Math Observation

In order to improve my instructional practices, I analyzed instructional data from district math diagnostic and proficiency assessments. The most recent assessment assessed student’s abilities to count, add and subtract, and their understanding of place value. My students scored below not only the other first grade students at the school, but also all first grade students in the district. 81.6% of my students could count, read, and write numbers to 120. This was an improvement from their diagnostic assessment. However, only 66.7% could relate counting to addition and subtraction, and only 45% demonstrated understanding of place value in two digit numbers.

Jazmine was introduced to two digit addition. My first lesson focused on drawing tens and ones to solve two digit addition. This strategy would provide Jazmine with the visuals she needs to solve the problem. First, I did a quick review on how to draw tens and ones to represent a number. She was given three examples ranging from easy to hard. Jazmine showed no signs of difficulty and was able to complete the task. Then, I demonstrated how to use the drawings to add two digit numbers. I explained how she must draw the picture for each addend. Then, I explained that she must count the tens first and then the ones. She smiled and said “that's easy”. We went through a couple of problems together and Jazmine displayed that she understood the strategy of drawing tens and ones to solve two digit

Students had previously covered the topic of developing fluency in multiplication by 2-digit numbers. After that topic students moved on to cover number sense, dividing by 1-digit divisors using mental math to prepare them for the following topic of my learning segment. The topic of my learning segment consists of developing fluency, dividing by 1-digit divisors. I designed my lesson as a three-day unit focusing on long division by modeling division with place-value blocks, dividing 2-digit by 1-digit numbers, and dividing 3-digit by 1-digit numbers. Students were introduced to division prior to my learning segment but the struggled to understand and comprehend division because students were only introduced to the division algorithm and were not provided with a mnemonic to help them recall the steps. Students also weren’t introduced to division with manipulatives or drawings. Therefore, I

[As a result of the step by step direction in the reengagement lesson, I want students to be able fully grasp the concept of addition; and how the knowledge of addition can be used to provide answers to expressions that require the decomposition of numbers totaling 8, 9, 10. The state standard that I am addressing in this reengagement lesson is 1.OA.1 Common Core State standards; use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together,

Teachers play an important role in fostering mathematics skills. In the “play dough” (Appendix A) episode, the educators can push student thinking and place the burden of thought on the student. Strategic questioning can really promote higher order thinking a natural integration between math and play (National Council of Teachers of Mathematics [NCTM], 1999). Questions such as “How can you tell which one is the biggest/smallest? How do you put them in order? Teachers should be encouraged to think about, not only the questions they are asking as children are working but also the frame that sets students off to larger problem solving and mathematical discoveries – measure and compare the lengths and capacities (ACARA, 2016). It is important for teachers to think about the questions that are embedded in the task itself but must also analyse the questions to ensure that children are set on a path to deeper understanding of the concept being taught rather than rote regurgitation – as evident in the play dough experience chosen. When it comes to questioning, educators “need to know when to probe, when to wait for answers and when to reinforce responses and when not ta ask questions” (NCTM, 1999, p.187). As seen in the ‘play dough’ (Appendix A) activity chosen, educators can introduce the mathematical concept of measurement and connect new knowledge with old through the use of effective questioning which crates a “link between actions and the language” (Knaus, 2013,

At: Students at grade level will be expected to complete 6-8 of the three digit addition problems during the provided activity time. At grade level students will be expected to use at least one of the provided strategies to solve for the sum. Students who finish early will be asked to draw a picture or write and explanation of the strategy/strategies they used to find the sum. The teacher will direct students who are early finishers to complete this task individually. Slow finishes will be provided with three, two-digit addition problems

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After reminding Mike about regrouping and completing extra math problems he appeared to recognize when he needs to regroup. There were instances when he needed to use another manipulative besides his fingers to guide him with his math homework. One of the manipulative he enjoyed using is the counter that has a total of 100 beads. He eventually did not need my assistance on regrouping math problems.

• He is excellent in his addition skills. He understands how to add numbers together, but he is just confused about this set up of addition. His error pattern is that if he has a two digit number in the first column he will put both numbers in the answer instead of the number in the ones place. For example, in the first problem he adds 6 + 7 correctly (13) but he puts both the ones and the tens in the answer. Then he brings down the 1 instead of what it should have been 1 + 1 (2) to make the answer 23. He follows this same pattern in problems 4, 5, 7, and 8 as well. In the third problem he adds the tens digits first 3 + 8 (11) and puts one 1 in the answer and the other 1 over the ones place. Then adds 5 + 1 + 1 (7) instead of adding 5 + 1 (6) and 3 + 8 (11) making the answer 116. He follows this pattern with number six too.

The professionally performed lesson that I chose is titled “Quick Images: Visualizing Number Combinations.” I found the lesson on The Teaching Channel website, which is a professional organization. The teacher that performed the lesson is Stephanie Latimer and she is a kindergarten teacher at Lakeridge Elementary School in Seattle, Washington. This lesson aligns with the Common Core State Standard Math.K.OA.A.1 and Math.K.OA.A.3. These standards are: represent addition and subtraction with objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations and decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation. The teacher does an effective job of using differentiation, providing a respectful learning environment, actively engaging the learner in the skill and content, and promotes critical thinking among her students.

Multiplicative thinking, fractions and decimals are important aspects of mathematics required for a deep conceptual understanding. The following portfolio will discuss the key ideas of each and the strategies to enable positive teaching. It will highlight certain difficulties and misconceptions that children face and discuss resources and activities to help alleviate these. It will also acknowledge the connections between the areas of mathematics and discuss the need for succinct teaching instead of an isolated approach.

Multiplication by ten gives students opportunity to explore larger numbers, and can also be extended on(Reys et al. ch. 11.4). In addition, multiples of 10 give students the knowledge that all digits move left one place and an additional place hundreths. This concept can be used to introduce the decimal place which is also moving place each time something is multiplied by tens. Exposing students to a range of examples which displays patterns that occur when multiplying by tens and hundreths will generate meaning of digits moving place (Reys et al., ch. 11.4).

These functions were entered into the graphics calculator and were both found to have x-intercepts of 0.25 or 14 . A value for ‘C’ was added in the form of y=lnB(x+C) to create a horizontal shift. A positive C value moves the function to the left and negative moves it to the right. As the current x-intercept is 0.25 and the wanted x-intercept is 3.5, the function y=ln4(x-3.25) was created. This function was then simplified to y=(4x-13). The result is shown below.

Mathematics, like every creation of man, have evolved without really knowing how far you can get with them: the scope of the computer, physics, chemistry, algebra, all are evidence of this. Every aspect of our culture is based in some way or another in Mathematics: language, music, dance, art, sculpture, architecture, biology, daily life. All these areas of measurements and calculations are accurate. Even in nature, everything follows a precise pattern and a precise order: a flower, a shell, a butterfly, day and night, the seasons. All this makes mathematics essential for human life and they can not be limited only to a matter within the school curriculum; here lies the importance of teaching math in a pleasure, enjoyable and understandable way. Mathematics is an aid to the development of the child and should be seen as an aid to life and not as an obstacle in their lifes.

The lack of adopted curriculum also means that most, if not all, teachers are supplementing both materials and instructional routines. These students need to pass the state-mandated Smarter Balanced Assessment (SBA) which requires completion of a problem-solving performance task. Students need to know which operation(s) to use (addition, subtraction, multiplication, and/or division) and how to apply them appropriately. This problem has