Journal - Roles of manipulatives

<This journal of mine got the highest grade in our Math Subject. Hope that my work helps other educators too! >

December 13, 2011, Tuesday at 6:09 in the late afternoon, I am reading my journal in Geometry. I do not have choice but to do it because it is our duty- a duty for us to accomplish this requirement. The deadline of submission is on December 16, 2011, Friday. I only have three more days to complete my reaction paper. I hope I can finish it before that day comes. I hope I have the ideas to fill up the empty space in the bond paper. I hope I have an open mind to understand what I will be reading. Oh gosh! My time starts at 1, 2… 3!

               I figure out doing that intro so that Ma’am can know that I am really reading my journal. Ha-ha! Another reason is for me to react immediately on what I have read. It is because my thoughts are fading easily. That is why I have to write at once. If I do not respond to this, I will have hard time thinking on what I will put on this paper. Well, anyways, let us proceed with my reflection.

               “… children were more successful with manipulative than with pictures …, all children were more likely to rotate their paper or physical shape when this action could help them identify the shape.” These are some lines that can be found in my journal. While I was reading these, I remembered Prof. Pabayos, exclusively during the time she is teaching the prisms. As she draws the geometric figure, specifically the cube-figure, I and my classmates are thoroughly watching. When she is done, we try to stop ourselves from laughing at her drawing. I won’t describe anymore what the image looks like. But what makes it more funny is when she told us, “Isipin niyo na lang na cube ‘yan. [Smile].” After that, one of my classmates volunteered to improve the drawing. Suddenly, our professor told us, “Hindi talaga ako marunong mag-drawing.” And then, we laughed again.

               I did not include that just to make fun of our professor. I would simply like to address the issue that not all teachers in Mathematics, particularly in Geometry, are good in illustrating a certain figure. There were some who cannot draw the object as good as how they want the image to appear. However, this doesn’t mean that they are not good in teaching their chosen field. It was just they don’t know how. So, to help them show to their students what their image truly looks, they have the visual shapes or manipulatives or the hands-on objects during the lesson. It is because students, especially elementary students, are more visual-oriented. They learn easily when they can see, touch, move or manipulate the objects by themselves.

               “… manipulations still help children expand their investigations in the physical environment thereby advance their thinking.” This is the abstract formed by Taylor Martin, Ayiesha Lukong and Raven Reaves, faculties of the College of Education in The University of Texas at Austin, in their study entitled “The Roles of Manipulatives in Arithmetic and Geometry Tasks”. This study contains the effects of manipulatives not only in Geometry but also in Arithmetic. On the other hand, they did not forget to mention in their study that these manipulatives may have possible different effects in these two fields. They also noted that action with manipulatives supports learning when it provides a way for children to simultaneously and iteratively adapt and interpret their environment.

               Many researchers and teachers and even I believe that these hands-on objects can help students learn mathematics concepts. For example, when the topic of the day is about fraction, the teacher would prepare fraction pies. These are broken pieces shaped like a piece of pizza taken from the whole. The teacher will use this to illustrate the concepts found in fractions. Thus, help him or her in teaching the students the fraction operations and meanings in the easy way.

I was once a student who learned fractions from my first year professor with the help of these fraction pies or as what they call it manipulatives. I am a student who really has a bad background in understanding fraction operations. Honestly, I always got low grades when fractions are the topic of the day. That is why I am easily irritated and don’t even have the patience to listen and participate during class discussions. But during my first semester in my first year college, my views about fractions change. Through these manipulatives, I am convinced to understand, somehow, the nature of fractions and learn to think of ways how I can solve fractional problems in my own ways. Up to now, that serves as my inspiration to think and use things that can help me teach my lessons to the students in the way that they can understand it easily. And so, I also believe what the researchers wrote about their study “On one hand, working with manipulatives improves ones’ performance on mathematical tasks in some cases.

