Math Applet Review #2

"Cubes" Grade 3-5 http://illuminations.nctm.org/ActivityDetail.aspx?ID=6

The objective of this applet is for students to help students understand volume of a cube. Students will have to determine a rule for finding the volume of the box. Students are given a box, a cube, a row of cubes, and a layer of cubes. They use all of those things to fill the box and determine the volume. The students are able to fold the sides of the box up or down so they are able to visualize the box when it is filled. The dimensions of the box can easily be changed. The students can determine the width, depth, and height that they desire for their box. Students can easily add and take away cubes from the box. After the student fills the box with the appropriate number of cubes, then their is an exploration tab they can clock on. The exploration portion explains more about what volume is, and a very brief and vague explanation of volume. Students then use that explanation and the box they have filled with cubes to determine the volume and how it was discovered.

I did not find this applet to be very effective. I thought that it did not explain why they (the student) will be filling the box with cubes. I thought that the activity did not accomplish what it said it would they way I thought it should. The applet did not give the student any indication of a correct answer. I thought this could cause a lot of confusion among students. The applet also did not include a way for the student to check if the volume they found was correct. I think that a teacher could use this applet as an additional tool to represent how volume is found and what it is. A student who did not know anything about volume may struggle with this activity.

Math Applet Review #1

"Five Frame" Grades Pre-K - 2 http://illuminations.nctm.org/ActivityDetail.aspx?ID=74

Through the use of this activity, students will learn basic number facts. Specifically, students will develop their counting and addition skills. Students use pictures on a grid to determine how many of the object there are on the grid, or how many spaces on the grid are empty. If the student answers the question correctly a happy face appears on the screen. A score of how many they answered correctly is kept at the side. If a question is answered incorrectly, it does not count against them and they have the chance to answer the question again. There are a total of four different activities in this Applet. In the other activities, students must determine how many circles it will take to fill the grid, or place the appropriate amount of circles in the grid. The fourth activity has students using the cirlcles and the grid to represent addition problems. Students are able to easily manipulate the pieces on the screen. The students can continue with the game for as long as they would like to because there is no end.

I believe that this applet is a great way for younger students to become comfortable with counting and addition in an interactive and visual way. This applet quality information regarding directions. This applet would be most beneficial for beginner to intermediate learners. The applet did provide problems that were more challenging, therefore not promoting much growth in math content and process knowledge. This applet would be useful for integration in a beginning level lesson about addition and counting. This applet would be useful for teachers to use as supplementary activities in the classroom. Students could use this applet at school during free time, or at home for additional practice. This applet does not provide the teacher with information regarding how well the student did completing the problems. That does not allow the teacher to assess how well students understand the concept from this applet.

Rubrics at Play by McGatha and Darcy - MTMS

Darcy, P., & McGartha, M. B. (2010). Rubrics at play. Mathematics Teaching in the Middle School, 15(6), 328-336.

Rubrics at Play is an article about rubrics and how they should be used to be most beneficial. The authors stated that assessment must be formative and rubrics are often found to be useful as formative assessment tools. Holistic, analytic, specific, and general rubrics were all explained in the article. The authors explained that rubrics should be viewed as more than just an assessment tool. Rubrics can help provide the teacher with feedback, further students'understanding of the topic being learned, and they can facilitate the discussion of ideas. The process of creating rubrics using student work, and the assessment task are given. Student-created rubrics were also highlighted. The authors provide many examples of how students can be involved in the process of creating a rubric. Student involvement in rubric creation promotes students to take ownership of the assessment process. This strategy allows the students to understand what is expected of them from the assignment. When a rubric is created correctly it can be a beneficial formative assessment tool. Rubrics help teachers by acting as a guide for analyzing the work of students. Rubrics also provide the teacher with feedback regarding their instruction. Rubrics also enable to teacher to provide each student with feedback that is specific to them. The specific feedback allows the students to move to higher skill levels. This encourages students to become independent learners. The article included examples of different types of rubrics, a personal story of creating a rubric, and reflection and discussion questions for teacher to use.

