Seeing Algebra in Arithmetic Through Mathematical Problem Posing

Jinfa Cai,Stephen Hwang 대한수학교육학회 2022 수학교육학연구 Vol.32 No.3

This paper proceeds from the position that elementary- and middle-school students can learn and should be exposed to algebraic ideas and that a fruitful mechanism for this is to help them to see the algebra in arithmetic. After a brief survey of the literature on helping students see algebra in arithmetic, the main focus of the paper is on the use of mathematical problem posing in the classroom to help students see the algebra in arithmetic. To illustrate this, we present three cases of teaching mathematics through problem posing and discuss the perspectives they offer on developing students’ algebraic thinking. The paper concludes with an examination of how teachers might be supported in using problem posing to help their students see the algebra in arithmetic.

Research on Mathematical Problem Posing: What We Know and Where We Are Going

( Prof. Jinfa Cai ) 한국수학교육학회 2014 뉴스레터 Vol.30 No.5

There is a long history of integrating mathematical problem solving into school curricula. In contrast, problem-posing research is a relatively new endeavor. Nevertheless, there have been efforts to incorporate problem posing into school mathematics at different educational levels around the world in the past two decades These efforts indicate interest among many researchers and practitioners in making problem posing a more prominent feature of classroom instruction. In this plenary, I will present the current state of knowledge in problem-posing research and suggest some directions for future study. In particular, my discussion will be organized based on the following ten questions: (1) Why is problem posing important in school mathematics? (2) Are teachers and students capable of posing important mathematical problems? (3) Can students and teachers be effectively trained to pose high quality problems? (4) What do we know about the cognitive processes of problem posing? (5) How are problem-posing skills related to problem-solving skills? (6) Is it feasible to use problem posing as a measure of creativity and mathematical learning outcomes? (7) How are problem-posing activities included in mathematics curricula? (8) What does a classroom look like when students engage in problem-posing activities? (9) How can technology be used in problem-posing activities? (10) What do we know about the impact of engaging in problem -posing activities on student outcomes? Each of these questions represents a rich area for problem-posing research and I will summarize what we know as a field, and then point out possible future directions of research on mathematical problem posing.

OSCILLATION OF ONE ORDER NEUTRAL DIFFERENTIAL EQUATION WITH IMPULSES

Cheng, Jinfa,Chu, Yuming Korean Mathematical Society 2011 대한수학회논문집 Vol.26 No.2

Explicit sufficient conditions are established for the oscillation of the one order neutral differential equations with impulsive $(x(t)+{\sum\limits^n_{i=1}}c_ix(t-{\sigma}_i))'+px(t-{\tau})=0$, $t{\neq}t_{\kappa}$, ${\Delta}(x(t_{\kappa})+{\sum\limits^n_{i=1}}c_ix(t_{\kappa}-{\sigma}_i))+p_0x(t_{\kappa}-{\tau})=0$, $c_i{\geq}0$, $i=1,2,{\ldots}n$, $p{\tau}$>0, $p_0{\tau}$>0, ${\Delta}(x_{\kappa})=x(t^+_{\kappa})-x(t_{\kappa})$. Explicit sufficient and necessary condition are established when $c_i$ = 0, i = 1, 2, ${\ldots}$, n.

A Systematic Review of Literature on Mathematical Problem Posing in Korea

한재필,여승현,김은혁,Stephen Hwang,Jinfa Cai 대한수학교육학회 2023 수학교육학연구 Vol.33 No.3

In this systematic literature review, we reviewed 48 original empirical papers focusing on Korean students’ and teachers’ mathematical problem-posing (MPP) in classrooms. All the included papers were published in peer-reviewed mathematics education research journals and located through comprehensive database searches and individual journal searches involving Korean students and teachers. We categorized the papers into two main groups based on the type of participants: 34 students’ MPP papers and 14 teachers’ MPP papers. We further categorized the papers based on the characterization of MPP used: MPP as a construct, intervention, or variable. For students’ MPP papers, most were identified as intervention papers that examined the impacts of MPP interventions on students’ cognitive domains (e.g., problem posing, creativity, problem solving) or affective domains (e.g., attitude, interest). For teachers’ MPP papers, more than half of the papers were identified as documenting teachers’ various types of knowledge related to MPP. This systematic literature review will shed light on the research evidence found by these Korean researchers and how their empirical studies were conducted. It will also help disseminate research evidence regarding Korean students’ and teachers’ MPP internationally.

The role of memorization in students’ self-reported mathematics learning: a large-scale study of Chinese eighth-grade students

Qimeng Liu,Xiaofeng Du,Shuxin Zhao,Jian Liu,Jinfa Cai 서울대학교 교육연구소 2019 Asia Pacific Education Review Vol.20 No.3

This study examined over 48,000 eighth-grade Chinese students’ mathematics performance and use of learning strategies. In particular, this study explored how the use of learning strategies and their combinations are related to students’ mathematics performance in Chinese context. This study examined three kinds of learning strategies derived from the Programme for International Student Assessment (PISA) 2012: memorization, elaboration, and control. The findings indicate that few students chose the memorization strategy as their predominant way of learning mathematics. Instead, students usually chose a combination of learning strategies. The choice of combinations of learning strategies was highly correlated with students’ mathematics performance. Students who chose control strategies outperformed those who chose memorization strategies or elaboration strategies. This study also examined the relationship between learning strategy use and mathematics performance of students who were only children (students with no siblings, born under the “one child” policy) and students living in nonagricultural residential locations (hukou status), both of which are background variables unique to Chinese context. The findings indicate that only-child and nonagricultural students outperformed non-only-child and agricultural students when choosing the same learning strategies. However, those who chose control-dominant strategies performed better than those who chose memorization-dominant strategies, regardless of their background. This study provides a new lens for considering the relationship between learning strategy use and mathematics performance, demonstrating that various learning strategies should be considered together rather than separately.