According to the researchers, the best instructional strategy is to use multiple manipulatives to teach mathematical concepts. They do believe that exposure to multiple representations leads to better understanding of underlying mathematical principles. These manipulatives are viewed as external resources that primarily help problem solvers keep track of the problem elements without wasting internal memory resources. Based on how I understand these lines, this strategy can help the students solve problems in distressful ways. Just take my example with the drawing of Prof. Pabayos. We might have a hard time solving geometrical problems such as finding the lateral and surface area and even the volume if she didn’t show us how the figure really looks like. Though we know the formula, it is still better to keep track on determining the personal location of the length, width and height in the certain prism. This is also to check if each one of us really knows how to locate especially personally the length and the width.

These manipulatives could be more helpful in geometry because they are more similar to the objects operated on and resembles the outcomes of problem solving. Another thing, in geometry, physical shapes and children concepts of shapes may nearly identical, particularly in early stages of learning. Lastly, working with the virtual manipulatives helped children develop conceptual and procedural knowledge in geometry, and that virtual manipulatives are more motivating than paper and pencil tasks.

Comparison in Paragraph

“My Friendlier High School Teachers”

            My high school teachers are friendlier than my elementary teachers. They are like my batch mates. They do have time to bond with us. They even crack jokes and share what are the latest happenings around the world. My high school teachers are more concern than my elementary teachers. For reasons that they always find time to talk to each one of us to know if my classmates and I are ok and they are willing to listen more than what my elementary teachers do. My high school teachers do not fail to make everybody feel that we all belong. They have shown us no favoritism. They give us equal attention when someone makes mistake. To sum up, I’ll treasure them more, even greater than my elementary teachers.

Simple Paragraph

“I Love to Eat”

Eating is my passion. I love to eat because foods give me strength. It also gives me satisfaction. Another, it gives me way to escape. These are the three reasons why I love to eat.

First from the list is, I love to eat because food gives me strength. Of course, it does. It is due to the nutritional value the foods have inside. We get our daily energy from these nutrients. It is now up to our body on how it will process the vitamins and minerals. Thus, it makes us alive and alert all the day.

Second, foods give me satisfaction. In what way? It satisfies the cravings of my tongue and the needs of my stomach. Those cravings are the result of my envy to those mouthwatering food commercials on television. It makes die just to find ways on how can I have a taste of it. Hence, as I taste the foods of my dream, I could think of my life being a hundred percent complete.

            And the last reason from the list, foods give me way to escape. These foods aren’t not just only for the satisfaction of my tongue and mouth, but to also satisfy my innate mood and feelings due to the stressors in life. It makes me happy every time my cravings are being supplemented. Whenever problem approaches, I could rely on eating many possible foods that my money can buy to divert my feelings toward the delicious tastes of the foods.

            I know that we all love to eat. And sometimes, we do it even if it is more than the limitations that our stomach can hold. But do not forget to still be aware on what we eat so it won’t harm the health status of our sacred body. For you, can you tell me why you love to eat?

Reaction Paper - Rizal sa Dapitan

Pastores, Tiffany Rae R.

II-5 BEEd

Prof. Armi Evangel Pena

Rizal and his works

Reaction Paper

“Rizal sa Dapitan”

“Noon hanggang sa kasalukuyan”

            Wala ng sasakit pa sa isang ina ang mamatayan ng anak na una ay ipinatapon sa kung saan.

            Iyan ang naramdaman ng isang Teodora Agoncillo sa pagkawala ng kanyang anak. Labis ang kalungkutan ang dumapo sa kanyang pangangatawan.

            Sa umpisa ng pelikulang ito ay may mga pangyayaring na hindi ko maintindihan. Hanggang sa ipakita ang kawawang ina ni Rizal.

            Ngunit nalito ako nang may ipakita na may inililibing at tila hinahanap ng isang babae at pagkatapos nuon ay biglang ipinakita si Rizal noong unang gabing ipinatapon siya sa Dapitan.