I thought this article was very informative. I liked that the article provided examples of rubrics. It can be difficult to create rubrics and providing examples helps explain the proper way to create a rubric. The authors included a chart with the four categories, excellent, proficient, marginal, and satisfactory. I liked that the description of these would be useful to a teacher because it helps them create a clear line between each grade that could be given. The information in this article would be useful for a classroom teacher because it provides steps for creating a rubric that can be used as formative assessment. I thought that the incorporation of a teacher's story about creating a rubric, and creating a rubric with their class was useful, because it gave a real life example of how the process carried out. It can give a teacher a better understanding of how the rubric formation process will be done.

Classroom Characters Coach Students to Success -Edwards

Anderson, G., Edwards, S.A., & Maloy, R.W. (2010). Classroom characters coach students to success. Teaching Children Mathematics, 16(6), 342-349.

This article explains the instructional mode called "1-2-3 Time." This instructional mode divides the class into small groups, that rotate through different instructional activities. 1-2-3 Time allows for the integration of technology, children's literature, writing, and even board games into daily activities and lessons. While using this strategy half to 2/3 of the class are completing independent learning activities, and the remaining students are working with the teacher. The article continues by explaining how the entire instructional mode is considered teacher-led instruction. The system has four math coaches. These coaches offer different suggestions about problem solving from many differing viewpoints. These math coaches are represented by four different stuffed animals or dolls. Students have these objects to represent the four viewpoints and remind them to use them. The article then continues by explaining how math learning games and reading and writing activities are integrated into "1-2-3 Time."

I thought that this article was very interesting. The concept of having a stuffed animal or doll represent a problem-solving strategy was very novel. I think that the instructional mode that was outlined in this article would be very beneficial in the classroom. More and more often teachers are stressed to include visual representations in a lesson to strengthen students' learning. I liked that 1-2-3 Time is an instructional mode that is not specifically for math. The integration of the different content areas could make it more attractive to a teacher because they will not have to worry about switching to a different instructional mode.

Review of Two PBLs

PBL: ADOPT-A-LOT

Summary

The PBL called “Adopt-a-lot” is a about a school that was given a piece of land and $35,000. The 5^th grade class had to design a park that met the needs of the community. They are given the $35,000 to go towards the building of the park, but once they exceeded that amount they would have to decide how to fundraise. Throughout the PBL, the students will create and explain graphs, and surveys used to collect data about the environment. They would also gain experience of creating, prioritizing, and distributing a budget. Students will solve problems involving scale factors. Students will have to recognize and apply mathematics in situation outside of the mathematics classroom.

Strengths and Weaknesses

A strong point of the PBL was overall design of the PBL. This PBL did a great job on the overall design. The grade level given for the math being done was not appropriate, but it was organized well. A weakness was that the math level being used by students was not aligned with the grade level given for the PBL.. The work that the students would complete was at a 3^rd grade level. The overview of the PBL stated that it was designed for 5^th and 6^th graders.

Appropriate Grade Level?

This PBL did not have the appropriate grade level listed. The PBL was supposed to be used in a 5^th or 6^th grade classroom. The work that was asked of the students was at around the 3^rd grade level.

Assessment

The assessment of the math content and process was very vague. The rubric that was given gave too much slack in each point value. It allowed too much leniency.

PBL: LOUNGING AROUND

Summary

This PBL is for 8^th grade students where the students must design an addition to the school that will house more space for the 8^th grade because of the dramatic increase in the class population. The students will build on data analysis and probability, geometry, number and operations, algebra, and measurement. This PBL will take place over 22 days.

Strengths and Weaknesses

A strength of this PBL is how the objectives are presented in the daily plan and on the objectives page. One the objectives page, it was nice to have them organized by content areas. Having the objectives for each individual day plan was nice. It is important to have the specific objectives that should be reach that day stated directly on the page. A weakness of the PBL is how the daily plan is organized. Having to read through an entire paragraph to find information can be tedious. Using bullet points for the Daily plan is more effective. It is easier to find specific information when it is formatted as individual bullet points. Another weakness is that there was no PBL web. The group did not create a web for the PBL. The work had a weak overall format of the work. There was not an organized overview of the important points of the PBL. Listing grade level, duration, rationale, math focus, and higher level thinking in a list form, it allows the teacher to quickly see the important points.

