lessons for every age group depending on their topic of learning and can always become more advanced and challenging. I hope to use this in my own classroom to engage the students in a fun, thought provoking, educational activity which can be used to better their general knowledge and understanding of shapes.