            Ang unang impresyon ni Rizal? Malungkot ang Dapitan. Ngunit ito ay pinabulaan ng isang heneral. Sinabi niya na hindi malungkot ang Dapitan kung hindi, ito ay tahimik at mapaya. Walang gulo. Kung ako naman ang tatanungin, papanig ako sa sinabi ng heneral. Dahil kung ang isang taong kagaya ni Rizal na madami ang poblema, mas mapapalagay ang kanyang isipan sa isang maaliwalas at mapayapang lugar. Isang paraiso para sa mga namomoblema.

            Isa-isa ding binanggit ni Rizal ang kanyang mga ninanais na reporma para sa Pilipinas- ang dahilan kung bakit siya ay nagbalik dito sa bansa kapalit ng kaligtasan niya sa Europa. Kaya naman idolo ko si Rizal dahil sa kanyang mga balak na gawin para sa mga Pilipino na hindi maintindihan ng iba. Una na dito ay ang pagkakaruon ng kinatawan ng mga Pilipino para maipaabot sa hari ng Espanya ang mga hinanaing ng mga Pilipino. Pangalawa, ang pagbabawas ng pangingialam ng mga prayle sa mga ginagawa ng mga tinatawag nilang indio. Ngunit ito ay napakahirap makuha o makamtan sapagkat malakas at makapangyarihan ang pagkakakapit ng mga prayle sa ating bansa.

            Natuwa din ako ng makita ko sa pelikulang iyon ang mga pinagkaabalahan ni Rizal sa Dapitan. Nakapagtanim siya doon ng mga iba’t-ibang klaseng mga puno at nakagawa siya ng daluyan ng tubig mula sa sapa hanggang sa kanyang taniman gamit ang mga dugtong-dugtong ng mga kawayan. O ‘di ba? Ang galing talaga ni Rizal at sadyang kamangha-mangha talaga ang kanyang mga ginawa.

            Ang isa din sa pinagkaabalahan ni Rizal ay ang pagbibigay edukasyon sa mga batang hindi nakakapasok sa paaralan sa kabayanan ng Dapitan. Kahit pilit na sinisiraan ng prayleng tagapamahala sa lugar na iyon ang pagkukusang-loob ni Rizal, ang mga mamamayan na naktira doon ay desidido pa din na ipasok ang kanilang mga anak sa eskwelahaan ni Rizal sapagkat naniniwala sila na tanging ang edukasyon lamang ang kanilang maipapamana sa kanilang mga anak.

            Ako, bilang isang pang-kinabukasang guro, pipiliin ko din na manilbihan kahit saglit na panahon sa mga batang walang kakayahan ang mga magulang na pag-aralin sila sa paaralan. Sapagkat, bilang isang guro, tungkulin ko ang magbigay kaalaman sa mga bata o maski sa mga taong walang nalalaman. Kung tunay kang guro, magsisilbi ka kahit na wala itong kapalit na kung ano pa man.

            Masakit na balita ang suamlubong sa mabuting tanung ni Rizal sa kanyang ina at ilang mga kapatid nang nagsipunta ang mga ito sa Dapitan. Naitanung ni Rizal kung kamusta na si Leonor, ang pinsan na kanyang kauna-unahang minahal. Ang tumambad sa kanyang kasagutan ay ang pagkamatay ng babaeng kanyang iniirog.

            Isang natatanging pag-ibig din ang namuo sa oras na pananatili niya sa Dapitan. Doon niya nakilala si Josephine Bracken, ang kahuli-hulihang babae sa buhay ni Rizal. Kamangha-mangha ang kanyang kagandahan. Isang babeng di matutularan ang ganda. Sa kanyang kagandahan ay hindi niya nakuha ang luob ng mga kapatid ni Rizal. Dahil sa bigat ng nararamdaman ang bata sa kanyang sinapupunan ay namatay. Ang nagiisang anak ni Rizal ay namatay.