The Iron Deficiency Response Regulators IAA-LEUCINE RESISTANT3 and bHLH104 Possess Different Targets and Have Distinct Effects on Photosynthesis in Arabidopsis

Mengshu Li,Jie Zhang,Hong-Lei Jin,Dongru Feng,Jinfa Wang,Hong-Bin Wang,Bing Liu 한국식물학회 2019 Journal of Plant Biology Vol.62 No.2

In higher plants, iron (Fe) is an essential elementfor photosynthesis and growth. Two basic helix-loop-helix(bHLH) transcription factors, bHLH104 and IAA-LEUCINERESISTANT3 (ILR3), positively regulate Fe uptake inArabidopsis. Furthermore, an E3 ubiquitin ligase, BRUTUS(BTS) functions as a negative regulator upstream of bHLH104and ILR3 in the Fe homeostasis pathway. Interestingly, wecharacterized a lesion of BRUTUS (BTS), which exhibitedpale-green leaves and retarded in growth. Genetic analysesshowed that only loss of ILR3 could entirely compromise thechlorosis in bts-2 mutants. To further investigate whetherbHLH104 and ILR3 have different roles in functioningdownstream of BTS other than Fe absorption, we obtainedbHLH104-, and ILR3-overexpressing plants. Interestingly,similar to bts-2, overexpression of ILR3 displayed chloroticleaves. Moreover, overexpressing ILR3 also caused theabundance of thylakoid proteins reduced, along withphotosynthetic genes decreased. However, there was novisible difference between bHLH104-overexpressing plantsand WT. Furthermore, we found that bHLH104 and ILR3may act independently on different downstream targets. bHLH104, but not ILR3, could bind to the promoter of At-NEET, which acts as a Fe-S/Fe cluster donor in chloroplasts. Collectively, our data demonstrate that bHLH104 and ILR3possess different downstream targets that may have distincteffects on photosynthesis, although they share a commonfunction in Fe deficiency responses.

Domain of Unknown Function 143 is required for the functioning of PEP-associated protein DG238 in the chloroplast

Menglong Wang,Lan Jiang,Qingen Da,Jun Liu,Dongru Feng,Jinfa Wang,Hong-Bin Wang,Hong-Lei Jin 한국식물학회 2017 Journal of Plant Biology Vol.60 No.6

Plastid-encoded plastid RNA polymerase (PEP) isessential for chloroplast development and plastid geneexpression in Arabidopsis thaliana. However, PEP is a largecomplex, and many proteins in this complex remain to beidentified. We previously reported that Delayed Greening238 (DG238) interacts with PEP subunit protein FLN1 andmay function as a PEP-associated protein and participate inearly chloroplast development and PEP-dependent plastidgene expression. DG238 contains Domain of UnknownFunction 143 (DUF143), whose function is currently unknown. Here, we found that a deficiency of the DUF143 domain inDG238 affected its localization, which resulted in abnormalinteractions with PEP-associated proteins in the chloroplast. Furthermore, DG238 lacking the DUF143 domain or DG238with only this domain failed to function. Interestingly, thelack of conserved amino acids 193–217 of the DUF143domain in DG238 also affected its function. In addition toFLN1, DG238 also interacts with other PEP-associatedproteins, including FSD2, FSD3, MRL7-L, and MRL7, toregulate plastid gene expression. These results suggest thatthe DUF143 domain is necessary for the functioning of thePEP-associated protein DG238 in chloroplasts.

Adsorption of Fluoride Ions from Water by SF/PP Nonwoven Fabrics

Zuoze Fan,Yanfei Gao,Xin Ning,Fukui Pan,Jinfa Ming 한국섬유공학회 2019 Fibers and polymers Vol.20 No.4

Silk fibroin/polypropylene (SF/PP) nonwoven fabrics were prepared via electrospinning method. The compositematerials combine the advantage of nanofibers with the high specific surface area and the strong affinity toward fluoride. SF/PP nonwoven fabrics were characterized, and the adsorption of fluoride was investigated. The results showed the diameter ofSF nanofibers increased from 950±37 nm to 2400±50 nm in nonwoven fabrics with the increase of SF concentration from5.0 wt% to 10 wt%. Before fluoride adsorption, no crystal particles were deposited on the surface of SF/PP nanofibers. Afteradsorption 5 min, only several white crystals were deposited. Within the increase of adsorption times from 10 min to 60 min,many larger crystals were grown. Fluoride ions were confirmed in crystals by EDS. From adsorption rate curve, the rate offluoride removal was rapid initially and slowed down gradually until it attained equilibrium. At the same time, a largefraction of fluoride ions was removed within 20 min of contact times in all the experimental various studied. Therefore, thisnonwoven fabric has a great potential as a novel adsorbent material for the fluoride removal from drinking water.