Appropriate Grade Level

The focus of the PBL is half on math, and half on other subject areas. The math that is required by the students is repeated very often throughout the PBL. Students are not building on skills constantly, but they are just using the same ones more often.

Assessment

The assessment rubrics were not detailed enough. They left a lot of room for students to question what each grade required. Some of the areas being assessed on the rubrics repeat.

Compare and Contrast the 2 PBLS

These two PBL’s contrasted regarding the appropriate grade level given to it. The first PBL was not appropriate for the grade level stated, but the second PBL was. Both PBL’s had great organization, although one had a more organized overall layout of the PBL, and the other had better organization of the objectives. Both PBL groups had weak assessments. Both groups need to improve their rubrics.

PBL Article - "How to Buy a Car 101"

How to Buy a Car 101 is an article about the instructional strategy called problem-based learning, or PBL. PBL is based on the primary concept of relating the curriculum to an real-life situation. The explanation of the PBL design is given, beginning with the teacher asking the students an engaging question. The explanation continues to through the process as students are comparing possible solutions and researching the best option. The PBL that was described was about how to buy a car. The benefits of PBL were given. The benefits of PBL are numerous. There are also many adaptations that can be made to PBL for special needs learners and ESL students. Finally, the author gave tips for teachers that were attempting PBL for the first time.

In the article, under the adaptations section, the author stated that a way to adapt PBL for special needs kids is placing them in a group with students who do not have special needs. This could cause more problems for the special needs student. They may work slower and the other students may just do the work for them. This does not allow the special needs student to benefit from PBL. The article did a great job of maintaining a constant theme of buying a car throughout the entire article. I thought a strength of the article was that it included tips for teachers using PBL for the first time. Many teachers are intimidated by PBL. It is scary to think that you are only a guide and the students are making their own decisions. Another strength of the article is that it includes the rubric used for the PBL. It helps understand how PBL can be assessed.

Flores, C. A. (2006). How to buy a car 101. Mathematics Teaching in the Middle School, 12(3), 161-164.

PBL Readings

Problem-based learning helps students develop better problem solving skills and expand disciplinary knowledge bases and skills. Problem-based learning places students in an active role of problem solving. Students are faced with poorly phrased problems that tend to mimic real-life problems. PBL is a student-centered instructional strategy. Students must work together to find a solution to the problem they have been faced with. The teacher acts as a coach or facilitator to the students throughout the PBL process. Once the students have received their problem, they must define the challenge or problem. They must determine what they know from prior knowledge, what they need to know, and how they are going to get to the solution. The use of a chart similar to a KWL will help students answer these questions. The teacher should provide resource advice and ask questions throughout this process to act as a guide. Students should list many possible solutions and rank them according to how successful they will be. Once they determine which solution will be most successful, they begin research the knowledge and data that will support the solution. The group needs to discuss the possible resources they can utilize as well as assigning and scheduling research tasks for each member of the group. Deadlines should be established so students are completing work in a timely manner, but the student should set their own individual deadlines for each part of the PBL. The teacher gives the final deadline for the project. Students then organize the information they found through research and the solution and present their findings to the group. When students present their findings, they need to include the problem statement, questions they asked, the data that was gathered, an analysis of the data, and support for solutions or recommendations based on the data analysis. It is pertinent that students reflect on the overall problem and the work they conducted to solve the problem. This encourages the students to learn how to learn. When completed, the PBL would have promoted the integration of knowledge, critical thinking, problem solving, communication, reasoning, learner empowerment, interpersonal skills, and decision making.

Problem-based learning is used in many ways in the classroom, but it is also used outside of the classroom. Problem-based learning can be used in the classroom with a mini-lecture. The students work in small groups and they material resources are provided for them. The students then solve the problem in that class period. We solve problems in our day-to-day lives. When solving the problems we face, we determine the best and most efficient and effective way of solving the problem. We research how to reach the solution and then we execute it. PBL is an important strategy in a student's learning.