            Siguro kapalaran na rin iyon para kay Rizal at sa bata. Ito ay para na rin na hindi dumanas ng hirap at pang-aapi ang bata dahil sa mga pinaggagawa ng kanyang ama, ang pagsasama ng kanyang ama at ina ng hindi sila ikinakasal at maski sa ilalim ng mga prayle ay mkakatikim siya ng pagdudurusa.

            At bago matapos ang pelikula, ako ay naiyak sa ipinakita ng mga bata o estudyante ni Rizal. Maski sino mang guro ay mamangha at malulungkot kapag ang mga tinuruan mo ay nakita mong pinahahalagahan ang lahat ng ginawa moh para sa kanila.

            Hinaplos ng pagmamahal ni Rizal ang bawat mamayan sa Dapitan. Hindi lamang doon at noon kundi maski na rin sa buong isla ng Pilipinas simula noon hanggang sa ka

Bayaning 3rd World - Reaction paper

Pastores, Tiffany Rae R.

II-5 BEEd

Prof. Armi Evangel Pena

Rizal and his works

Reaction Paper

“Bayaning Third World”

“Si Pepe ay si Pepe”

“Ang pelikulang ito ay tungkol sa paggawa ng pelikula tungkol kay Jose Rizal. Nothing is taken for granted pati ang pagkabayani mismo ng National Hero. Kung kasalanan ang pagduduhan ang pagkabayani ni Rizal, mukhang magkakasala kami sa pelikulang ito.”

Ang aking mga nabanggit ay ang mga unang sinabi sa pelikulang “Bayaning Third World”. Natuwa ako nang marinig ko ito bilang paunang panimula. Parang magugustuhan kong panuorin ito dahil tungkol ito kay Rizal at mukhang kapanapanabik ang magiging takbo ng istorya. Maaari ang layunin nito ay upang tuligsain ang mga pangyayari sa buhay ni Rizal lalo na tungkol sa kanyang pagkabayani.

Nagumpisa ang kwento sa tanung na “Sino/ano si Rizal?” “Siya ang National hero. The first Filipino-indio Bravo” Iyan ang sagot ng aktor sa tanung na ito. Tama nga naman siya kasi maski ako iyon din ang sagot at pati na rin kung sino mang Pilipino ang tanungin ng ganyan. Maliban na lang kung direct descendant ka o napatunayan mo na related ka dahil ikaw ang anak ng asawa ng pinsan ng asawa ni o anak ng anak ng anak ng isa sa mga kapatid ni Rizal ay maari mo siyang matawag na Lolo Rizal.

4’11” lang ang height daw ni Rizal pero sobrang galing niya at sobrang talino pa. Walang duda kung bakit ang daming naghihinala sa kanyang pagkabayani. Maliit nga siya sa taas ng katawan ngunit isang napakalaking Rizal ang kanyang naiguhit at naisulat sa kasaysayan. Nakakamangha mang isipin pero ganoon nga yung nararamdaman ko ngayon para kay Rizal.

Piso. Diyan nga matatagpuan si Rizal. Nakalipas man ang madaming dekada pati ang mga taong namumuno dito sa Pilipinas, nananatili pa ding nasa piso si Rizal. Sa modernong pagaanalisa o pagiintindi, tinuturing numero uno pa rin si Rizal ng mga kapwa kong Pilipino. At dahil tinitingala siya ng mga kababayan ko, nakakagulat malaman na isununod sa kanyang pangalan ang halos karamihan sa mga gawang Pinoy.

Dito ko lang din nalaman na nuong nagtatag ng sariling simbahan si dating Bishop Gregorio Aglipay, ginawa niyang santo si Dr. Jose Rizal. Naging paranoid din kasi ang simbahang Katoliko sa pagkabayani ni Rizal. Nakakagulat malaman na nangyari pala ang mga bagay na iyon. At nang dahil dito, may namuong mga relihiyosong grupo na sumasamba sa kadakilaan ni Rizal. Mas lalo akong natawa nang margining ko ang aktor na tinawag niya si Rizal ng San Jose Rizal.

Sumasang-ayon naman ako sa sinabi ng mga aktor na dahil sa pagbaril kay Rizal, napatalsik ang mga konyo boys na pinalitan ng amerikan boys na pintalsik ng mga honda boys na pinatalsik ulit ng mga amerikan boys. Kaya ayun! Nagwagi tayo. Nagwagi ang lahing Pilipino – ang lahing pinagmulan ni Rizal. Ikinagulat ko din naman ang nalaman ko na may aso pa lang tumakbo at umaligid kay Rizal nang mamatay siya.

“Ang isang bansang walang bayani ay isang bansang walang kasaysayan”

Sa mga linyang iyan na sinabi ng isang binata sa pelikula ay tinututulan ko. Ito ay sa kadahilanan na hindi porket wala tayong bayani ay wala na din tayong kasaysayan sapagkat mayroon tayong mga sinaunang mga katutubo na naninirahan sa Pilipinas bago pa lamang dumating sila Rizal maski ang mga Espanyol.

Pero, siguro, kaya lamang iyan nasabi ay upang ipaalam sa atin na kung wala tayong bayani, walang magagawang pananaliksik at kung walang magagawang pananaliksik, hindi matutuklasan ang anumang pangyayari sa ating bayan. Ang mga magiging pananaliksik na iyon ang magiging batayan natin tungkol sa ating Kasaysayan.

Kung ang sasabihin nila na andiyan naman si Bonifacio at pinilit lamang tayo ng mga Amerikano na piliin si Rizal bilang ating bayani, hay naku! Diyan ako makikipagtalo at handang magkaroon ng pananaliksik para ipagtanggol si Rizal. Hindi naman sa ayaw ko kay Bonifacio at hindi din naman dahil sa populyar si Rizal. Sa tingin ko lamang ay mas nagging makabuluhan ang layunin ni Rizal kung paano niya ikakalas ang Pilipinas sa Espanya. Ginamit ni Rizal ang kanyang kakayahan sa pagsusulat at ang kanyang angking talino upang tuligsain ang gobyerno ng mga Espanyol. Gusto ni Rizal na hindi magkaroon ng madugong pakikipaglaban laban sa mga Espanyol. Gusto niyang idaan ito sa maayos na pamamaraan upang ipagtanggol tayo sa pamamagitan ng pagkamit ng bawat mamamayan Pilipino ng Edukasyon. At kapag nakuha na ng halos karamihan ang kaalamang nararapat para sa kanila, doon maguumipsa ang pagnananais na pakikipaghiwalay sa Espanya. Sa pakiramdam ko, kung ginamit tayo ng Espanya mas mabuti na ding gamitin na natin sila.

Muli ulit akong natuwa nang sinubukan ulit nilang tanungin ang mga sarili nila tungkol kay Josephin Bracken, ang babaeng minahal ni Rizal noong ipinatapon siya sa Dapitan. Si Josephin daw ay nagging isang mananayaw sa Hongkong kung saan nanatili si Rizal. Marahil siguro dun sila nagkakilala at nagkasabay lamang sila ng pagpunta o pauwi dito sa Pilipinas. Naitanung muli nila kung si Binibing Bracken ba ay nagging isang inspirasyon o isang panggulo para kay Rizal. At hindi lang iyon, mas ikinatuwa ko na naman na marinig nung sinabi nilang ano ang nangyare sa kanya nung namatay si Rizal – kung ito daw ba ay umalis o nanatili dahil sa karangalan sapagkat ang kanyang minamahal ay nagging isang bayani.

Nadagdagan din aking nalalaman nang margining ko galing sa pelikula na si Josephin ay hindi tanggap ng pamilya ni Rizal maliban na lang kay Narcisa. Ang nagging dahilan kasi ng hindi pagtanggap ng pamilya ni Rizal kay Josephine ay dahil hindi sila ikinasal ni Rizal ngunit nagsasama sila. Isa pang dahilan ay marahil siya raw ay isang espiya ng mga prayle. Ngunit pinabulaan ito ni Josephin. Mahal niya daw talaga si Rizal at minahal niya talaga ito ng totoo. Sa palagay ko, si Rizal yata ang nagpauso ng Live-in dito sa Pilipinas dahil hindi sila nagpakasal ni Bracken. Nagsama lamang kasi sila at nagkaruon ng anak.

Kung ako ang tatanungin, base sa napanuod ko, makulit at pilya si Bracken.

Pilit na hinahanap ng mga aktor ang sagot sa kanilang mga katanungan at mga ebidensya para sa kanilang mga pagdududa. Para sa akin, nakuha ko na ang sagot sa aking pagdududa. Hindi man malinaw pero katanggap-tanggap naman malaman mismo kay Narcisa, kapatid ni Rizal, ang sagot na “Si Pepe ay si Pepe.” Sabagay, hindi natin masisisi si Rizal sa mga ginawa niya at binalak niyang gawin. Maski din naman kasi tayo ganun ang kadalasang ginagawa. Tayo lamang ay nakikinig sa  mga payo nang iba pero maari naming tayong mamili kung susundin ba natin iyon o gagawa tayo ng sarili nating hakbang at desisyon.

Itong pelikulang ito ay tungkol sa pagkabayani ni Rizal, sa kanyang mga ginawa, ang laban niya sa gobyerno ng mga Espanyol, ang kanyang buhay kasama si Josephin Bracken, ang kanyang retraksyon o pagbabalik katoliko, at ang nagging epekto niya sa bawat Pilipino. Ito ay isang kabigha-bighaning pelikula kung saan ipinaparating sa buong mamamayang Pilipino na pare-parehas lang ang mga pagdududa natin, na halos lahat tayo ay nagdududa, magdududa sa pagkabayani ni Rizal, na maraming maaring kasagutan upang bigyang tiwala ang mga ginawa ni Rizal.

Maaring isipin ng iba na ito ay isang bias na pelikula na kakaunti lamang ang nilabas ng mga negatibong bagay tungkol kay Rizal at pawang mga mababaw lamang na pwedeng masagot ng walang kahirap-hirap. Ngunit, subalit, datapwat, ako ay handang magsalita sa ngalan ng pelikulang ito. Ito ay sa kadahilanan na napakahirap gumawa ng ganitong pelikula sapagkat kailangan munang mangalap ng mga totoong ebidensya para lamang mapatunayan ang mga ginawa at sinabi ni Rizal. At kung hindi nila iyon gagawin, maaring mas maraming tao ang mas tumaligsa sa kanila kaysa kay sa pagkabayani ni Rizal.

Ika nga nila, “Kanya-kanyang Rizal,” Ibig sabihin, may sari-sarili at iba’t ibang istorya ang mga istoryador tungkol sa talagang pagkabayani ni Rizal.

Reaction to the Roles of Manipulatives in Arithmetic and Geometric Tasks

December 13, 2011, Tuesday at 6:09 in the late afternoon, I am reading my journal in Geometry. I do not have choice but to do it because it is our duty- a duty for us to accomplish this requirement. The deadline of submission is on December 16, 2011, Friday. I only have three more days to complete my reaction paper. I hope I can finish it before that day comes. I hope I have the ideas to fill up the empty space in the bond paper. I hope I have an open mind to understand what I will be reading. Oh gosh! My time starts at 1, 2… 3!

               I figure out doing that intro so that Ma’am can know that I am really reading my journal. Ha-ha! Another reason is for me to react immediately on what I have read. It is because my thoughts are fading easily. That is why I have to write at once. If I do not respond to this, I will have hard time thinking on what I will put on this paper. Well, anyways, let us proceed with my reflection.

               “… children were more successful with manipulative than with pictures …, all children were more likely to rotate their paper or physical shape when this action could help them identify the shape.” These are some lines that can be found in my journal. While I was reading these, I remembered Prof. Pabayos, exclusively during the time she is teaching the prisms. As she draws the geometric figure, specifically the cube-figure, I and my classmates are thoroughly watching. When she is done, we try to stop ourselves from laughing at her drawing. I won’t describe anymore what the image looks like. But what makes it more funny is when she told us, “Isipin niyo na lang na cube ‘yan. [Smile].” After that, one of my classmates volunteered to improve the drawing. Suddenly, our professor told us, “Hindi talaga ako marunong mag-drawing.” And then, we laughed again.

               I did not include that just to make fun of our professor. I would simply like to address the issue that not all teachers in Mathematics, particularly in Geometry, are good in illustrating a certain figure. There were some who cannot draw the object as good as how they want the image to appear. However, this doesn’t mean that they are not good in teaching their chosen field. It was just they don’t know how. So, to help them show to their students what their image truly looks, they have the visual shapes or manipulatives or the hands-on objects during the lesson. It is because students, especially elementary students, are more visual-oriented. They learn easily when they can see, touch, move or manipulate the objects by themselves.

               “… manipulations still help children expand their investigations in the physical environment thereby advance their thinking.” This is the abstract formed by Taylor Martin, Ayiesha Lukong and Raven Reaves, faculties of the College of Education in The University of Texas at Austin, in their study entitled “The Roles of Manipulatives in Arithmetic and Geometry Tasks”. This study contains the effects of manipulatives not only in Geometry but also in Arithmetic. On the other hand, they did not forget to mention in their study that these manipulatives may have possible different effects in these two fields. They also noted that action with manipulatives supports learning when it provides a way for children to simultaneously and iteratively adapt and interpret their environment.

               Many researchers and teachers and even I believe that these hands-on objects can help students learn mathematics concepts. For example, when the topic of the day is about fraction, the teacher would prepare fraction pies. These are broken pieces shaped like a piece of pizza taken from the whole. The teacher will use this to illustrate the concepts found in fractions. Thus, help him or her in teaching the students the fraction operations and meanings in the easy way.

I was once a student who learned fractions from my first year professor with the help of these fraction pies or as what they call it manipulatives. I am a student who really has a bad background in understanding fraction operations. Honestly, I always got low grades when fractions are the topic of the day. That is why I am easily irritated and don’t even have the patience to listen and participate during class discussions. But during my first semester in my first year college, my views about fractions change. Through these manipulatives, I am convinced to understand, somehow, the nature of fractions and learn to think of ways how I can solve fractional problems in my own ways. Up to now, that serves as my inspiration to think and use things that can help me teach my lessons to the students in the way that they can understand it easily. And so, I also believe what the researchers wrote about their study “On one hand, working with manipulatives improves ones’ performance on mathematical tasks in some cases.

According to the researchers, the best instructional strategy is to use multiple manipulatives to teach mathematical concepts. They do believe that exposure to multiple representations leads to better understanding of underlying mathematical principles. These manipulatives are viewed as external resources that primarily help problem solvers keep track of the problem elements without wasting internal memory resources. Based on how I understand these lines, this strategy can help the students solve problems in distressful ways. Just take my example with the drawing of Prof. Pabayos. We might have a hard time solving geometrical problems such as finding the lateral and surface area and even the volume if she didn’t show us how the figure really looks like. Though we know the formula, it is still better to keep track on determining the personal location of the length, width and height in the certain prism. This is also to check if each one of us really knows how to locate especially personally the length and the width.

These manipulatives could be more helpful in geometry because they are more similar to the objects operated on and resembles the outcomes of problem solving. Another thing, in geometry, physical shapes and children concepts of shapes may nearly identical, particularly in early stages of learning. Lastly, working with the virtual manipulatives helped children develop conceptual and procedural knowledge in geometry, and that virtual manipulatives are more motivating than paper and pencil tasks.

 http://www.scientificjournals.org/journals2007/articles/1073.htm